5 - Term Structure of Interest Rates.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import newton"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def equivRate(rate, from_freq=1, to_freq=1):\n",
    "  if from_freq == np.inf:\n",
    "    return (np.exp(rate / to_freq) - 1) * to_freq\n",
    "  elif to_freq == np.inf:\n",
    "    return np.log(1 + rate / from_freq) * from_freq\n",
    "  else:\n",
    "    return to_freq * ((1 + rate/from_freq)**(from_freq/to_freq) - 1)\n",
    "\n",
    "def coupon_bond_ytm(n, pmt, pv, fv=100, cf_freq=1, comp_freq=1, beg=False):\n",
    "    def f(x):\n",
    "        return coupon_bond_pv(n=n, pmt=pmt, rate=x, fv=fv, cf_freq=cf_freq, comp_freq=comp_freq, beg=beg) - pv\n",
    "    root = newton(f, 0)\n",
    "    return root\n",
    "\n",
    "def coupon_bond_pv(n, pmt, rate, fv=100, cf_freq=1, comp_freq=1, beg=False):\n",
    "    rate = equivRate(rate, from_freq=comp_freq, to_freq=cf_freq) / cf_freq\n",
    "    old_settings = np.seterr(invalid='ignore')\n",
    "    pvPMT = np.where(rate == 0, n, np.divide(1 - (1+rate)**-n, rate)) * pmt\n",
    "    np.seterr(**old_settings)\n",
    "    pvFV = fv / (1 + rate)**n\n",
    "    return np.where(beg, (pvPMT + pvFV) * (1 + rate), pvPMT + pvFV)\n",
    "\n",
    "def coupon_bond_fv(n, pmt, rate, terminal_payment, cf_freq=1, comp_freq=1, beg=False):\n",
    "    rate = equivRate(rate, from_freq=comp_freq, to_freq=cf_freq) / cf_freq\n",
    "    old_settings = np.seterr(invalid='ignore')\n",
    "    fvPMT = np.where(rate == 0, n, np.divide((1+rate)**n - 1, rate)) * pmt\n",
    "    np.seterr(**old_settings)        \n",
    "    return np.where(beg, fvPMT * (1 + rate) + terminal_payment, fvPMT + terminal_payment)\n",
    "\n",
    "def coupon_bond_pmt(n, rate, pv, fv, cf_freq=1, comp_freq=1):\n",
    "    rate = equivRate(rate, from_freq=comp_freq, to_freq=cf_freq) / cf_freq\n",
    "    pvaf = np.where(rate == 0, n, np.divide(1 - (1+rate)**-n, rate))\n",
    "    return (pv - (fv/(1+rate)**n)) / pvaf\n",
    "\n",
    "def zero_bond_ytm(n, pv, fv=100, freq=2):\n",
    "    if freq == np.inf:\n",
    "        return np.log(fv/pv) * (1/n)\n",
    "    return ((fv/pv)**(1/(n*freq)) - 1) * freq\n",
    "\n",
    "def zero_bond_pv(n, rate, fv=100, freq=2):\n",
    "    if freq == np.inf:\n",
    "        return fv / np.exp(rate*n)\n",
    "    return fv / ((1 + rate/freq)**(n*freq))\n",
    "\n",
    "def zero_bond_fv(n, rate, pv, freq):\n",
    "    if freq == np.inf:\n",
    "        return pv * np.exp(rate*n)    \n",
    "    return pv * ((1 + rate/freq)**(n*freq))\n",
    "\n",
    "def irr_newton(cf, cf_t, per=1):\n",
    "    def price(rate, cf, cf_t, per=1):\n",
    "        discount_factor = (1 + rate/per)**(-cf_t)\n",
    "        return np.dot(cf, discount_factor)\n",
    "    def f(x):\n",
    "        return price(x, cf, cf_t, per=per)\n",
    "    return newton(f, 0)\n",
    "\n",
    "def irr_newton_no_scipy(stream, cf_t, per=1, tol=1e-12):\n",
    "    rate = 0.0\n",
    "    for steps in range(50): \n",
    "        r = np.array(cf_t)\n",
    "        m = max(-rate * r / per)  \n",
    "        f = np.exp(-rate * r / per - m)\n",
    "        t = np.dot(f, stream)\n",
    "        if abs(t) < tol * np.exp(-m):\n",
    "            break\n",
    "        u = np.dot(f * r, stream)\n",
    "        rate = rate + np.clip(t / u, -1.0, 1.0)\n",
    "    annualized_rate = (np.exp(rate / per) - 1) * per \n",
    "    return annualized_rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Yield Curves"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yield curves are a snapshot of interest rates in that market—a simple yet often informative graph that plots yields to maturity on the vertical axis and times to maturity on the horizontal axis for a homogeneous set of securities.\n",
    "\n",
    "The idea of any yield curve in principle is to display visually the relationship between interest rates on securities that are alike on all dimensions except maturity. Ideally, all the observations would be for securities that have the same credit risk, same liquidity, same periodicity, and same tax status. \n",
    "\n",
    "Most yield curves are based on government securities. That’s so we can hold constant all the listed factors other than time to maturity that impact investors’ required rates of return. The yields to maturity ideally would be for zero‐coupon securities so that coupon reinvestment risk is not a factor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is no perfect data set for term structure analysis. Typically seen yield curves are plots of street convention yields on coupon-bearing Treasury notes and bonds instead of yields on Treasury STRIPS. In particular, the yields displayed usually are for on‐the‐run issues (i.e., the most recently auctioned Treasury securities). These are actively traded and typically are priced close to par value, thereby minimizing the effects of the deferral for tax purposes of the gains and losses from buying at a discount or a premium. The problem is that there are gaps in the times to maturity, so some yields have to be interpolated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forward Curve Intuition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that yields to maturity on 1‐year, 2‐year, and 3‐year zero‐coupon government bonds are 1.00%, 2.00%, and 2.50%, respectively (quoted on semiannual basis). These rates are *0y1y*, *0y2y*, *0y3*, (*0y* securities trade in the \"cash market\"). The first number is the starting date or read as \"years ahead\" and the second number is the tenor of the bond."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x125294b59a0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(num=0, dpi=120)\n",
    "plt.plot(np.array([1, 2, 3]), np.array([0.01, 0.02, 0.025]), label=\"Spot Curve\")\n",
    "plt.title('Yield Curve')\n",
    "plt.xlabel('Years to Maturity')\n",
    "plt.ylabel('Yield to Maturity')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the simple yield curve to infer the 1y1y, 1y2y, and 2y1y forward rates. These are implied yields on the 1-year bonds starting from one year and two years into the future (i.e. forward in time). \n",
    "\n",
    "At what rate must one be able to reinvest the proceeds of an investment in a shorter‐term bond to equal the proceeds of an investment in a longer‐term bond? The answer to this question is an Implied Forward Rate (IFR). \n",
    "\n",
    "Intuitively, the 1y1y IFR must be about 3.00% and the 2y1y IFR must be about 3.50% (ignore compounding for the this section). The idea is that if an investor can buy a 1‐year bond to yield 1.00% and reinvest for the second year at 3.00% (1y1y), the total return matches that of 2.00% per year on the 2‐year bond. Likewise, if an investor can buy the 2‐year at 2.00% and reinvest for the third year at 3.50% (2y1y), the same total return is obtained as on buying the 3‐year bond at 2.50%. Similarly, if a 1-year bond is purchased earning 1.00% for the first year and the proceeds are reinvested for the next two years at 3.25% per year (1y2y), the strategy produces the same return over the three years as buying the 3-year bond at an annual yield of 2.50%.\n",
    "\n",
    "The simplified calculation (neglecting compounding) can be formalized as follows: let $Rate_{0yAy}$ be the shorter-term rate for the 0yAy time period, $Rate_{0yBy}$ for the longer-term rate for 0yBy period, and $Rate_{Ay(B-A)y}$ the implied forward rate starting from Ay for a tenor of B-Ay. \n",
    "\n",
    "$$Rate_{0yBy} \\approx \\left(\\frac{AYears}{BYears}\\times Rate_{0yAy}\\right) + \\left(\\frac{BYears - A Years}{BYears}\\times Rate_{Ay(B-A)y}\\right)$$\n",
    "$$Rate_{Ay(B-A)y} \\approx \\frac{BYears \\times Rate_{0yBy} - AYears \\times Rate_{0yAy}}{BYears-AYears}$$\n",
    "\n",
    "\n",
    "The *longer‐term rate is a weighted average of the shorter‐term rate and the implied forward rate*, whereby the *weights are the shares of the overall time frame*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_1y1y = 3.00%\n",
      "ifr_1y2y = 3.25%\n",
      "ifr_2y1y = 3.50%\n"
     ]
    }
   ],
   "source": [
    "def approx_ifr(short_rate, short_period, long_rate, long_period):\n",
    "  return (long_period * long_rate - short_period * short_rate) / (long_period - short_period)\n",
    "\n",
    "ifr_1y1y = approx_ifr(0.01, 1, 0.02, 2)\n",
    "print(f'{ifr_1y1y = :0.2%}')\n",
    "ifr_1y2y = approx_ifr(0.01, 1, 0.025, 3)\n",
    "print(f'{ifr_1y2y = :0.2%}')\n",
    "ifr_2y1y = approx_ifr(0.02, 2, 0.025, 3)\n",
    "print(f'{ifr_2y1y = :0.2%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The analogy of the implied forward rate is the same as the marginal cost (MC) and average cost (AC) in macroeconomics. The marginal cost curve intersects the average cost curve at its lowest point because the increasing marginal cost curve pulls the average cost down until the marginal cost increases past the average cost and begins to pull up the average cost curve, thus intersecting at the lowest point on the average cost curve.\n",
    "\n",
    "Similarly, the buyer of a 2-year bond at 2.00% obtains an incremental, or marginal, return of 3.00% for the second year after earning 1.00% for the first year. The buyer of the 3‐year at 2.50% gets a marginal return of 3.50% for the third year after earning 2.00% for the first two years (or a 1‐year rate of 1.00% followed by 3.00%). This leads naturally to using the implied forward rate in **maturity choice decisions**. The issue will be how **one’s own expectation for a future rate compares to that priced into the forward curve**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider an investor who has a known, certain 2‐year horizon and can buy any of these three zero‐coupon government bonds. The obvious strategy is to buy the 2‐year zero at 2.00% and lock in the rate of return (barring default on the government bond and neglecting inflation). But our investor might consider “riding the yield curve” and buy the 3‐year at 2.50%. The hope is that the yield at the time of sale is “low” (and the sale price is “high”). How low? Lower than 3.50%, the 2y1y IFR. The companion fear is that the yield is above 3.50%. Our investor might also consider buying the 1‐year at 1.00% and hope that rates rise for the second year. How high? Higher than 3.00%, the 1y1y implied forward rate. The risk is that the reinvestment rate is less than 3.00%. The forward curve is the benchmark for your hopes and fears.\n",
    "\n",
    "The key point is that the investor’s maturity choice decision depends, in part at least, on the held view on future cash market rates vis‐à‐vis the implied forward rates. Other factors undoubtedly matter as well—the risk of underperforming the obvious maturity‐matching strategy, the cost of reinvesting cash, the cost and risk of having to sell the bond at the horizon date. In any case, implied forward rates provide information useful in making the decision."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Theories of The Term Structure of Interest Rates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. **Expectations Theory**: This theory posits that the shape of the yield curve reflects market participants' expectations about future short-term interest rates because investors (maximize expected rate of return) and issuers (minimize cost of borrowed funds) want to maximize outcomes. An upward-sloping yield curve suggests rising future rates, a downward-sloping curve indicates falling rates, while a flat curve indicates steady interest rates. The key assumption is that investors are *risk-neutral*, and the implied forward rate represents an unbiased forecast of future spot rates.\n",
    "   1. **Key Assumption**: Investors are risk-neutral, meaning they do not demand additional compensation for holding long-term bonds over short-term ones. They are indifferent to the risk of future interest rate changes (the standard deviation), so they base their decisions entirely on expected returns (mean return).\n",
    "   2. **Implication**: The yield curve reflects market expectations about future short-term interest rates. An upward-sloping yield curve means that short-term rates are expected to rise in the future, while a downward-sloping curve means they are expected to fall.\n",
    "   3. **Forward Rates**: The forward rate (the rate implied by current long-term rates) is considered an unbiased predictor of future short-term rates. There is no risk premium.\n",
    "2. **Segmented Markets Theory**: This theory suggests that the bond market is divided into segments based on maturities, and investors and issuers operate only within their preferred segment. As a result, the yield curve is determined by supply and demand conditions in each maturity segment independently, with no connection between short- and long-term rates. Risk aversion prevents investors from shifting between segments, so forward rates do not predict future short-term rates.\n",
    "   1. **Key Assumption**: Investors and borrowers have strong preferences for certain maturities and typically do not switch between short-term and long-term bonds. Each maturity segment (short-term, medium-term, long-term) operates independently based on its own supply and demand.\n",
    "   2. **Implication**: The yield curve is shaped by the independent supply and demand conditions in each segment, rather than expectations about future interest rates. For example, if there is more demand for short-term bonds, their yields may be lower than long-term bonds, even if future short-term rates are expected to remain unchanged.\n",
    "   3. **No Relationship Between Segments**: Since investors don’t move between segments, short-term and long-term rates are determined separately. The forward rate does not predict future short-term rates.\n",
    "3. **Liquidity Preference Theory**: This theory builds on the Expectations Theory by recognizing that investors are risk-averse and prefer short-term bonds due to their lower risk. To compensate for the increased risk of holding longer-term bonds (which are more sensitive to interest rate changes), investors demand a \"liquidity premium.\" This results in an upward-sloping yield curve even when future short-term rates are expected to remain steady. The forward rate, therefore, tends to overestimate the expected future short-term rate due to this risk premium.\n",
    "   1. **Key Assumption**: Investors are risk-averse and prefer short-term bonds because they are less risky (less sensitive to interest rate fluctuations). To hold long-term bonds, investors demand a liquidity premium as compensation for the higher risk.\n",
    "   2. **Implication**: Even if investors expect future short-term rates to remain steady, the yield curve is typically upward-sloping because of the liquidity premium attached to long-term bonds. Longer-term bonds require higher yields to attract investors due to their greater risk.\n",
    "   3. **Forward Rates Overestimate**: The forward rate reflects both expected future short-term rates and the liquidity premium. This means the forward rate tends to overestimate future short-term rates since it includes compensation for risk. If it were somehow possible to extract each risk premium, we would have the \"core yield\" curve based only on expectations. However, with liquidity premiums built into the implied forward rates, forward rates are overestimates of the future rates.\n",
    "\n",
    "**In Summary**:\n",
    "1. **Expectations Theory**: The yield curve reflects pure expectations of future short-term rates, with no premium for risk.\n",
    "2. **Segmented Markets Theory**: The yield curve is shaped by separate supply and demand dynamics in each maturity segment, independent of expectations about future rates.\n",
    "3. **Liquidity Preference Theory**: The yield curve reflects both expectations of future short-term rates and a premium for holding longer-term, riskier bonds."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implied Forward Curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An accurate formula for implied forwards that includes compounding for specific periodicity (PER) for the yields is based on the expression shown below:\n",
    "\n",
    "$$i_{t_{1},t_{2}}=\\left[\\frac{(1+i_{t_{0},t_{2}})^{t_{2}-t_{0}}}{(1+i_{t_{0},t_{1}})^{t_{1}-t_{0}}}\\right]^{\\frac{1}{(t_{2}-t_{1})}}-1$$\n",
    "\n",
    "$$(1+i_{t_{0},t_{2}})^{t_{2}-t_{0}}=(1+i_{t_{0},t_{1}})^{t_{1}-t_{0}} (1+i_{t_{1},t_{2}})^{t_{2}-t_{1}}$$\n",
    "\n",
    "$$\\left(1+\\frac{Rate_{t_{0},t_{1}}}{Per}\\right)^{(t_{1}-t_{0})} \\times \\left(1+\\frac{Rate_{t_{1},t_{2}}}{Per}\\right)^{(t_{2}-t_{1})}  = \\left(1+\\frac{Rate_{t_{0},t_{2}}}{Per}\\right)^{(t_{2}-t_{0})} $$\n",
    "\n",
    "$$Rate_{t_{1},t_{2}} = \\left(\\left[\\frac{\\left(1+\\frac{Rate_{t_{0},t_{2}}}{Per}\\right)^{(t_{2}-t_{0})}}{\\left(1+\\frac{Rate_{t_{0},t_{1}}}{Per}\\right)^{(t_{1}-t_{0})}}\\right]^{\\frac{1}{(t_{2}-t_{1})}} - 1 \\right) \\times Per$$\n",
    "\n",
    "$t_{A},t_{B}$ or *AyBy* or *AmBy* mean: A years ahead (forward time period/starting period), B tenor of the underlying security\n",
    "\n",
    "The first term is the proceeds per unit invested for $t_{1}$ years assuming that the $t_{0},t_{1}$ rate is an APR quoted for PER periods per year. That amount is reinvested for the remaining time period out to year $t_{2} - t_{1}$ (i.e., at the $t_{1},t_{2}$ implied forward rate). The compounded total return equals the proceeds per unit invested for $t_{2}$ years at the $t_{0},t_{2}$ rate. It is important that all three rates are annualized for the same periodicity.\n",
    "\n",
    "[FRED Reference](https://fredblog.stlouisfed.org/2023/05/constructing-forward-interest-rates-in-fred/)\n",
    "\n",
    "Note that the formulas are appropriate for bond yields and not money market rates as these require some modifications."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_1y1y = 3.0050%\n",
      "ifr_1y2y = 3.2542%\n",
      "ifr_2y1y = 3.5037%\n"
     ]
    }
   ],
   "source": [
    "def ifr(rate_t0t1, t1, rate_t0t2, t2, t0 = 0, per=2):\n",
    "    t2_term = (1 + rate_t0t2/per)**(t2 - t0)\n",
    "    t1_term = (1 + rate_t0t1/per)**(t1 - t0) \n",
    "    return ((t2_term / t1_term)**(1/(t2 - t1)) - 1) * per\n",
    "\n",
    "ifr_1y1y = ifr(0.01, 1, 0.02, 2)\n",
    "print(f'{ifr_1y1y = :0.4%}')\n",
    "ifr_1y2y = ifr(0.01, 1, 0.025, 3)\n",
    "print(f'{ifr_1y2y = :0.4%}')\n",
    "ifr_2y1y = ifr(0.02, 2, 0.025, 3)\n",
    "print(f'{ifr_2y1y = :0.4%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Money Market Implied Forward Rates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Money market instrument rates have different periodicities and the basis in which the forward rate is quoted should match the manner in which a similar security would be quoted and traded. Thus, the function to compute the implied forward rate for add-on rates and discount rates are as following:\n",
    "\n",
    "IFR on an Add-On Basis (bank CDs, LIBOR, repos):\n",
    "$$\\left[1+\\left(AOR_{t_{0},t_{1}}\\frac{t_{1} Days}{Year}\\right)\\right] \\times \\left[1+\\left(AOR_{t_{1},t_{2}}\\frac{t_{2} - t_{1} Days}{Year}\\right)\\right]  = \\left[1+\\left(AOR_{t_{0},t_{2}}\\frac{t_{2} Days}{Year}\\right)\\right] $$\n",
    "\n",
    "$$AOR_{t_{1},t_{2}} = \\left[\\frac{t_{2} Days \\times AOR_{t_{0},t_{2}} - t_{1} Days \\times AOR_{t_{0},t_{1}}}{t_{2} - t_{1} Days}\\right] \\times \\left[\\frac{1}{1 + \\left(AOR_{t_{0},t_{1}}\\times \\frac{t_{1} Days}{Year}\\right)}\\right]$$\n",
    "\n",
    "IFR on a Discount Rate Basis (commercial paper, bankers acceptances, and Treasury bills in the U.S):\n",
    "$$\\left[1-\\left(DR_{t_{0},t_{1}}\\frac{t_{1} Days}{Year}\\right)\\right] \\times \\left[1-\\left(DR_{t_{1},t_{2}}\\frac{t_{2} - t_{1} Days}{Year}\\right)\\right]  = \\left[1-\\left(DR_{t_{0},t_{2}}\\frac{t_{2} Days}{Year}\\right)\\right] $$\n",
    "\n",
    "$$DR_{t_{1},t_{2}} = \\left[\\frac{t_{2} Days \\times DR_{t_{0},t_{2}} - t_{1} Days \\times DR_{t_{0},t_{1}}}{t_{2} - t_{1} Days}\\right] \\times \\left[\\frac{1}{1 - \\left(DR_{t_{0},t_{1}}\\times \\frac{t_{1} Days}{Year}\\right)}\\right]$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that 90‐day LIBOR is 1.00% (periodicity of 4) and 180‐day LIBOR is 2.00% (periodicity of 2). What rate would a true believer in the expectations theory of the yield curve anticipate for 90‐day LIBOR, 90 days into the future (*90d90d*)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_90d90d =  2.9925%\n",
      "ifr_180d180d =  28.5714%\n"
     ]
    }
   ],
   "source": [
    "# Implied Forward Curve - MM Add-On & Discount Rate\n",
    "def ifr_mm(rate_t0t1, t1, rate_t0t2, t2, t0 = 0, year=360, aor=True):\n",
    "    rollover_avg = (t2 * rate_t0t2 - t1 * rate_t0t1) / (t2 - t1)\n",
    "    adjust = 1/(1 + (rate_t0t1 * t1/year)) if aor else 1/(1 - (rate_t0t1 * t1/year))\n",
    "    return rollover_avg * adjust\n",
    "\n",
    "\n",
    "d90 = 90\n",
    "r90 = 0.01\n",
    "d180 = 180\n",
    "r180 = 0.02\n",
    "year = 360\n",
    "\n",
    "# IFR - Add-On Rate\n",
    "ifr_90d90d = ifr_mm(r90, d90, r180, d180, 0, 360, True)\n",
    "print(f'{ifr_90d90d = : 0.4%}')\n",
    "\n",
    "d180 = 180\n",
    "r180 = 0.1\n",
    "d360 = 360\n",
    "r360 = 0.2\n",
    "year = 360\n",
    "\n",
    "ifr_180d180d = ifr_mm(r180, d180, r360, d360, 0, 360, True)\n",
    "print(f'{ifr_180d180d = : 0.4%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_90d90d =  3.0075%\n",
      "ifr_180d180d =  31.5789%\n"
     ]
    }
   ],
   "source": [
    "d90 = 90\n",
    "r90 = 0.01\n",
    "d180 = 180\n",
    "r180 = 0.02\n",
    "year = 360\n",
    "\n",
    "# IFR - Discount Rate\n",
    "ifr_90d90d = ifr_mm(r90, d90, r180, d180, 0, 360, False)\n",
    "print(f'{ifr_90d90d = : 0.4%}')\n",
    "\n",
    "d180 = 180\n",
    "r180 = 0.1\n",
    "d360 = 360\n",
    "r360 = 0.2\n",
    "year = 360\n",
    "\n",
    "ifr_180d180d = ifr_mm(r180, d180, r360, d360, 0, 360, False)\n",
    "print(f'{ifr_180d180d = : 0.4%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implied Spot (Zero-Coupon) Rates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implied spot curve is the sequence of spot (or zero‐coupon) rates that are consistent with the prices and yields on coupon bonds.\n",
    "\n",
    "Building the implied spot curve is a great example of **“bootstrapping”** in that the result of one calculation is used in the subsequent one. This is not going to involve a specific formula; instead it is a process best learned by working through an example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that we observe price and yield data on four actively traded benchmark securities for the same risk class, for instance, government bonds.\n",
    "\n",
    "| Maturity (Years) | Coupon Rate | Price (% of Par Value) | Yield to Maturity |\n",
    "| ---------------- | ----------- | ---------------------- | ----------------- |\n",
    "| 1                | 0%          | 97.0625                | 3.0264%           |\n",
    "| 2                | 3.25%       | 100.8750               | 2.7941%           |\n",
    "| 3                | 4.50%       | 102.7500               | 3.5181%           |\n",
    "| 4                | 4.00%       | 99.3125                | 4.1902%           |\n",
    "\n",
    "We need some simplifying *assumptions* to illustrate bootstrapping:\n",
    "- We require a starting place in the money market where we observe the pricing on a short‐term zero‐coupon bond. Here the 1‐year represents the **starter zero**. But keep in mind that in practice we would use the price on a **T‐bill or commercial paper or a time deposit that pays LIBOR** which is obtained from the money market.\n",
    "- The 2‐year, 3‐year, and 4‐year bonds are assumed make **annual coupon payments** to simplify the example. \n",
    "- Assume that **we are on a coupon date and the payment has just been made** so that there is **no accrued interest**.\n",
    "  - In general, you would need to use the total current market value including accrued interest on the left side of the equation.\n",
    "- The internal rates of return are street convention yields for a periodicity of 1 (i.e., they are **effective annual rates**)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.03026401 0.0279408  0.03518092 0.04190249]\n"
     ]
    }
   ],
   "source": [
    "years = np.array([1, 2, 3, 4])\n",
    "coupon = np.array([0, 3.25, 4.5, 4])\n",
    "price = np.array([97.0625, 100.875, 102.75, 99.3125])\n",
    "face = np.full(4, 100)\n",
    "ytm = np.vectorize(coupon_bond_ytm)(n=years, pmt=coupon, pv=price, fv=face, cf_freq=1, comp_freq=1, beg=False)\n",
    "print(ytm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We know the 0y1y zero-coupon/spot rate is 3.0264%. Using this we will bootstrap the spot rates for rest of the maturities. \n",
    "\n",
    "**0y2y**: The implied 2‐year spot rate (the 0y2y) is 2.7903%; it is the solution for *z* in the below expression. The algebra problem is to find the 2‐year spot rate such that when the second cash flow is discounted by that rate, the sum is the price of the bond.\n",
    "\n",
    "$$100.8750 = \\frac{3.25}{1.030264} + \\frac{103.25}{(1+\\mathit{z})^{2}}, \\mathit{z} = 0.027903$$\n",
    "\n",
    "**0y3y**: The implied 3‐year spot rate 0y3y is 3.5476%. Our 0y2y result is now an input into the equation and is used to discount the second cash flow. This is what is meant by bootstrapping the curve.\n",
    "\n",
    "$$102.7500 = \\frac{4.50}{1.030264} +  \\frac{4.50}{(1.027903)^{2}} +  \\frac{104.50}{(1+\\mathit{z})^{3}}, \\mathit{z} = 0.035476$$\n",
    "\n",
    "**0y4y**: The implied 4-year spot rate (the 0y4y) is 4.2525%. The formula uses the inital 0y1y starter zero and the 0y2y and 0y3y implied rates. \n",
    "\n",
    "$$99.3125 = \\frac{4}{1.030264} +  \\frac{4}{(1.027903)^{2}} + \\frac{4}{(1.035476)^{3}} +  \\frac{104}{(1+\\mathit{z})^{3}}, \\mathit{z} = 0.042525$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.03026401 0.0279033  0.03547566 0.04252524]\n"
     ]
    }
   ],
   "source": [
    "def spot_rate(years, coupon, spots, price, face):\n",
    "    pvPMT = np.sum(np.full(years-1, coupon) * ((1 + spots)**-np.arange(1,years)))\n",
    "    return ((face + coupon) / (price - pvPMT))**(1/years) - 1\n",
    "\n",
    "spots = [ytm[0]]\n",
    "for i in range(1,len(ytm)):\n",
    "    spots.append(spot_rate(years[i], coupon[i], np.array(spots), price[i], face[i]))\n",
    "\n",
    "spots = np.array(spots)\n",
    "print(spots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12539d51cd0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(num=0, dpi=120)\n",
    "plt.plot(years, ytm, label=\"YTM\")\n",
    "plt.plot(years, spots, \"--g\", label=\"Implied Spot Curve\")\n",
    "plt.title('Yield Curves')\n",
    "plt.xlabel('Years to Maturity')\n",
    "plt.ylabel('Yields')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These equations demonstrate why a yield‐to‐maturity statistic can be interpreted as a “present value average” of the zero‐coupon rates. Consider the 4‐year bond in this example. Its price is the sum of the discounted cash fl ows using either the yield to maturity or the sequence of spot rates.\n",
    "\n",
    "$$\\frac{4}{1.030264} +  \\frac{4}{(1.027903)^{2}} + \\frac{4}{(1.035476)^{3}} +  \\frac{104}{(1.042525)^{3}} = 99.3125$$\n",
    "\n",
    "$$\\frac{4}{1.041902} +  \\frac{4}{(1.041902)^{2}} + \\frac{4}{(1.041902)^{3}} +  \\frac{104}{(1.041902)^{3}} = 99.3125$$\n",
    "\n",
    "Here 4.1902% is a “weighted average” of 3.0264%, 2.7903%, 3.5476%, and 4.2525%, with most of the weight on the last spot rate because it corresponds to the largest cash flow."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Par Curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The implied spot curve can be used to derive a related description of the market, assuming no arbitrage. This is the **par curve**—the sequence of yields such that the bond for each time to maturity trades at par value.\n",
    "\n",
    "Consider for example for earlier:\n",
    "\n",
    "| Maturity (Years) | Coupon Rate | Price (% of Par Value) | Yield to Maturity |\n",
    "| ---------------- | ----------- | ---------------------- | ----------------- |\n",
    "| 1                | 0%          | 97.0625                | 3.0264%           |\n",
    "| 2                | 3.25%       | 100.8750               | 2.7941%           |\n",
    "| 3                | 4.50%       | 102.7500               | 3.5181%           |\n",
    "| 4                | 4.00%       | 99.3125                | 4.1902%           |\n",
    "\n",
    "We have bootstrapped the Spot Rates:\n",
    "| Maturity (Years) | Coupon Rate | Price (% of Par Value) | Yield to Maturity | Spot Rates |\n",
    "| ---------------- | ----------- | ---------------------- | ----------------- |------------|\n",
    "| 1                | 0%          | 97.0625                | 3.0264%           | 3.0264%    |\n",
    "| 2                | 3.25%       | 100.8750               | 2.7941%           | 2.7903%    |\n",
    "| 3                | 4.50%       | 102.7500               | 3.5181%           | 3.5476%    |\n",
    "| 4                | 4.00%       | 99.3125                | 4.1902%           | 4.2525%    |\n",
    "\n",
    "Par Rate for 0y4y:\n",
    "\n",
    "$$100 = \\frac{PMT}{1.030264} + \\frac{PMT}{(1.027903)^{2}} + \\frac{PMT}{(1.035476)^{3}} + \\frac{PMT + 100}{(1.042525)^{4}}, PMT = 4.1876$$\n",
    "\n",
    "Each cash flow is discounted using the corresponding implied spot rate. So, while the actual 4%, 4‐year bond is trading at a small discount to yield 4.1902%, we now deduce that a hypothetical 4.1876%, 4‐year bond would be priced at par value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To convert **spot rates** (or zero-coupon yields) into **par rates** we use a process that involves discounting future payments. To formalize the conversion from **zero-coupon yields** to **par rates**, let's break it down mathematically.\n",
    "\n",
    "1. **Spot Rate (Zero-Coupon Yield):**\n",
    "The spot rate $z_t$ (or zero-coupon yield) for year $t$ represents the yield of a zero-coupon bond maturing in $t$ years. The price $ P_t$ of this zero-coupon bond is calculated as:\n",
    "\n",
    "$$P_t = \\frac{1}{(1 + z_t / f)^t}$$\n",
    "Where:\n",
    "- $z_t$ is the spot rate for year $t$,\n",
    "- $f$ is the frequency of coupon payments (typically $f = 1$ for annual payments),\n",
    "- $t$ is the year or time to maturity.\n",
    "\n",
    "2. **Annuity Calculation:**\n",
    "The **annuity** in the code is the present value of receiving a series of coupon payments over time, discounted at the spot rates. Mathematically, for a bond with a coupon $C$ paid over $T$ periods, the annuity $A_T$ at year $T$ is:\n",
    "\n",
    "$$A_T = \\sum_{t=1}^{T} \\frac{C}{(1 + z_t / f)^t}$$\n",
    "\n",
    "In this case, since the coupon rate is normalized (the par rate itself is calculated), the annuity becomes the sum of the discounted values of the coupon payments.\n",
    "\n",
    "3. **Present Value of Redemption:**\n",
    "The **present value of the redemption** refers to the discounted value of the bond's face value at maturity (which is usually 100):\n",
    "\n",
    "$$PV_{\\text{redeem}} = \\frac{1}{(1 + z_T / f)^T}$$\n",
    "\n",
    "Where $T$ is the maturity period. This term represents the value of receiving the face value at maturity, discounted by the spot rate for that period.\n",
    "\n",
    "4. **Present Value of Coupons (PV of Coupons):**\n",
    "The **PV of coupons** is the complement to the redemption value:\n",
    "\n",
    "$$PV_{\\text{cpns}} = 1 - PV_{\\text{redeem}}$$\n",
    "\n",
    "This represents the proportion of the total value attributed to the coupon payments, after accounting for the face value repayment.\n",
    "\n",
    "5. **Par Rate Calculation:**\n",
    "The **par rate** is the coupon rate that makes the bond's price equal to its face value (typically 100) when discounted at the spot rates. It can be expressed as:\n",
    "\n",
    "$$\\text{Par Rate}_T = \\frac{PV_{\\text{cpns}}}{A_T} \\times f$$\n",
    "\n",
    "Where:\n",
    "- $PV_{\\text{cpns}}$ is the present value of coupons (the complement to redemption),\n",
    "- $A_T$ is the annuity (present value of coupon payments over time),\n",
    "- $f$ is the payment frequency (e.g., 1 for annual payments).\n",
    "\n",
    "In the code, this par rate is computed iteratively by summing the present value of coupons (through the annuity) and adjusting for the present value of the face value redemption.\n",
    "\n",
    "**Formalization of the Conversion Function**:\n",
    "Now, we can formalize the steps of the function **zero_to_par**:\n",
    "\n",
    "1. **Zero-Coupon Bond Price:** Calculate the price of zero-coupon bonds based on the given spot rates:\n",
    "   $$P_t = \\frac{1}{(1 + z_t / f)^t}, \\quad t = 1, 2, \\ldots, T$$\n",
    "\n",
    "2. **Annuity (Sum of Coupon Payments):** Compute the present value of coupon payments (annuity):\n",
    "   $$A_T = \\sum_{t=1}^{T} P_t$$\n",
    "\n",
    "3. **Present Value of Redemption:** Calculate the present value of redeeming the bond at maturity:\n",
    "   $$PV_{\\text{redeem}} = P_T$$\n",
    "\n",
    "4. **Present Value of Coupons:** The present value of the coupons is:\n",
    "   $$PV_{\\text{cpns}} = 1 - PV_{\\text{redeem}}$$\n",
    "\n",
    "5. **Par Rate Calculation:**\n",
    "   $$\\text{Par Rate}_T = \\frac{PV_{\\text{cpns}}}{A_T} \\times f$$\n",
    "\n",
    "---\n",
    "\n",
    "In summary:\n",
    "- The function computes the **par rate** by balancing the discounted present value of coupon payments against the present value of redeeming the bond at face value.\n",
    "- The **par rate** is the coupon rate that equates the bond's price to its face value, taking into account the zero-coupon yields (spot rates)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.03026401 0.02793574 0.03524051 0.0418762 ]\n"
     ]
    }
   ],
   "source": [
    "# Convert spot rates (zero yields) to par rates\n",
    "def zero_to_par(zero_yields, freq=1):\n",
    "    # Time periods (1, 2, 3, ..., n)\n",
    "    t = np.arange(len(zero_yields)) + 1\n",
    "    \n",
    "    # Zero-coupon bond prices based on spot rates\n",
    "    zero_prices = (1 + zero_yields / freq) ** (-t)\n",
    "    \n",
    "    # Initialize variables\n",
    "    annuity = 0\n",
    "    par = np.empty_like(zero_prices)\n",
    "    \n",
    "    # Calculate par rates iteratively\n",
    "    for i, zero_price in enumerate(zero_prices):\n",
    "        annuity += zero_price  # Update annuity (sum of discounted coupon payments)\n",
    "        pv_redeem = zero_price  # Present value of redeeming the bond\n",
    "        pv_cpns = 1 - pv_redeem  # Present value of coupons (complement to redemption)\n",
    "        \n",
    "        # Par rate calculation\n",
    "        par[i] = (pv_cpns / annuity) * freq\n",
    "        \n",
    "    return par\n",
    "\n",
    "# Run the function to convert spot rates to par rates\n",
    "par_rates = zero_to_par(spots)\n",
    "print(par_rates)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.03026401 0.02793574 0.03524051 0.0418762 ]\n"
     ]
    }
   ],
   "source": [
    "def zero_to_par_new(zero_prices=None, zero_yields=None, freq=1):\n",
    "    if zero_prices is None:\n",
    "        zero_yields, freq = np.array(zero_yields), np.array(freq)\n",
    "        t = np.arange(len(zero_yields)) + 1\n",
    "        zero_prices = (1 + zero_yields / freq) ** (-t)\n",
    "    else:\n",
    "        zero_prices, freq = np.array(zero_prices), np.array(freq)\n",
    "    par = ((1 - zero_prices) / np.cumsum(zero_prices)) * freq\n",
    "    return par\n",
    "\n",
    "par_rates = zero_to_par_new(zero_yields=spots)\n",
    "print(par_rates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>zero_yields</th>\n",
       "      <th>zero_prices</th>\n",
       "      <th>forward_rates</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.030264</td>\n",
       "      <td>0.970625</td>\n",
       "      <td>0.030264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.027903</td>\n",
       "      <td>0.946445</td>\n",
       "      <td>0.025548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.035476</td>\n",
       "      <td>0.900700</td>\n",
       "      <td>0.050788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.042525</td>\n",
       "      <td>0.846552</td>\n",
       "      <td>0.063963</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   zero_yields  zero_prices  forward_rates\n",
       "0     0.030264     0.970625       0.030264\n",
       "1     0.027903     0.946445       0.025548\n",
       "2     0.035476     0.900700       0.050788\n",
       "3     0.042525     0.846552       0.063963"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from bond_pricing import par_yld_to_zero\n",
    "\n",
    "par_yld_to_zero(par_rates, freq=1, return_dataframe=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forward Curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An obvious application for bootstrapping the implied spot curve is to get the zero‐coupon rates needed to derive the implied forward curve. That is, the implied spot curve can be just an intermediate step to get to get the information we need to help make a maturity\n",
    "choice decision."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.03026401 0.025548   0.05078814 0.06396326]\n"
     ]
    }
   ],
   "source": [
    "forwards = [spots[0]]\n",
    "for i in range(len(spots)-1):\n",
    "    forwards.append(ifr(rate_t0t1=spots[i], t1=(i+1), rate_t0t2=spots[i+1], t2=(i+2), per=1))\n",
    "\n",
    "forwards = np.array(forwards)\n",
    "print(forwards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1253c63c7a0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(num=0, dpi=120)\n",
    "plt.plot(years, ytm, label=\"YTM\")\n",
    "plt.plot(years, spots, label=\"Implied Spot Curve\")\n",
    "plt.plot(years, forwards, label=\"Implied Forward Curve\")\n",
    "plt.plot(years, par_rates, label=\"Par Curve\")\n",
    "plt.title('Yield Curves')\n",
    "plt.xlabel('Years to Maturity')\n",
    "plt.ylabel('Yields')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Credit Spread Over Benchmark Bonds - *Z-Spread*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another clever application of the implied spot curve is in calculating the credit spread over benchmark bonds. Suppose we are analyzing a 4‐year, level‐payment, fully amortizing bank loan. The bank loan is priced at par value and makes an annual payment of 28.2 (percent of par value), including both principal and interest. Its yield to maturity is 4.9982%.\n",
    "\n",
    "$$100 = \\frac{28.2}{1+\\mathit{y}} + \\frac{28.2}{(1+\\mathit{y})^{2}} + \\frac{28.2}{(1+\\mathit{y})^{3}} + \\frac{28.2}{(1+\\mathit{y})^{4}}, y = 0.049982$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loan_yield = 4.998%\n",
      "4-year par yield = 4.188%\n",
      "credit_spread = 81.06bps\n",
      "credit_spread = 80.79bps\n"
     ]
    }
   ],
   "source": [
    "# 4-year loan priced at par (pv = 100) \n",
    "loan_yield = coupon_bond_ytm(n=4,pmt=28.2, pv=100, fv=0, cf_freq=1, comp_freq=1)\n",
    "print(f'{loan_yield = :0.3%}')\n",
    "\n",
    "# 4-year par yield - Treasuries\n",
    "print(f'4-year par yield = {par_rates[3]:0.3%}')\n",
    "\n",
    "# Approx - Credit Spread\n",
    "credit_spread = (loan_yield - par_rates[3]) * 10_000 # Using Par Yield\n",
    "print(f'{credit_spread = :0.2f}bps')\n",
    "credit_spread = (loan_yield - ytm[3]) * 10_000 # Using Actual 4-Year Bond Yield\n",
    "print(f'{credit_spread = :0.2f}bps')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The problem with these is that the “average life” of this amortizing bank loan is less than four years—the 4‐year Treasury yield is not the right benchmark.\n",
    "\n",
    "A better way to assess the compensation for the credit risk (as well as any difference in liquidity and taxation) is to calculate the **static spread**, also known as the **zero‐volatility spread** or just **Z‐spread**. It is the uniform (hence, static) spread over the benchmark implied spot rates. It is the solution for the static spread, denoted *ss*, in this expression:\n",
    "\n",
    "$$100 = \\frac{28.2}{1.030264 + ss} + \\frac{28.2}{(1.027903 + ss)^{2}} + \\frac{28.2}{(1.035476 + ss)^{3}} + \\frac{28.2}{(1.042525 + ss)^{4}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "static_spread = 140.48bps\n"
     ]
    }
   ],
   "source": [
    "def z_spread(spots, installment, n, price, face):\n",
    "    def bond_price(rates, years, coupon, face=100):\n",
    "        pvPMT = np.sum(np.full(years, coupon) * (1 + rates)**-np.arange(1, years+1))\n",
    "        pvFV =  face / (1 + rates[-1])**years\n",
    "        return pvPMT + pvFV\n",
    "    \n",
    "    def f(ss):\n",
    "        rates = spots + ss\n",
    "        return bond_price(rates=rates, years=n, coupon=installment, face=face) - price\n",
    "    root = newton(f, 0.0, disp=False)\n",
    "    return root\n",
    "\n",
    "static_spread = z_spread(spots=spots, installment=28.2, n=4, price=100, face=0) * 10_000\n",
    "print(f'{static_spread = :0.2f}bps')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### More Applications for the Implied Spot and Forward Curve"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An obvious application for bootstrapping the implied spot curve is to get the zero‐coupon rates needed to derive the implied forward curve. That is, the implied spot curve can be just an intermediate step to get to get the information we need to help make a maturity\n",
    "choice decision.\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These examples and cases below demonstrate the interconnectedness between the underlying yield curve on traded coupon bonds, the implied spot, and implied forward rates. The connection is the **assumption of no arbitrage**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Maturity-Choice Decision"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decision to invest over a long period to invest short-term and rollover:\n",
    "\n",
    "| Maturity (Years) | Coupon Rate | Price (% of Par Value) | Yield to Maturity | Spot Rates |   IFR   |\n",
    "| ---------------- | ----------- | ---------------------- | ----------------- |------------|---------|\n",
    "| 1                | 0%          | 97.0625                | 3.0264%           | 3.0264%    | 3.0264% |\n",
    "| 2                | 3.25%       | 100.8750               | 2.7941%           | 2.7903%    | 2.5548% |   \n",
    "| 3                | 4.50%       | 102.7500               | 3.5181%           | 3.5476%    | 5.0788% |\n",
    "| 4                | 4.00%       | 99.3125                | 4.1902%           | 4.2525%    | 6.3963% |\n",
    "\n",
    "\n",
    "Suppose you have a 4‐year investment horizon and can buy any of the four government bonds in the preceding example. You are deciding whether to buy the 1‐year zero and reinvest at higher yields in each future year, you hope, or to buy the 4%, 4‐year bond. How high would rates have to be to prefer the rollover strategy? The answer, of course, is higher than the IFRs (computed after bootstrapping implied spot rates). To expect a higher total return after four years by buying and rolling over 1‐year bonds, you project the 1‐year yield to track a path, on average, above 2.55%, 5.08%, and 6.40%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decision to borrow in the money market on 6-month or 12-month LIBOR:\n",
    "\n",
    "Now suppose that you are a commercial banker working with a middle market business customer on a 12‐month loan to build up working capital. The loan rate will be tied to 6‐month or 12‐month LIBOR. If the customer chooses 12‐month LIBOR (currently 4.00%), the cost of funds is set. But if the customer chooses 6‐month LIBOR (currently 3.50%), there is interest rate risk at the reset date in six months. Your customer asks for your recommendation. You know that the maturity‐choice decision depends on the rate view (i.e., where 6‐month LIBOR is expected to be vis‐à‐vis the implied forward rate). You also know that the 6m6m IFR is not 4.50% because of the periodicity problem. We can obtain the level for LIBOR of 4.42% (assuming 180 and 360 days).\n",
    "\n",
    "The customer’s decision turns on whether 6‐month LIBOR is expected to be above or below 4.42% in six months. That might or might not be the rate that market participants in general are expecting. That does not matter—what matters is the decision maker’s own rate view. The commercial banker here can help the process by providing some historical data, the bank economist’s view on monetary policy and economic conditions, and the like. The advantage of the IFR is that as a breakeven rate it provides a framework for the above‐or‐below decision."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "libor_6m6m = 4.4226%\n"
     ]
    }
   ],
   "source": [
    "aor_t0t1 = 0.035\n",
    "t1 = 180\n",
    "aor_t0t2 = 0.04\n",
    "t2 = 360\n",
    "year = 360\n",
    "\n",
    "libor_6m6m = ifr_mm(rate_t0t1=aor_t0t1, t1=t1, rate_t0t2=aor_t0t2, t2=t2, t0=0, year=year, aor=True)\n",
    "print(f'{libor_6m6m = :0.4%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bond Valuation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The implied spot curve can be used in bond valuation. In the example, the 4‐year actively traded benchmark bond has a coupon rate of 4% and is priced at 99.3125 to yield 4.1902% on an annually compounded street convention basis.\n",
    "\n",
    "| Maturity (Years) | Coupon Rate | Price (% of Par Value) | Yield to Maturity | Spot Rates |   IFR   |\n",
    "| ---------------- | ----------- | ---------------------- | ----------------- |------------|---------|\n",
    "| 1                | 0%          | 97.0625                | 3.0264%           | 3.0264%    | 3.0264% |\n",
    "| 2                | 3.25%       | 100.8750               | 2.7941%           | 2.7903%    | 2.5548% |   \n",
    "| 3                | 4.50%       | 102.7500               | 3.5181%           | 3.5476%    | 5.0788% |\n",
    "| 4                | 4.00%       | 99.3125                | 4.1902%           | 4.2525%    | 6.3963% |\n",
    "\n",
    "Suppose that we want to calculate the fair value on another 4‐year bond, this one having a 9% coupon rate. We neglect taxation and assume that this bond has the same liquidity and default risk as the four benchmark securities. The key point is that in a world of no arbitrage, this bond will not be priced to yield 4.1902%. Instead, its (no‐arbitrage) price is the present value of the cash flows discounted at the implied spot rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price =  117.6341\n",
      "ytm =  4.1274%\n"
     ]
    }
   ],
   "source": [
    "coupon = np.full(4, 9)\n",
    "coupon[-1] += 100\n",
    "discount_factor = ((1 + spots)**-(np.arange(4)+1))\n",
    "\n",
    "price = np.dot(coupon, discount_factor)\n",
    "print(f'{price = : 0.4f}')\n",
    "\n",
    "ytm = coupon_bond_ytm(n=4, pmt=9, pv=price, fv=100, cf_freq=1, comp_freq=1)\n",
    "print(f'{ytm = : 0.4%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The usual candidates to explain why the yields on any two bonds differ are **time to maturity** (the *shape of the yield curve*), **credit risk** (the probability of default and the assumed recovery rate), **liquidity risk**, and **taxation**. This example reveals another reason—**coupon structure**. \n",
    "\n",
    "We have three 4‐year bonds for the same risk class: one yielding 4.2525% (the implied 0% coupon bond), another yielding 4.1902% (the benchmark 4% coupon bond), and this one yielding 4.1274% (the 9% coupon bond). The yield differences are entirely due to coupon structure. The more “weight” that is placed on the first few cash fl ows (i.e., the higher the coupon rate), the lower the yield to maturity. Of course, that conclusion depends on the shape of the curve."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Corporate Finance - Bonds of Corporate Issuers (same rating or same issuer) & DCF Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implied zero‐coupon rates can have applications in corporate finance as well. Let’s suppose now that the four **benchmark bonds are corporate securities for a specific bond rating**, say, single A. Better yet, we could assume that they are **unsecured liabilities of the same A‐rated issuer**. Even though there might be no market for zero‐coupon corporate bonds, we still can carry out the implied spot rate bootstrapping calculations. The idea is that if such corporate zeros did exist, they would have to trade at those spot yields if there were to be no arbitrage opportunities (and assuming no transactions costs to exploit those opportunities)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that we need to value some project that has credit risk deemed to be equivalent to the benchmark corporate bonds. Clearly, this is a valuation problem begging for discounted cash fl ow (DCF) analysis. Assume first that our analyst does the obvious—this is a 4‐year project, so he or she uses the 4‐year yield to maturity of 4.1902% to do the discounting. I have always wondered why DCF corporate finance problems, at least in the textbooks I’ve seen, invariably use a single discount rate or cost of capital for all time periods. Coming from a bond market perspective, I see the usually upward slope to the yield curve instructing us to discount year‐1 cash flow at a lower rate than year‐2 cash flow. \n",
    "\n",
    "Better analysis, in my opinion, is to use the implied spot rates (i.e., 3.0264%, 2.7903%, 3.5476%, and 4.2525%) instead of the yield on the maturity‐matching coupon bond. These implied spot rates correspond to the timing of the specific cash flows, which are no different than the face values on four zero‐coupon bonds. Depending on the amount and timing of the projected cash flows, this DCF calculation could produce a higher valuation for the project. All we have done to get the more appropriate discount rates is reconfigure data from the underlying yield curve and add the assumption of no arbitrage.\n",
    "\n",
    "To be fair, the source of error in most corporate finance valuation problems is not the lack of precision in the discount rates in the denominators. Instead, the difficulty is uncertainty regarding the expected cash flows in the numerators. Often those numbers are just best‐guess projections of future sales and operating costs. Then our “laser‐sharp” implied spot rates represent bond math overkill. In those circumstances, we should use appropriate technology and discount all cash flows at some reasonable rate. However, there are situations when the numerators are scheduled amounts on scheduled dates—for instance, with financial contracts such as lease agreements or interest rate swaps. Then the implied spots could produce a better valuation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Identify Arbitrage Opportunity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For hedge funds and proprietary trading desks at financial institutions, the implied spot curve is used to identify arbitrage opportunities. The two strategies discussed earlier are: (1) coupon stripping—buy the coupon bond and sell the cash flows separately as zero‐coupon coupon bonds (e.g., TIGRS, CATS, LIONS back in the early 1980s and Treasury STRIPS since 1985), and (2) bond reconstitution—buy the zero‐coupon bonds in sufficient quantity to build and sell a coupon bond. The implied spot curve identifies when one of these arbitrage strategies might be profitable.\n",
    "\n",
    "By design, the implied spot curve is the sequence of zero‐coupon rates such that those trading two strategies break even. If actual zero‐coupon bonds are trading at yields above those implied rates, a bond reconstitution strategy might work. Actual zeros would have “high yields” and therefore “low prices” relative to breakeven. The arbitrageur buys the zeros, builds the coupon bond, and sells it for a profit. To be sure, the profit would have\n",
    "to cover transactions costs. Those could be included directly, but then we would not have an implied spot curve; instead we would have an **implied spot cone**. An arbitrage opportunity arises when actual zeros are trading outside the cone. If actual zero‐coupon bonds can be sold at yields below the implied spot curve (or below the cone), the arbitrageur undertakes the coupon‐stripping strategy, as Merrill Lynch did in the 1980s when it created TIGRS."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Pricing Interest Rate Derivatives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A hugely important application for implied spot and forward rates is in pricing interest rate derivatives. We see this in interest rate swaps. The idea is that the forward curve is a sequence of “hedge‐able” future rates. They indicate the rates that can be locked in using derivatives. Once again the caveats are that there are no arbitrage opportunities and transactions costs are small enough to be neglected. Those are fine and acceptable assumptions in normal financial market conditions and active trading in derivatives.However, during a financial crisis when liquidity dries up, some arbitrage opportunities can lie there unexploited."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Horizon Yield on Coupon Bonds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A horizon yield on a coupon bond depends critically on coupon reinvestment rates. Remember that one of the assumptions in using the yield to maturity as a measure of an investor’s total return is that all coupons are reinvested at that same yield. Obviously, future rates are random. But suppose we can hedge that interest rate risk using costless and riskless\n",
    "derivatives and can lock in rates along the implied forward curve. \n",
    "\n",
    "Consider again the 4‐year, 4% annual payment government bond priced at 99.3125 to yield 4.1902%. We calculated the IFRs above: The 1y1y is 2.5547%, the 2y1y is 5.0790%, and the 3y1y is 6.3961%. What will be the 4‐year horizon yield (i.e., the total pretax return after four years assuming no default) if coupons are in fact reinvested at those specific rates?\n",
    "\n",
    "The total return turns out to be 117.314087 (percent of par value). The initial coupon is rolled over at the 1y1y, then the 2y1y and 3y1y IFRs. The second coupon is reinvested at the 2y1y and 3y1y, while the third is rolled over only once at the 3y1y IFR. The last coupon is received at maturity along with the principal.\n",
    "\n",
    "Notice that 4.2525% is the 0y4y **implied spot rate**. Derivatives (in particular, costless and riskless derivatives) lock in for the investor the 4‐year spot rate, not the 4.1902% yield to maturity on the 4‐year bond."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total return at the end of holding period: 117.31410346428962\n",
      "ytm = 4.2525%\n"
     ]
    }
   ],
   "source": [
    "n = 4\n",
    "coupon = 4\n",
    "face = 100\n",
    "price = 99.3125\n",
    "\n",
    "reinvestable_coupons = np.full(n-1, coupon)  \n",
    "reinvestable_forwards = forwards[1:]\n",
    "\n",
    "compound_factors = np.array([np.prod(1 + reinvestable_forwards[i:]) for i in range(n-1)]) \n",
    "\n",
    "reinvestment_proceeds = np.sum(reinvestable_coupons * compound_factors)\n",
    "\n",
    "# Holding Period Return (HPR)\n",
    "total_return = reinvestment_proceeds + coupon + face\n",
    "print(\"Total return at the end of holding period:\", total_return)\n",
    "\n",
    "ytm = (total_return/price)**(1/n) - 1\n",
    "print(f'{ytm = :0.4%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total return at the end of holding period: 117.31410346428962\n",
      "ytm = 4.2525%\n"
     ]
    }
   ],
   "source": [
    "n = 4\n",
    "coupon = 4\n",
    "face = 100\n",
    "price = 99.3125\n",
    "\n",
    "reinvestable_coupons = np.full(n-1, coupon)  \n",
    "reinvestable_forwards = forwards[:0:-1]\n",
    "\n",
    "compound_factors = np.cumprod(1 + reinvestable_forwards) \n",
    "\n",
    "reinvestment_proceeds = np.sum(reinvestable_coupons * compound_factors)\n",
    "\n",
    "# Holding Period Return (HPR)\n",
    "total_return = reinvestment_proceeds + coupon + face\n",
    "print(\"Total return at the end of holding period:\", total_return)\n",
    "\n",
    "ytm = (total_return/price)**(1/n) - 1\n",
    "print(f'{ytm = :0.4%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That is not a coincidence. Suppose that the bond buyer has only a 3‐year investment horizon. What is the 3‐year horizon yield assuming coupon reinvestment at the 1y1y and 2y1y IFRs and the ability to lock in using derivatives the sale price of the bond at the end of the third year at the 3y1y IFR? The total return after three years is 110.261642 (percent of par value). \n",
    "\n",
    "When the bond is sold, the proceeds are just the final coupon and principal discounted at the 3y1y IFR. The 3‐year horizon yield is 3.5476%, which—no surprise now—is the 0y3y implied spot rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total return at the end of holding period: 110.26142345401517\n",
      "ytm = 3.5476%\n"
     ]
    }
   ],
   "source": [
    "n = 3\n",
    "coupon = 4\n",
    "face = 100\n",
    "price = 99.3125\n",
    "\n",
    "reinvestable_coupons = np.full(n-1, coupon)  \n",
    "reinvestable_forwards = forwards[1:n]\n",
    "\n",
    "compound_factors = np.array([np.prod(1 + reinvestable_forwards[i:]) for i in range(n-1)]) \n",
    "\n",
    "reinvestment_proceeds = np.sum(reinvestable_coupons * compound_factors)\n",
    "\n",
    "# Holding Period Return (HPR)\n",
    "total_return = reinvestment_proceeds + coupon + ((coupon + face)/(1 + forwards[-1]))\n",
    "print(\"Total return at the end of holding period:\", total_return)\n",
    "\n",
    "ytm = (total_return/price)**(1/n) - 1\n",
    "print(f'{ytm = :0.4%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total return at the end of holding period: 110.26142345401517\n",
      "ytm = 3.5476%\n"
     ]
    }
   ],
   "source": [
    "n = 3\n",
    "coupon = 4\n",
    "face = 100\n",
    "price = 99.3125\n",
    "\n",
    "reinvestable_coupons = np.full(n-1, coupon)  \n",
    "reinvestable_forwards = forwards[2:0:-1]\n",
    "\n",
    "compound_factors = np.cumprod(1 + reinvestable_forwards) \n",
    "\n",
    "reinvestment_proceeds = np.sum(reinvestable_coupons * compound_factors)\n",
    "\n",
    "# Holding Period Return (HPR)\n",
    "total_return = reinvestment_proceeds + coupon + ((coupon + face)/(1 + forwards[-1]))\n",
    "print(\"Total return at the end of holding period:\", total_return)\n",
    "\n",
    "ytm = (total_return/price)**(1/n) - 1\n",
    "print(f'{ytm = :0.4%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These examples demonstrate the interconnectedness between the underlying yield curve on traded coupon bonds, the implied spot, and implied forward rates. The connection is the assumption of no arbitrage."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discount Factors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to calculate implied spot and forward rates is with discount factors. In fact, this is how yield curve analysis is carried out in practice using spreadsheets. **A discount factor is by definition the present value of one unit of currency at some future date.** A financial institution that has a multitude of loans, bonds, and derivative contracts to value needs discount factors that correspond to each future date for which cash is received or paid out. The key point is that **spot rates and discount factors contain the same information**. Discounting with spot rates is more intuitive, but using discount factors is easier implemented in code.\n",
    "\n",
    "\n",
    "$$DF_{n} = \\frac{1}{(1 + \\mathit{z}_{n}/per)^{n\\times per}}$$\n",
    "$$\\mathit{z}_{n} = \\left(DF^{-\\frac{1}{n\\times per}}_{n}-1\\right)\\times per$$\n",
    "\n",
    "$\\mathit{z}_{n}$ is the spot rate (zero-coupon rate) at time *n* and DF is the discount factor (the present value of one unit of currency at time n)\n",
    "\n",
    "We can calculate the implied forward rates (eg. for 1 year tenor) as ratios of consecutive discount factors for 1y1y, 2y1y, 3y1y, etc.\n",
    "\n",
    "$$IRF_{t_{0},t_{1}} = \\frac{DF_{0y,t_{0}y}}{DF_{0y,t_{1}y}}$$\n",
    "\n",
    "$$IFR_{1y1y}=\\frac{DF_{0y1y}}{DF_{0y2y}}$$\n",
    "$$IFR_{2y1y}=\\frac{DF_{0y2y}}{DF_{0y3y}}$$\n",
    "\n",
    "$$DF_{0yNy} = \\frac{1}{(1 + \\mathit{z}_{0yNy}/per)^{n\\times per}}$$\n",
    "$$\\mathit{z}_{t_{0},t_{1}} = \\left(DF^{-\\frac{1}{n\\times per}}_{t_{0},t_{1}}-1\\right)\\times per$$\n",
    "$$\\mathit{z}_{t_{1},t_{2}} = \\left(\\frac{DF_{t_{0},t_{1}}}{DF_{t_{0},t_{2}}}^{\\frac{1}{(t_{2} - t_{1})\\times per}}-1\\right)\\times per$$\n",
    "\n",
    "\n",
    "Working with continuous compounding:\n",
    "$$FV = PV \\times e^{\\mathit{z} \\times n}$$\n",
    "$$PV = \\frac{FV}{e^{\\mathit{z} \\times n}}$$\n",
    "$$DF = \\frac{1}{e^{\\mathit{z} \\times n}}$$\n",
    "$$DF = e^{-\\mathit{z} \\times n}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the below annual payment securities to illustrate the discount factor bootstrapping process.\n",
    "\n",
    "| Maturity (Years) | Coupon Rate | Price (% of Par Value) | Yield to Maturity |\n",
    "| ---------------- | ----------- | ---------------------- | ----------------- |\n",
    "| 1                | 0%          | 97.0625                | 3.0264%           |\n",
    "| 2                | 3.25%       | 100.8750               | 2.7941%           |\n",
    "| 3                | 4.50%       | 102.7500               | 3.5181%           |\n",
    "| 4                | 4.00%       | 99.3125                | 4.1902%           |\n",
    "\n",
    "The 1‐year bond has a coupon rate of zero and is priced at 97.0625 per 100 of par value. This one is easy: The price of zero‐coupon bond is its discount factor. So, the 1‐year discount factor, denoted $DF_{1}$ , is simply 0.970625. The 2‐year bond in the table has a coupon rate of 3.25% and is priced at 100.8750. The 2‐year discount factor is the solution for $DF_{2}$ in this equation.\n",
    "\n",
    "$$100.8750 = (3.25 \\times 0.970625) + (103.25 \\times DF_{2}), DF_{2} = 0.946445$$\n",
    "\n",
    "The bootstrapping process proceeds as in the section above where the implied spot rates are obtained. The difference is that now the algebra is much easier.\n",
    "\n",
    "The 3‐year and 4‐year bonds have coupon rates of 4.50% and 4.00% and prices of 102.7500 and 99.3125, respectively. Working your way out the yield curve sequentially gets the next two annual discount factors. The output from the previous step becomes an input in the next step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discount Factors =  [0.970625   0.94644522 0.90070033 0.84655209]\n",
      "Implied Spot Rates =  [0.03026401 0.0279033  0.03547566 0.04252524]\n",
      "Par Rates =  [0.03026401 0.02793574 0.03524051 0.0418762 ]\n",
      "Implied Forwards Rates =  [0.03026401 0.025548   0.05078814 0.06396326]\n"
     ]
    }
   ],
   "source": [
    "years = np.array([1, 2, 3, 4])\n",
    "coupon = np.array([0, 3.25, 4.5, 4])\n",
    "price = np.array([97.0625, 100.875, 102.75, 99.3125])\n",
    "face = np.full(4, 100)\n",
    "\n",
    "# Bootstrapping implied spot rate using discount factor of the first year zero-coupon bond\n",
    "df = [price[0]/100]\n",
    "for i in np.arange(1, len(coupon)):\n",
    "    coupon_cf = np.full(i, coupon[i]) # coupon cash flows for each bond and years to maturity\n",
    "    pv_coupon = np.sum(coupon_cf * np.array(df)) # present value of n-1 coupons discounted by earlier DF\n",
    "    new_df = (price[i] - pv_coupon) / (coupon[i] + face[i]) # compute new DF for the par and last coupon\n",
    "    df.append(new_df) # append to DF list for use in later coupon discounts\n",
    "    \n",
    "df = np.array(df)\n",
    "print(\"Discount Factors = \",df)\n",
    "\n",
    "spots = df**-(1/years) - 1\n",
    "print(\"Implied Spot Rates = \",spots)\n",
    "\n",
    "par_rates = (1-df)/np.cumsum(df)\n",
    "print(\"Par Rates = \",par_rates)\n",
    "\n",
    "forwards = df[:-1]/df[1:] - 1 # Implied forward rates as ratios of consecutive discount factors.\n",
    "forwards = np.insert(forwards, 0, spots[0], axis=0)\n",
    "print(\"Implied Forwards Rates = \", forwards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discount Factors =  [0.970625   0.94644522 0.90070033 0.84655209]\n",
      "Implied Spot Rates =  [0.03026401 0.0279033  0.03547566 0.04252524]\n",
      "Par Rates =  [0.03026401 0.02793574 0.03524051 0.0418762 ]\n",
      "Implied Forwards Rates =  [0.03026401 0.025548   0.05078814 0.06396326]\n"
     ]
    }
   ],
   "source": [
    "df = [price[0]/100]\n",
    "\n",
    "for i in range(1, len(coupon)):\n",
    "    pv_cf = np.sum(np.full(i, coupon[i]) * np.array(df))\n",
    "    df.append((price[i] - pv_cf) / (100 + coupon[i]))\n",
    "    \n",
    "df = np.array(df)\n",
    "print(\"Discount Factors = \",df)\n",
    "\n",
    "spots = df**-(1/years) - 1\n",
    "print(\"Implied Spot Rates = \",spots)\n",
    "\n",
    "par_rates = (1-df)/np.cumsum(df)\n",
    "print(\"Par Rates = \",par_rates)\n",
    "\n",
    "forwards = df[:-1]/df[1:] - 1 # Implied forward rates as ratios of consecutive discount factors.\n",
    "forwards = np.insert(forwards, 0, spots[0], axis=0)\n",
    "print(\"Implied Forwards Rates = \", forwards)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once you have the discount factors, valuing fixed‐income bonds is straightforward. Remember the 9%, 4‐year bond in the previous section? Its price turned out to be 117.6342 when each payment is discounted using the implied spot rates. Now we just need to multiply the scheduled payments by the discount factors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "117.63411318972062\n"
     ]
    }
   ],
   "source": [
    "n = 4\n",
    "cash_flows = np.full(4, 9)\n",
    "cash_flows[-1] += 100\n",
    "price = np.sum(cash_flows * df)\n",
    "print(price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another application of the discount factors is to get the 4‐year **par yield**, which is the coupon rate on a bond that has a (flat) price equal to par value. It’s the solution for PMT in this equation.\n",
    "\n",
    "$$100-\\frac{100}{(1+r_{n})^{n}} = \\left(\\frac{1}{(1+r_{1})^{1}}+\\frac{1}{(1+r_{2})^{2}}+\\cdot+\\frac{1}{(1+r_{n})^{n}}\\right)\\times PMT$$\n",
    "\n",
    "$$DF = \\frac{1}{(1 + z_t / f)^t}$$\n",
    "\n",
    "$$PV = (DF_{1} \\times PMT) + (DF_{2} \\times PMT) + \\cdots + (DF_{n} \\times PMT) + (DF_{n} \\times FV)$$ \n",
    "\n",
    "where, $DF_{n} \\times FV = PV_{\\text{Discount Bond Redemption}}$\n",
    "\n",
    "and if FV = 1, $DF_{n} = PV_{\\text{Discount Bond Redemption}}$\n",
    "\n",
    "thus, $PV_{coupon} = 1 - PV_{\\text{Discount Bond Redemption}}$\n",
    "\n",
    "$$1 - PV = (DF_{1} \\times PMT) + (DF_{2} \\times PMT) + \\cdots + (DF_{n} \\times PMT)$$ \n",
    "\n",
    "$$1 - PV = \\sum_{n=1}^{N} DF \\times PMT$$\n",
    "$$PMT = \\frac{1 - PV}{\\sum_{n=1}^{N} DF}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.970625   0.94644522 0.90070033 0.84655209]\n",
      "par_coupon = 4.18762\n"
     ]
    }
   ],
   "source": [
    "year = 4\n",
    "print(df)\n",
    "\n",
    "par_coupon = (1 - (df[year-1]))/np.sum(df[:year]) * 100\n",
    "print(f'{par_coupon = :0.7}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see how the spot rates, forward rates and discount factors are interrelated, think about how the 3y1y is calculated with the 3‐year and 4‐year spot rates:\n",
    "\n",
    "$$IFR_{3y1y} = \\left[\\frac{\\left(1+Rate_{0y4y}\\right)^{4}}{\\left(1+Rate_{0y3y}\\right)^{3}}\\right] - 1$$\n",
    "\n",
    "The function is equivalent to:\n",
    "\n",
    "$$IFR_{3y1y} = \\frac{\\frac{1}{\\left(1+Rate_{0y3y}\\right)^{3}}}{\\frac{1}{\\left(1+Rate_{0y4y}\\right)^{4}}} - 1$$\n",
    "\n",
    "The numerator is $DF_{3}$ , the present value of 1 discounted back to date 0 using the 3‐year spot rate; the denominator is $DF_{4}$ .\n",
    "\n",
    "$$IFR_{3y1y} = \\frac{DF_{3}}{DF_{4}} - 1$$\n",
    "\n",
    "The ratio between the discount factors minus one is the 3y1y implied forward rate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that 4‐year and 5‐year zero‐coupon bonds are priced at 89.75 and 86.25 (percent of par value), respectively. What is the 4y1y implied forward rate quoted on a semiannual bond basis?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.04017617880900426\n",
      "0.0401761788090047\n"
     ]
    }
   ],
   "source": [
    "ifr_4y1y = ((89.75/86.25)**(1/((5-4)*2))-1)*2\n",
    "print(ifr_4y1y)\n",
    "\n",
    "rate_t0t1 = zero_bond_ytm(4, 89.75, 100, freq=2)\n",
    "rate_t0t2 = zero_bond_ytm(5, 86.25, 100, freq=2)\n",
    "ifr_4y1y = ifr(rate_t0t1, 4, rate_t0t2, 5, 0, 2)\n",
    "print(ifr_4y1y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Questions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def equivRate(rate, from_freq=1, to_freq=1):\n",
    "  if from_freq == np.inf:\n",
    "    return (np.exp(rate / to_freq) - 1) * to_freq\n",
    "  elif to_freq == np.inf:\n",
    "    return np.log(1 + rate / from_freq) * from_freq\n",
    "  else:\n",
    "    return to_freq * ((1 + rate/from_freq)**(from_freq/to_freq) - 1)\n",
    "\n",
    "def coupon_bond_ytm(n, pmt, pv, fv=100, cf_freq=1, comp_freq=1, beg=False):\n",
    "    def f(x):\n",
    "        return coupon_bond_pv(n=n, pmt=pmt, rate=x, fv=fv, cf_freq=cf_freq, comp_freq=comp_freq, beg=beg) - pv\n",
    "    root = newton(f, 0)\n",
    "    return root\n",
    "\n",
    "def coupon_bond_pv(n, pmt, rate, fv=100, cf_freq=1, comp_freq=1, beg=False):\n",
    "    rate = equivRate(rate, from_freq=comp_freq, to_freq=cf_freq) / cf_freq\n",
    "    old_settings = np.seterr(invalid='ignore')\n",
    "    pvPMT = np.where(rate == 0, n, np.divide(1 - (1+rate)**-n, rate)) * pmt\n",
    "    np.seterr(**old_settings)\n",
    "    pvFV = fv / (1 + rate)**n\n",
    "    return np.where(beg, (pvPMT + pvFV) * (1 + rate), pvPMT + pvFV)\n",
    "\n",
    "def coupon_bond_fv(n, pmt, rate, terminal_payment, cf_freq=1, comp_freq=1, beg=False):\n",
    "    rate = equivRate(rate, from_freq=comp_freq, to_freq=cf_freq) / cf_freq\n",
    "    old_settings = np.seterr(invalid='ignore')\n",
    "    fvPMT = np.where(rate == 0, n, np.divide((1+rate)**n - 1, rate)) * pmt\n",
    "    np.seterr(**old_settings)        \n",
    "    return np.where(beg, fvPMT * (1 + rate) + terminal_payment, fvPMT + terminal_payment)\n",
    "\n",
    "def coupon_bond_pmt(n, rate, pv, fv, cf_freq=1, comp_freq=1):\n",
    "    rate = equivRate(rate, from_freq=comp_freq, to_freq=cf_freq) / cf_freq\n",
    "    pvaf = np.where(rate == 0, n, np.divide(1 - (1+rate)**-n, rate))\n",
    "    return (pv - (fv/(1+rate)**n)) / pvaf\n",
    "\n",
    "def zero_bond_ytm(n, pv, fv=100, freq=2):\n",
    "    if freq == np.inf:\n",
    "        return np.log(fv/pv) * (1/n)\n",
    "    return ((fv/pv)**(1/(n*freq)) - 1) * freq\n",
    "\n",
    "def zero_bond_pv(n, rate, fv=100, freq=2):\n",
    "    if freq == np.inf:\n",
    "        return fv / np.exp(rate*n)\n",
    "    return fv / ((1 + rate/freq)**(n*freq))\n",
    "\n",
    "def zero_bond_fv(n, rate, pv, freq):\n",
    "    if freq == np.inf:\n",
    "        return pv * np.exp(rate*n)    \n",
    "    return pv * ((1 + rate/freq)**(n*freq))\n",
    "\n",
    "def irr_newton(cf, cf_t, per=1):\n",
    "    def price(rate, cf, cf_t, per=1):\n",
    "        discount_factor = (1 + rate/per)**(-cf_t)\n",
    "        return np.dot(cf, discount_factor)\n",
    "    def f(x):\n",
    "        return price(x, cf, cf_t, per=per)\n",
    "    return newton(f, 0)\n",
    "\n",
    "def irr_newton_no_scipy(stream, cf_t, per=1, tol=1e-12):\n",
    "    rate = 0.0\n",
    "    for steps in range(50): \n",
    "        r = np.array(cf_t)\n",
    "        m = max(-rate * r / per)  \n",
    "        f = np.exp(-rate * r / per - m)\n",
    "        t = np.dot(f, stream)\n",
    "        if abs(t) < tol * np.exp(-m):\n",
    "            break\n",
    "        u = np.dot(f * r, stream)\n",
    "        rate = rate + np.clip(t / u, -1.0, 1.0)\n",
    "    annualized_rate = (np.exp(rate / per) - 1) * per \n",
    "    return annualized_rate\n",
    "\n",
    "def ifr(rate_t0t1, t1, rate_t0t2, t2, t0 = 0, per=2):\n",
    "    t2_term = (1 + rate_t0t2/per)**(t2 - t0)\n",
    "    t1_term = (1 + rate_t0t1/per)**(t1 - t0) \n",
    "    return ((t2_term / t1_term)**(1/(t2 - t1)) - 1) * per\n",
    "\n",
    "def ifr_mm(rate_t0t1, t1, rate_t0t2, t2, t0 = 0, year=360, aor=True):\n",
    "    rollover_avg = (t2 * rate_t0t2 - t1 * rate_t0t1) / (t2 - t1)\n",
    "    adjust = 1/(1 + (rate_t0t1 * t1/year)) if aor else 1/(1 - (rate_t0t1 * t1/year))\n",
    "    return rollover_avg * adjust"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.\tWhich statement best describes a conclusion of the expectations theory of the term structure of interest rates?\n",
    "    1. **An implied forward rate is an unbiased expectation of the future spot rate.**\n",
    "    2. An implied forward rate is unrelated to the future spot rate.\n",
    "    3. An implied forward rate is a downwardly biased expectation of the future spot rate.\n",
    "    4. An implied forward rate is an upwardly biased expectation of the future spot rate.\n",
    "   \n",
    "The expectations theory is based on the assumptions that bond investors and issuers are risk neutral and they can choose any maturity that maximizes their expected outcomes—buyers maximize the expected rate of return and sellers minimize the expected cost of borrowed funds over known time horizons. Given those assumptions, market participants make buy and sell decisions such that\n",
    "the expected horizon yield is the same for each maturity strategy. This gives the result that the implied forward rate is the expected future spot rate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.\tWhich statement best describes a conclusion of the segmented markets theory of the term structure of interest rates?\n",
    "    1. An implied forward rate is an unbiased expectation of the future spot rate.\n",
    "    2. **An implied forward rate is unrelated to the future spot rate.**\n",
    "    3. An implied forward rate is a downwardly biased expectation of the future spot rate.\n",
    "    4. An implied forward rate is an upwardly biased expectation of the future spot rate.\n",
    "\n",
    "The segmented markets theory is based on assumption that investors and issuers are risk averse and only choose maturities that align with their underlying business needs and known time horizons. Therefore, the shape and level of the forward curve depend on the demand and supply of funds in separate markets and not on expectations of future spot rates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3.\tWhich statement best describes a conclusion of the liquidity preference theory of the term structure of interest rates?\n",
    "    1. An implied forward rate is an unbiased expectation of the future spot rate.\n",
    "    2. An implied forward rate is unrelated to the future spot rate.\n",
    "    3. An implied forward rate is a downwardly biased expectation of the future spot rate.\n",
    "    4. **An implied forward rate is an upwardly biased expectation of the future spot rate.**\n",
    "\n",
    "The liquidity preference theory essentially adds **market price risk** (greater degree of change in prices due to changes in interest rates) to the expectations theory. In addition to their expectations about future rates, investors and issuers know and care that prices on longer-term bonds generally are more volatile than on short-term bonds when interest rates change. Therefore, there is a risk premium built into longer-term yields. That means an implied forward rate reflects this risk premium in addition to the expected future spot rate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Base your answers to Questions 4 to 6 on these price data for zero-coupon Treasury P-STRIPS, which are quoted as a percentage of par value. The yields to maturity are quoted on a semiannual bond basis having a periodicity of 2.\n",
    "\n",
    "| Maturity |     Price | Yield to Maturity |\n",
    "| -------- | --------- | ----------------- |\n",
    "|  1 year  | 99.2      | 0.80%             |\n",
    "|  2 years | 96.5      | 1.79%             |\n",
    "|  3 years | 93.8      | 2.14%             |\n",
    "|  4 years | 89        | 2.93%             |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "years = np.arange(4) + 1\n",
    "prices = np.array([99.2, 96.50, 93.80, 89])\n",
    "ytm = np.vectorize(zero_bond_ytm)(n=years, pv=prices, fv=100, freq=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4.\tThe implied forward 1-year rate, two years into the future (the 2×3 forward rate, or in alternate notation the 2y1y), stated on a semiannual bond basis, is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_2y1y = 2.858%\n"
     ]
    }
   ],
   "source": [
    "# Method 1\n",
    "rate_t0t1 = ytm[1]\n",
    "rate_t0t2 = ytm[2]\n",
    "\n",
    "ifr_2y1y = ifr(rate_t0t1=rate_t0t1, t1=2, rate_t0t2=rate_t0t2, t2=3, t0=0, per=2)\n",
    "print(f'{ifr_2y1y = :.3%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_2y1y = 2.858%\n"
     ]
    }
   ],
   "source": [
    "# Method 2\n",
    "dr = (1 + (ytm/2))**-(years*2)\n",
    "ifr_2y1y = ((dr[1] / dr[2])**(1/2) - 1) * 2\n",
    "print(f'{ifr_2y1y = :.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5. The implied forward 1-year rate, three years into the future (the 3×4, or 3y1y, forward rate), stated on a semiannual bond basis, is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_3y1y = 5.322%\n"
     ]
    }
   ],
   "source": [
    "# Method 1\n",
    "rate_t0t1 = ytm[2]\n",
    "rate_t0t2 = ytm[3]\n",
    "\n",
    "ifr_3y1y = ifr(rate_t0t1=rate_t0t1, t1=3, rate_t0t2=rate_t0t2, t2=4, t0=0, per=2)\n",
    "print(f'{ifr_3y1y = :.3%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_3y1y = 5.322%\n"
     ]
    }
   ],
   "source": [
    "# Method 2\n",
    "dr = (1 + (ytm/2))**-(years*2)\n",
    "ifr_3y1y = ((dr[2] / dr[3])**(1/2) - 1) * 2\n",
    "print(f'{ifr_3y1y = :.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6. According to the expectations theory of the term structure of interest rates, the annual yield on 3-year P-STRIPS one year into the future, quoted on a semiannual bond basis, will be closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_1y3y = 3.650%\n"
     ]
    }
   ],
   "source": [
    "# Method 1\n",
    "rate_t0t1 = ytm[0]\n",
    "rate_t0t2 = ytm[3]\n",
    "\n",
    "ifr_1y3y = ifr(rate_t0t1=rate_t0t1, t1=1, rate_t0t2=rate_t0t2, t2=4, t0=0, per=2)\n",
    "print(f'{ifr_1y3y = :.3%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_1y3y = 3.650%\n"
     ]
    }
   ],
   "source": [
    "# Method 2\n",
    "dr = (1 + (ytm/2))**-(years*2)\n",
    "ifr_1y3y = ((dr[0] / dr[3])**(1/((4-1)*2)) - 1) * 2\n",
    "print(f'{ifr_1y3y = :.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Base your answers to Questions 7 and 8 on these rate data for bank time deposits. The rates are quoted on an add-on rate basis for a 360-day year.\n",
    "\n",
    "| Maturity |  Rate |\n",
    "| -------- | ----- |\n",
    "|  30 days | 2.50% |\n",
    "|  60 days | 3.00% |\n",
    "|  90 days | 3.50% |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "mat = np.array([30,60,90])\n",
    "rates = np.array([0.025,0.03,0.035])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7.\tThe implied forward 30-day bank deposit rate, 60 days into the future (i.e., the 60×90, or 60d30d, forward rate), stated on an add-on rate basis for a 360-day year, is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_60d30d = 4.48%\n"
     ]
    }
   ],
   "source": [
    "rate_t0t1 = rates[1]\n",
    "rate_t0t2 = rates[2]\n",
    "\n",
    "ifr_60d30d = ifr_mm(rate_t0t1,60,rate_t0t2,90,0,360,True)\n",
    "print(f'{ifr_60d30d = :0.2%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "8.\tAccording to Expectations Theory of the term structure of interest rates, the rate on 60-day bank deposits 30 days into the future, stated on an add-on rate basis for a 360-day year, is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_60d30d = 3.99%\n"
     ]
    }
   ],
   "source": [
    "rate_t0t1 = rates[0]\n",
    "rate_t0t2 = rates[2]\n",
    "\n",
    "ifr_60d30d = ifr_mm(rate_t0t1,30,rate_t0t2,90,0,360,True)\n",
    "print(f'{ifr_60d30d = :0.2%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Base your answers to Questions 9 and 10 on these rate data for commercial paper. The rates are quoted on a discount rate basis for a 360-day year.\n",
    "\n",
    "|   Maturity |   Rate |\n",
    "| ---------- | ------ |\n",
    "|    30 days | 4.80%  |\n",
    "|    60 days | 5.20%  |\n",
    "|    90 days | 5.60%  |\n",
    "|  180 days  | 6.00%  |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "mat = np.array([30,60,90,180])\n",
    "rates = np.array([0.048,0.052,0.056,0.06])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "9.\tThe implied forward 30-day commercial paper rate, 30 days into the future, stated on a discount rate basis for a 360-day year, is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_30d30d = 5.62%\n"
     ]
    }
   ],
   "source": [
    "rate_t0t1 = rates[0]\n",
    "rate_t0t2 = rates[1]\n",
    "\n",
    "ifr_30d30d = ifr_mm(rate_t0t1,30,rate_t0t2,60,0,360,False)\n",
    "print(f'{ifr_30d30d = :0.2%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10.\tAccording to expectations theory of the term structure of interest rates, the rate on 90-day commercial 90 days into the future, stated on a discount rate basis for a 360-day year, is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_30d30d = 6.49%\n"
     ]
    }
   ],
   "source": [
    "rate_t0t1 = rates[2]\n",
    "rate_t0t2 = rates[3]\n",
    "\n",
    "ifr_30d30d = ifr_mm(rate_t0t1,90,rate_t0t2,180,0,360,False)\n",
    "print(f'{ifr_30d30d = :0.2%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Base your answers to Questions 11 to 15 on the prices and yields for annual coupon payment benchmark government bonds. The prices are per 100 of par value and the yields to maturity are quoted as effective annual rates.\n",
    "\n",
    "| Maturity | Coupon Rate |     Price |      Yield to Maturity |\n",
    "| -------- | ----------- | --------- | ---------------------- |\n",
    "|  1 year  | 0%          | 96.4      | 3.73%                  |\n",
    "|  2 years | 4.25%       | 99.75     | 4.38%                  |\n",
    "|  3 years | 4.75%       | 100.375   | 4.61%                  |\n",
    "|  4 years | 5.00%       | 100.25    | 4.93%                  |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Yields to Maturity = [0.0373444  0.04383277 0.04613293 0.04929612]\n"
     ]
    }
   ],
   "source": [
    "years = np.arange(4) + 1\n",
    "coupon = np.array([0, 4.25, 4.75, 5])\n",
    "price = np.array([96.4, 99.75, 100.375, 100.25])\n",
    "ytm = np.vectorize(coupon_bond_ytm)(n=years, pmt=coupon, pv=price, fv=100, cf_freq=1, comp_freq=1, beg=False)\n",
    "print(\"Yields to Maturity =\", ytm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discount Factors =  [0.964      0.91753477 0.8729137  0.82359769]\n",
      "Implied Spot Rates =  [0.0373444  0.04397172 0.0463482  0.04971456]\n",
      "Par Rates =  [0.0373444  0.0438287  0.04613857 0.04930129]\n",
      "Implied Forwards Rates =  [0.0373444  0.05064138 0.0511174  0.05987876]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12539eef2f0>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RsbGx+X4cxN2Ri9uE3Rs5ciQzZszg4sWLTJ069a622b59OwBbt25l9+7dOdbHxMRgNBo5ceIEdevWzXU///77L1qt1nwRXXaFYf7eBg0aWF1uMBjo3r07X3zxBb///judOnUCMse7HT58mKeffhpfX19z+/w+nk8++SRjxozh//7v//j9999p3749TZs2pVq1anc9V/LMmTO5du2axbIuXbpQq1atu9q+ZcuWFnPgXr16lW3btvH666/TokULVq1aZT7v3bt3YzQacx1LnZ6eDmB1LGW9evVyLNPr9fj7+xMXF2deduzYMeLj42nYsCFBQUF3dQ657T9rTGv2/d9pm6xjWnu+Z82IcuHCBUJDQ83Lz58/z5QpU9i4cSPnz5/PMfbT2jhjyP15l2XlypWsX7+eihUrsnbtWkqXLp1n+/zYsmULkyZNsljWv39/unTpAmS+pgHatGmTY1sHBwdatGhBeHg4+/btM9c1YMAAvvjiC5YsWULnzp3N7ZcsWYJer6d3797mZVmvlfj4eKvPpaxxptaeS3d63B72cyFL1jn9999/Vs/pxIkTQOY5VatWrcA136sJEyaY6zOZTERHR7Nq1SpGjBjBqlWr2LVrl/nY9/I8yHK355R1jKzrCrLz9PSkVq1abN261WJ5nz59GDFiBNWqVaNnz560bNmSpk2bUrJkybt9GMQdSPAVdk+r1ZpndTAYDHe1TdbFU3cKyomJiXmuj4+Px8fHB71en2NdQEDAXdWSJTAwkKNHj+YaFh6EvGrM/sc8KwAuWbIEyAwK2eX38QwNDWXXrl1MnDiRdevW8eOPPwKZfxxGjhzJ66+/fsfaZ86cyblz5yyWlSlT5q6D7+1KlCjBE088gcFgoF27dgwbNsx83lnnt3v3bqvBPou154uXl5fVtg4ODhiNRvPPWSE+v9PuWdu/g0PmW3f2/Wfn6emZ6zZ5rcsK+JB5cWKDBg2Ii4ujefPmPPbYY3h6eqLT6QgPD2fJkiW5XuB5p9fG9u3bSU9Pp2HDhrlemJabrNdjeno6UVFRlCtXzmL9xIkTzeFnw4YNtGvXzmJ91gVIuc0Ek7U8+4euJk2aUKlSJX755Rfi4uLw9vbm33//5dChQ3Tp0sXiQ2LWc+mPP/7gjz/+yPU8rD2X7vS42eq5kHVO2S+QtOZuXx93qvl+0Gq1BAcH83//939ER0fzwQcf8P777zN//nzg3p4HWe72nLKO4e/vb/UY1n7fw4cPx9fXlzlz5vDpp58yc+ZMNBoNLVu2ZOrUqVZDt8gfmdVBFElZb+jx8fGozCE9Vv9Z+yR++35iY2Mt/ghkuXjxYr5qyuo13rhxY76202ozX6a5TcBu7Y05S169q02aNKFixYr88ssvXLt2jfT0dJYvX46vr685EGa5l8ezatWqrFixgqtXr7Jnzx4++ugjTCYTb7zxBl999dUdzzs8PDzH/u/H9GNZs2mcOHHC/Icp6/yGDRuW5/lt3rz5no+b9cfyYX7wKYjp06dz9epVvvrqK7Zs2cKnn37Ke++9x8SJE2nfvn2e296pV3/y5Mk8+eSTLFq0iBdeeMHqjBK5cXBwMP8O8/taglu/69xev1lX898eCvv160dqaiorVqwAcv+QmLXdrFmz8nwuLVq0KMex83vnyIcl65z++++/PM/p9sfCXmQ9X3bt2mVedq/Pg/zI2vbSpUtW1+d27H79+rFjxw6uXr3Kb7/9xosvvsiff/5J+/btrc5MIfJHgq8okho1agTAX3/9VaD91KlTB5PJxN9//51jXX5vJfv888+j1+v54YcfOHLkSJ5ts/ekeXt7AxAREZGj3alTp3KdQudu9O/fn5SUFFasWMFvv/3GlStX6N27d44e7oI8ng4ODtStW5c333zTPC3YqlWr7rnmgsr+VWRW4GrQoAFarbbAz5e8VKlSBS8vLw4cOJCv6fRs5dSpUwA8++yzOdbd/vVsfjk5ObFy5Uq6devG4sWL6du3b77urPXSSy8BMG3aNJKSkvJ17Kxp/Ky9fjMyMszPgTp16lis69evH1qtliVLllh8SMw+9AHu33uPPXlY56TT6R5IL3DWaz77B6x7fR7kR9a21l4v8fHx7N+/P8/tvby86NSpE1988QUDBgwgNjaWP//8857rEZkk+IoiaciQIej1eoYNG2Yef5ZdWlraXb2JP//88wCMHTuWlJQU8/LY2Fjef//9fNWUdUOFtLQ0OnfunOud2datW0fHjh3NP1epUgUPDw9+/vlnYmJizMuTk5PvashAXrL+mH/99dd8/fXXAFZ7VfP7eO7du9dqIM/q+XBxcSlQ3QWRdSvsmjVrmj9U+Pn50adPH/bs2cN7771n9Y/v6dOnOXv27D0fV6fTMXjwYJKTkxk0aFCOYQJpaWl21ZuTNTf07cHg999/58svvyzw/vV6PcuXL6dv374sX76cHj16WP1mxZq+ffvStm1bjh8/zhNPPJHrbYmtfRvSpUsXfHx8WL58OTt27LBYN3PmTM6ePcujjz6aY1xnSEgIbdq0YceOHcyaNYvLly9b/ZBYr149mjdvzo8//sjChQut1nXw4EGL17K9e/755/Hy8mLSpEkWvaZZTCZTvjsCrClRogSXL1/OdR7he5Gammqe/zb7dRn3+jzIj6eeegpvb2++/fbbHO/3EydOtPoeuXnzZvMcy9llPV9s+d5ZVMgYX1EkValShYULF/LCCy9QvXp1OnToQKVKlUhPT+f8+fP89ddflCxZMs9JxAF69erFihUr+OWXXwgLC+Opp54iPT2dlStXUr9+fU6fPp2vusaMGUNGRgaTJk2ifv36NGnShHr16plvWfznn39y8uRJi3Fcer2eN954g/fee4/atWvz9NNPk5GRwR9//EFQUFC+LpS6XUhICK1bt2bjxo04ODhQo0YNqze2yO/juXTpUubPn0+zZs0oX7483t7enD59ml9//RUnJyeGDh16zzXfrawbhmSJjY1l27Zt7N27F4PBwOeff27R/vPPP+fkyZOMHz+epUuX0qxZM/z9/YmKiuLo0aPs3r2b5cuXU7Zs2XuuacKECezcuZNff/2VSpUq8fjjj+Pu7k5ERATr169n6tSpdnM3ucGDB7No0SK6detG165dCQoK4tChQ6xbt47u3bubv/IvCJ1Ox5IlS3B2dubLL7/kmWeeYeXKlRZ3asxtux9//JF+/frx888/U65cOVq2bElYWBguLi5cvnyZw4cPs23bNhwdHS1uFuPm5sbChQvp1q0bLVu2pFu3bpQuXZq9e/eyfv16AgICzONAb9e/f382bNjAmDFjzD9b8+2339KmTRtefPFFPv30Uxo2bIiXlxcXLlzgwIEDHDp0iO3bt+Pn53ePj9zDVaJECVauXMnTTz9No0aNaNu2LdWrV0ej0RAREcH27du5evWqRefAvWjbti27d++mQ4cOtGjRAicnJx555BGeeOKJu9p+y5Yt5te8Uoro6GjWrl3LhQsXKFeuHGPHjjW3Lcjz4G65ubmxYMECevToQfPmzenRoweBgYH8/fffHDp0iBYtWuTowX366adxc3OjUaNGlClTBqUUf/31F7t376Zu3bo8+uijBapJcNvcTULYqdDQ0BzTvmTJ7QYWSil14MAB1b9/f1W6dGnl6OiovL29VfXq1dUrr7yiNm7caNHW2nRmSmXOWzpp0iRVtmxZ5ejoqEJDQ9WYMWNUSkpKvqYzy+7IkSNqyJAhqnr16srd3V3p9XoVEBCgOnTooL788sscc7yaTCb14YcfqnLlyim9Xq9CQkLUqFGj1I0bN/Kczuz2+WWtWbp0qXnqn6wbDeTmbh/PHTt2qEGDBqmaNWsqb29v5ezsrMqXL68GDBjwQG9eoVTu05k5OjqqsmXLqhdffDHHjSWypKamqs8++0w1btxYeXh4KEdHRxUSEqLatGmjZsyYoa5cuZLjOPmZZk6pzKmSPvvsM1W/fn3l6uqqXFxcVIUKFdTLL7+sTp48aW6XNUXT5s2bc+zj7NmzClD9+/e3WJ7bc1ipvF8nuR3rn3/+Ua1bt1ZeXl7Kzc1NNW3aVP3000+5nntex1cq9+elyWRSQ4YMUYB67LHH8jXP84YNG9Rzzz2nypcvr1xcXJRer1d+fn6qdevW6oMPPsgxjVWWXbt2qS5duihfX1/za2rQoEF5TjV348YN5eHhoQAVFhaWZ10JCQnqgw8+UHXq1FGurq7K2dlZlSlTRnXq1EnNnz9fJSYm3vFxudv11t6H7uX3fadjnT171jwftpOTk3J3d1eVK1dWffv2zXGjibyOn9vzJzExUQ0aNEgFBwcrnU5n9TluTW7Tmbm4uKiaNWuqsWPHWsxrnV1+ngf3ck5KKbV+/XrVtGlTZTAYlJeXl3ryySfV0aNHre5v7ty5qkuXLqps2bLKYDAob29vVatWLTVlyhSL6TfFvdMoZaVPXQghhBBCiCJGxvgKIYQQQohiQYKvEEIIIYQoFiT4CiGEEEKIYkGCrxBCCCGEKBYk+AohhBBCiGJBgq8QQgghhCgWJPgKIYQQQohiQe7cZkPXrl1j69athISE3PFORUIIIYQQwlJqaioRERG0bNkSLy+vO7aX4GtDW7dupUuXLrYuQwghhBCiUFu1ahVPPfXUHdtJ8LWhkJAQIPOXVaFCBRtXI4QQQghRuJw6dYouXbqYM9WdSPC1oazhDRUqVKB69eo2rkYIIYQQonC62yGjcnGbEEIIIYQoFiT4CiGEEEKIYkGCrxBCCCGEKBYk+AohhBBCiGJBLm6zcxkZGcTFxZGYmIhSytbliEJOo9Hg5OSEh4cHrq6uaDQaW5ckhBBCPDQSfO2YUooLFy6QnJyMTqfDwUF+XaJgjEYj8fHxxMfH4+Pjg5+fn4RfIYQQxYYkKTt2/fp1kpOT8fT0JDAwUAKKuC/S0tKIjo4mNjYWV1dX3NzcbF2SEEII8VDIGF87lpCQACC9cuK+cnR0JDAwELj1HBNCCCGKAwm+diw9PR0HBwcZ4iDuO0dHR/R6PampqbYuRQghhHhoJPjaMaUUWq38isSDodFo5IJJIYQQxYpdp6rU1FTefPNNgoKCMBgMNGzYkD/++OOuto2MjKR79+54eXnh4eHBU089xZkzZ6y2vXTpEgMHDiQ4OBhnZ2fKlCnDiy++WKB93i8yxEE8KPLcEkIIUdzY9XfoAwYMYOXKlQwdOpSKFSuyePFiOnXqxObNm2nWrFmu2yUmJtK6dWvi4+MZM2YMer2eGTNm0LJlS/bv30+JEiXMbSMiImjatCkAgwYNIjg4mKioKHbt2nXP+xRCCCGEEPbHboPvrl27+O6775g6dSojR44EoF+/foSFhTF69Gi2bduW67Zz5szh5MmT7Nq1i/r16wPQsWNHwsLCmDZtGpMnTza3HThwIA4ODuzevTvP8JqffQohhBBCCPtjt0MdVq5ciU6n45VXXjEvc3Z25sUXX2T79u1ERETkuW39+vXNARWgSpUqtG3blv/973/mZceOHWPt2rWMGjWKEiVKkJKSQnp6eoH2KYQQQggh7JPdBt99+/ZRqVIlPDw8LJY3aNAAgP3791vdzmQyceDAAerVq5djXYMGDTh9+jTXr18HYMOGDQD4+/vTtm1bDAYDBoOBjh07Eh4efk/7zE1MTAyHDx+2+Hfq1Kk8tynKOnbsiLe3N5cuXcqxLj4+nsDAQPz9/dFoNHf8t3jxYgDzzy+99JLVY44dO9bc5sqVKw/y9IQQQghhh+x2qEN0dLR5rtHsspZFRUVZ3S42NpbU1NQ7blu5cmVOnjwJwCuvvEL9+vVZsWIF58+fZ9KkSTz66KMcOHAAFxeXfO0zN3PmzGHSpEl3OOviY86cOYSFhTFs2DC+/fZbi3VjxozhypUrvPPOO5QvX968fM2aNSxfvpwZM2bg6+trXt6kSRPz/zs7O/PDDz8wZ84cHB0dLfa7fPlynJ2dSUlJeUBnJYQQQoiU4ydwDC2N1tnZ1qXkYLfBNzk5GScnpxzLnW8+iMnJybluB9zVtomJiQAEBATw22+/macOK1WqFL169eLbb7/lpZdeytc+czN48GC6detmsezUqVN06dIlz+2KqrJlyzJhwgTefPNNBgwYwGOPPQbA7t27mTdvHiNHjmTChAkW21y8eJHly5fTpUsXypQpY3W/HTp04JdffmHt2rU89dRT5uXbtm3j7NmzPPvss/zwww8P7LyEEEKI4uz6ps1EjhiBW7NmBM+cgUans3VJFux2qIPBYLA6uX5Wb53BYMh1O+Cuts36b/fu3S3my+3WrRsODg7mC+jys8/c+Pn5Ub16dYt/FSpUyHObom748OHUrFmTwYMHk5KSgtFoZNCgQYSGhuYIvXcrODiYFi1a5OhFXrZsGTVq1CAsLOx+lC6EEEKI28QuW8aFIUNQyclc37iR5H37bF1SDnbb4xsYGEhkZGSO5dHR0QAEBQVZ3c7HxwcnJydzu7y2zfqvv7+/RTudTkeJEiWIi4vL9z7F3XNwcGDBggU0adKE9957Dz8/P/7991/WrVuHi4vLPe+3d+/evPHGGyQmJuLm5kZGRgbff/89w4cPl2EOQgghxH2mTCZipn5C7KJFAGgMBoKnfYKLlWujbM1ug2+tWrXYvHkzCQkJFhe47dy507zeGq1WS40aNdizZ0+OdTt37qRcuXK4u7sDULduXYAcATstLY0rV65QsmTJfO/zYZn062GORCU81GPmplqQBxOeqH5P2zZs2JDBgwczdepUnJyc6NWrF+3bty9QPV27dmXIkCGsWrWKvn37sn79eq5cuUKvXr1YdPNFKYQQQoiCM6WkEDX6Ta6vXw+AzteXkLlzMdSwz29Y7Tb4du3alU8++YQFCxaY5/FNTU1l0aJFNGzYkJCQEADOnz9PUlISVapUsdj2rbfeYs+ePeaZGI4fP86mTZvM+wJo1aoVfn5+LFu2jDFjxpjH6y5evBij0Ui7du3yvc+H5UhUAjvPxj704z4IH3zwAStXriQpKYkZM2YUeH/e3t506NCB5cuX07dvX7799luaNGlCaGjofahWCCGEEAAZsbFceHUwyf/9B4Bj+fKEzJ+PY6lgG1eWO7sNvg0bNqRbt268/fbbxMTEUKFCBZYsWUJ4eDhfffWVuV2/fv3YunUrSinzssGDB/PFF1/QuXNnRo4ciV6vZ/r06fj7+zNixAhzOycnJ6ZOnUr//v1p0aIFzz33HOfPn2fWrFk0b96cZ555Jt/7fFiqBXncudFDUtBaPDw8qFy5MleuXMkx7ORe9e7d2/z7XLVqFR9//PF92a8QQgghIPXsWSIGDiL9/HkAXBo0oNRnn6Lz9LRxZXmz2+AL8PXXXzNu3DiWLl1KXFwcNWvWZPXq1bRo0SLP7dzd3dmyZQvDhg3j/fffx2Qy0apVK2bMmGEevpClX79+ODo68tFHHzFq1Ci8vLwYOHAgkydPRpftSsT87PNhuNehBcXFk08+iZOTE/379yc1NZXu3bvbuiQhhBCiSEjau5cLg/8PY3w8AJ5PPUnge++huW0aUXtk18HX2dmZqVOnMnXq1FzbbNmyxeryUqVK8f3339/VcXr27EnPnj3v2C4/+xS2ZTAY6NKlC9988w0dO3a0mPdXCCGEEPcmYc0aot56G5WWBoDv4MH4vjYEjUZj48rujl0HXyEKYuTIkZQvX77AF8sJIYQQxZ1SiqtffsnladMzFzg4EDhpEl7PPpP3hnZGgq8osh555BEeeeQRW5chhBBCFGoqI4OL773PtRUrANC6uVHq01m4ZrtzamEhwVcIIYQQQlhlTLxB5PBh3PjzLwAcAgMJmTcP58qVbFzZvdGo7NMhiIfq8OHDhIWFcejQIapXz3mx2pkzZwAoV67cwy5NFAPy/BJCCJGX9EuXiBj0KqlHjwLgVK0qIXPnoff3s3Flt9wpS93Obm9ZLIQQQgghbCPl+AnCe/Q0h17Xli0os3SpXYXeeyHBVwghhBBCmCX+8w/nevcm4+JFALx69iBk9my0rq42rqzgZIyvEEIIIYQA4NoPPxA9YSJkZADgN3IEPi++WGimK7sTCb5CCCGEEMWcUorLn37K1bnzANA4OhI05SM8Ona0cWX3lwRfIYQQQohizJSWRvTYd0j49VcAdF5elJozG5c6dWxc2f0nwVcIIYQQopgyxsdz4bXXSdq1CwB96dKUXjAfxzJlbFvYAyLBVwghhBCiGEq7cIGIVwaSdnN6S0OtWpSaMxsHHx8bV/bgyKwOQgghhBDFTPLBg4T36GkOve7t21N68aIiHXpBgq8QQgghRLFyfeNGzj3XD+PVqwD4vPgCwTOmo3V2tnFlD54MdRBCCCGEKCZil37DpcmTQSnQavF/Zyw+vXvbuqyHRoKvEEIIIUQRp4xGYj7+mNglXwOgMRgInj4N99atbVzZwyXBVwghhBCiCDMlJxM1ejTX/9gAgK6kLyFz52EIq27jyh4+GeMrbObgwYN07dqV0NBQnJ2dCQ4Opl27dnz22WcP9LhHjhxh4sSJhIeH52u7/fv307dvX0JCQnBycsLHx4dHH32URYsWYTQaH0yxQgghRAFkXL3Kuf4DzKHXqWIFyn73XbEMvSA9vsJGtm3bRuvWrSldujQvv/wyAQEBREREsGPHDmbNmsVrr732wI595MgRJk2aRKtWrShzl/MUfvnllwwaNAh/f3+ee+45KlasyPXr19m4cSMvvvgi0dHRjBkz5oHVLIQQQuRX6pmzRLzyCukXLgDg0qgRpT6dhc7Dw8aV2Y4EX2ETH3zwAZ6enuzevRsvLy+LdTExMbYpKhc7duxg0KBBNG7cmDVr1uDu7m5eN3ToUPbs2cOhQ4fuy7Fu3LiBq6vrfdmXEEKI4itp924ihryGKT4eAM8uXQh8dxIaR0cbV2ZbMtRB2MTp06epXr16jtAL4OfnZ/GzRqNhyJAhLFu2jMqVK+Ps7EzdunX5888/c2y7b98+OnbsiIeHB25ubrRt25YdO3aY1y9evJhu3boB0Lp1azQaDRqNhi1btuRa66RJk9BoNCxbtswi9GapV68eAwYMAGDLli1W9xceHo5Go2Hx4sXmZQMGDMDNzY3Tp0/TqVMn3N3d6dOnD0OGDMHNzY2kpKQcx+rVqxcBAQEWQyvWrl1L8+bNcXV1xd3dnc6dO3P48OFcz0cIIUTRFr/6N86/8KI59PoOGULgh5OLfegFCb7CRkJDQ9m7d+9d95Ru3bqVoUOH0rdvX959912uXr1Khw4dLLY/fPgwzZs357///mP06NGMGzeOs2fP0qpVK3bu3AlAixYteP311wEYM2YMS5cuZenSpVStWtXqcZOSkti4cSMtWrSgdOnSBTzrnDIyMmjfvj1+fn588sknPPvss/To0YMbN27w22+/5ajl119/pWvXruh0OgCWLl1K586dcXNzY8qUKYwbN44jR47QrFmzfI9hFkIIUbgppbgyfwFRI0ei0tPBwYHADz+k5JD/Q6PR2Lo8uyBDHYRNjBw5ko4dO1KrVi0aNGhA8+bNadu2La1bt0av1+dof+jQIfbs2UPdunUB6NmzJ5UrV2b8+PH8+OOPALzzzjukp6fz999/U65cOQD69etH5cqVGT16NFu3bqVcuXI0b96cTz/9lHbt2tGqVas86zx16hTp6enUqFHj/j4AN6WmptKtWzc+/PBD8zKlFMHBwaxYscLcOw3w22+/cePGDXr06AFAYmIir7/+Oi+99BILFiwwt+vfvz+VK1dm8uTJFsuFEEIUXSo9nYvvvsu171cCoHV3p9Rnn+LaqJGNK7MvEnwLq7VvwcWDtq4iU0AN6PhRvjZp164d27dv58MPP+T3339n+/btfPzxx5QsWZIvv/ySJ5980qJ948aNzaEXoHTp0jz11FP8+uuv5q/9169fT5cuXcyhFyAwMJDevXvzxRdfkJCQgEc+B/QnJCQAWB3icL+8+uqrFj9rNBq6devG/PnzSUxMxM3NDYAVK1YQHBxMs2bNAPjjjz+4du0avXr14sqVK+btdTodDRs2ZPPmzQ+sZiGEEPbDmJhI5NBh3Pj7bwAcggIpPX8+ThUr2rgy+yPBt7C6eBDO/W3rKgqkfv36/Pjjj6SlpfHff//x008/MWPGDLp27cr+/fupVq2auW1FKy/eSpUqkZSUxOXLl4HMoQCVK1fO0a5q1aqYTCYiIiKoXj1/07dkBeXr16/na7u75eDgQKlSpXIs79GjBzNnzuSXX36hd+/eJCYmsmbNGgYOHGj+uurkyZMAtGnTJs/ahRBCFF3pFy8SMXAQqcePA+BcrRql5s1Ff9v1MiKTBN/CKuDBfPV+TwpYi6OjI/Xr16d+/fpUqlSJ559/nu+//54JEybcpwLvXYUKFXBwcODgwbvrXc9tDFVu8/w6OTmh1eYcat+oUSPKlCnD//73P3r37s2vv/5KcnKyeZgDgMlkAjLH+QYEBOTYh4ODvLyFEKIoSzl2jIiBg8i4dAkAt1atCJ72CVqZHShX8pexsMrn0ILCol69egBER0dbLM/q3czuxIkTuLi4ULJkSQBcXFw4fvMTb3bHjh1Dq9USEhIC5B5OrXFxcaFNmzZs2rSJiIgI8z5y4+3tDcC1a9cslp87d+6uj5mle/fuzJo1i4SEBFasWEGZMmVolG2sVvny5YHMWTAeffTRfO9fCCFE4ZX4199EDh2K6cYNALx798J/zBg00umRJ5nVQdjE5s2bUUrlWL5mzRqAHEMWtm/fzr///mv+OSIigp9//pnHHnsMnU6HTqfjscce4+eff7aYzeDSpUt8++23NGvWzPzVf9Y8ubeH09xMmDABpRTPPfcciYmJOdbv3buXJUuWAJmzVeh0uhxTrc2ZM+eujpVdjx49SE1NZcmSJaxbt47u3btbrG/fvj0eHh5MnjyZ9PT0HNtnDQERQghRtMR9/z0RgwaZQ6/f6NH4jxsnofcuyCMkbOK1114jKSmJp59+mipVqpCWlsa2bdvMPZvPP/+8RfuwsDDat2/P66+/jpOTkzlITpo0ydzm/fff548//qBZs2YMHjwYBwcH5s+fT2pqKh9//LG5Xa1atdDpdEyZMoX4+HicnJxo06ZNjvmDszRp0oTZs2czePBgqlSpYnHnti1btvDLL7/w/vvvA+Dp6Um3bt347LPP0Gg0lC9fntWrV9/TTTnq1KlDhQoVGDt2LKmpqRbDHCBzDO/cuXN57rnnqFOnDj179qRkyZKcP3+e3377jaZNm/L555/n+7hCCCHsk1KKyzNncXX+fAA0Tk4ETZmCR4f2Nq6sEFHCZg4dOqQAdejQIavrT58+rU6fPv2Qq3o41q5dq1544QVVpUoV5ebmphwdHVWFChXUa6+9pi5dumTRFlD/93//p7755htVsWJF5eTkpGrXrq02b96cY7///vuvat++vXJzc1MuLi6qdevWatu2bTnaffHFF6pcuXJKp9MpwOq+brd3717Vu3dvFRQUpPR6vfL29lZt27ZVS5YsUUaj0dzu8uXL6tlnn1UuLi7K29tbDRw40Py7XrRokbld//79laura57HHDt2rAJUhQoVcm2zefNm1b59e+Xp6amcnZ1V+fLl1YABA9SePXvy3HdRfn4JIURRY0xNVRdGjFRHKldRRypXUccbNVY3/v3X1mXZ3J2y1O00Sln5vlk8FIcPHyYsLIxDhw5ZnW3gzJkzABbTcxVHGo2G//u//5Pey/tMnl9CCFE4GK9dI2LIEJL37AXAMTSUkAXzcQwNtXFltnenLHU7GeoghBBCCGGn0iIiiHhlIGlnzwJgqFOHUrM/x+HmxdQif+TiNiGEEEIIO5T833+E9+hpDr3uHTtQetFCCb0FID2+QgghhBB2JuGPP4gaNRqVkgJAiZdepOTw4WiszP0u7p4EX2H3ZBi6EEKI4iR2yRIufTQFlAKtloDx4/Du2dPWZRUJEnyFEEIIIeyAMhq59NEU4pYuBUDj4kKpGdNxa9nSxpUVHRJ8hRBCCCFszJSUROSo0SRu3AiAQ8mShMyfh3O1ajaurGiR4CuEEEIIYUMZV64Q8epgUg4eBMCpYkVCFsxHHxho48qKHgm+QgghhBA2knr6NBGvDCQ9MhIA1yaNCZ41C527u40rK5rk0kAhhBBCCBu4sWsX4b16m0Ov5zPPEDJ/voTeB0h6fIUQQgghHrL4X38lasxYSE8HoOQbr1Ni0CA0Go2NKyvaJPgKIYQQQjwkSimuzpvH5VmfZi7Q6wn64H08n3zStoUVExJ8hRBCCCEeApWeTvTEicT/8CMAWg8PSn32Ga4NG9i4suJDgq8QQgghxANmvH6dyDeGcmPbNgD0QUGELJiPU4UKNq6seJGL24RNLF68GI1GY/7n7OxMpUqVGDJkCJcuXXpodfz000907NgRX19fHB0dCQoKonv37mzatOmh1SCEEKJoS4+O5lyfvubQ6xwWRpkV30notQHp8RU29e6771K2bFlSUlL4+++/mTt3LmvWrOHQoUO4uLg8sOMqpXjhhRdYvHgxtWvXZvjw4QQEBBAdHc1PP/1E27Zt+eeff2jSpMkDq0EIIUTRl3L0KBEDB5EREwOAW5s2BH8yFe0D/BsncifBV9hUx44dqVevHgAvvfQSJUqUYPr06fz888/06tXrnvdrMplIS0vD2dnZ6vpp06axePFihg4dyvTp0y2uoh07dixLly7FwaHgLw+lFCkpKRgMhgLvSwghROGS+OefRA4dhikpCQDvvn3xf/stNDqdjSsrvmSog7Arbdq0AeDs2bMAfPLJJzRp0oQSJUpgMBioW7cuK1euzLGdRqNhyJAhLFu2jOrVq+Pk5MS6deusHiM5OZkPP/yQKlWq8Mknn1idOua5556jQYPMiw0mTpxotU3WcI3w8HDzsjJlyvD444/z+++/U69ePQwGA/PnzycsLIzWrVvn2IfJZCI4OJiuXbtaLJs5cybVq1fH2dkZf39/Bg4cSFxcXB6PnBBCCHsSt+J/RLw6ODP0ajT4v/0W/mPHSOi1MQm+wq6cPn0agBIlSgAwa9YsateuzbvvvsvkyZNxcHCgW7du/Pbbbzm23bRpE8OGDaNHjx7MmjWLMmXKWD3G33//TWxsLL1790b3AN6Ajh8/Tq9evWjXrh2zZs2iVq1a9OjRgz///JOLFy/mqCUqKoqePXualw0cOJBRo0bRtGlTZs2axfPPP8+yZcto37496TfnexRCCGGflMlEzLRpXJwwAYxGNE5OBM+aiU///jJHrx2QoQ6F1JRdUzgWe8zWZQBQxacKbzZ48562jY+P58qVK6SkpPDPP//w7rvvYjAYePzxxwE4ceKExTCBIUOGUKdOHaZPn07nzp0t9nX8+HEOHjxItWrV8jzm0aNHAahRo8Y91Xwnp06dYt26dbRv3968LCgoiPHjx7Ny5UqGDBliXr5ixQrc3NzM5/L333/z5ZdfsmzZMnr37m1u17p1azp06MD3339vsVwIIYT9MKWmEv322ySsWQuAzseHkLlzMDzyiI0rE1kk+BZSx2KPsefSHluXUWCPPvqoxc+hoaEsW7aM4OBgAIvQGxcXh9FopHnz5ixfvjzHvlq2bHnH0AuQkJAAgPsDuiVk2bJlLUIvQKVKlahVqxYrVqwwB1+j0cjKlSt54oknzOf5/fff4+npSbt27bhy5Yp5+7p16+Lm5sbmzZsl+AohhB3KiIvjwpDXSN67FwDHMmUIWTAfx9KlbVyZyE6CbyFVxaeKrUswK0gts2fPplKlSjg4OODv70/lypXRam+NwFm9ejXvv/8++/fvJzU11bzc2tdFZcuWvatjenh4AHD9+vV7rjsvudXRo0cPxowZQ2RkJMHBwWzZsoWYmBh69OhhbnPy5Eni4+Px8/Ozuo+Ym1cFCyGEsB9p588T8fIrpJ07B4ChXl1CPv8cnZeXbQsTOUjwLaTudWiBvWnQoIF5Vofb/fXXXzz55JO0aNGCOXPmEBgYiF6vZ9GiRXz77bc52t/tzAlVqmQG9YMHD9KlS5c7ts9tTJbRaLS6PLc6evTowdtvv83333/P0KFD+d///oenpycdOnQwtzGZTPj5+bFs2TKr+yhZsuQd6xVCCPHwJO/fT8SrgzHevADZo1MnAj+cjNbJycaVCWsk+Aq79cMPP+Ds7Mzvv/+OU7Y3kEWLFhVov82aNcPb25vly5czZsyYO17g5u3tDcC1a9fwyvbp/dzNT/Z3q2zZsjRo0MA83OHHH3+kS5cuFudWvnx5NmzYQNOmTWUKNCGEsHMJv68navRo1M1vJEu88golh76BRitzB9gr+c0Iu6XT6dBoNBY9q+Hh4axatapA+3VxceHNN9/k6NGjvPnmmyilcrT55ptv2LVrF5AZRgH+/PNP8/obN26wZMmSfB+7R48e7Nixg4ULF3LlyhWLYQ4A3bt3x2g08t577+XYNiMjg2vXruX7mEIIIe4vpRRXFy0mcujQzNCr0xHw7iT8hg+T0GvnpMdX2K3OnTszffp0OnToQO/evYmJiWH27NlUqFCBAwcOFGjfo0aN4vDhw0ybNo3NmzfTtWtXAgICuHjxIqtWrWLXrl1su3lryccee4zSpUvz4osvMmrUKHQ6HQsXLqRkyZKcP38+X8ft3r07I0eOZOTIkfj4+OS4uK9ly5YMHDiQDz/8kP379/PYY4+h1+s5efIk33//PbNmzbKY81cIIcTDpYxGLk3+kLibQ9K0Li4Ez5qJW/PmNq5M3A0JvsJutWnThq+++oqPPvqIoUOHUrZsWaZMmUJ4eHiBg69Wq+Xrr7/mqaeeYsGCBXzyySckJCRQsmRJWrRowccff0zjxo0B0Ov1/PTTTwwePJhx48YREBDA0KFD8fb25vnnn8/XcUuVKkWTJk34559/eOmll9Dr9TnazJs3j7p16zJ//nzGjBmDg4MDZcqUoW/fvjRt2rRA5y2EEOLemZKSiBwxksTNmwFw8PcnZP48nKvYzwXnIm8aZe17XvFQHD58mLCwMA4dOkT16tVzrD9z5gwA5cqVe9iliWJAnl9CCHH3Mi5fJmLQq6QcPgyAU+XKhMyfhz4gwMaVFW93ylK3k4EoQgghhBB5SD15kvAePc2h17VpU0KXfSOhtxCS4CuEEEIIkYsbO3YS3rsP6VFRAHh2fZaQeXPRubnZuDJxL2SMrxBCCCGEFddWrSJ63HhITweg5NChlBj4Sq7zuwv7J8FXCCGEECIbpRRX5szhymefA6DR6wmcPBnPJx63cWWioCT4CiGEEELcpNLSiJ4wkfiffgJA6+lJyOef4VK/vo0rE/eDBF8hhBBCCMB4/ToXXn+dpO07ANCXKkXIgvk4yew3RYYEXyGEEEIUe+lRUUQMHEjqyVMAONesScic2Tj4+tq4MnE/yawOQgghhCjWkg8f5myPHubQ6/ZoW0KXLJbQWwRJ8BVCCCFEsXV9yxbOPdcP4+UrAHj3e45Ss2ahNRhsXJl4EGSogxBCCCGKpbjly7n43vtgMoFGg//bb+HTr5+tyxIPkARfIYQQQhQrymQiZto0Yr9aCIDG2ZngT6bi/uijNq5MPGgSfIUQQghRbJhSUoh6622ur1sHgK5ECULmzsFQs6aNKxMPg4zxFTazePFiNBoNe/bsAWDixIloNBqr/+bNm2fe7vZ1Hh4etGzZkt9++81WpyKEEKIQyIiL4/zzL5hDr2PZspRZ8Z2E3mJEenyF3Zk7dy5ut90DvWHDhhY/t2vXjn79+qGU4ty5c8ydO5cnnniCtWvX0r59+4dZrhBCiEIgLTyc8wMHkn7uPAAu9etT6rNP0Xl52bYw8VBJ8BV2p2vXrvjeYQqZSpUq0bdvX/PPzz77LNWqVWPWrFkSfIUQQlhI+ncfFwYPxnjtGgAejz9O4OQP0Do62rYw8dBJ8BVFQtWqVfH19eX06dO2LkUIIYQdSVi3jqjRb6LS0gAo8eogSr7+OhqNxsaVCVuQ4CvsTmxsrMXPOp0Ob2/vPLeJj48nLi6O8uXLP8jShBBCFBJKKWIXLiRm6ieZC3Q6AidNxKtrV9sWJmxKgm8hdXHyZFKPHrN1GQA4Va1CwJgx921/lStXtvg5NDSU8PBwi2UpKSlcuXIFpRTnz5/nnXfewWg00lXe0IQQothTGRlc/OADri3/DgCtqyvBs2bh1qypjSsTtmbXwTc1NZXx48ezdOlS4uLiqFmzJu+//z7t2rW747aRkZEMGzaM9evXYzKZaN26NTNmzKBcuXIW7XL7quPDDz/krbfeMv88ceJEJk2alKOdk5MTKSkp+Tyzgks9eoyk3bsf+nEfhh9++AEPDw/zzwYrd8/56quv+Oqrr8w/6/V6Ro8ezfDhwx9KjUIIIeyT6cYNIoePIHHrVgAcAgIImT8P59s6VUTxZNfBd8CAAaxcuZKhQ4dSsWJFFi9eTKdOndi8eTPNmjXLdbvExERat25NfHw8Y8aMQa/XM2PGDFq2bMn+/fspUaKERfusGQKyq127ttV93z7jgE6nK8AZ3junqlVsclxr7nctLVq0uOPFbU899RRDhgwhLS2N3bt3M3nyZJKSktBqZYY+IYQortIvxRDx6iBSjxwFwKlKFULmz0Pv72/jyoS9sNvgu2vXLr777jumTp3KyJEjAejXrx9hYWGMHj2abdu25brtnDlzOHnyJLt27aJ+/foAdOzYkbCwMKZNm8bkyZMt2t8+Q0Be7mbGgYfhfg4tKIxKlSrFozfvsNOpUyd8fX0ZMmQIrVu35plnnrFxdUIIIR62lBMniBg4iIzoaABcmzcneMYMdG6uNq5M2BO77R5buXIlOp2OV155xbzM2dmZF198ke3btxMREZHntvXr1zeHXoAqVarQtm1b/ve//1ndJjk5+a6GLCilSEhIQCmVj7MRD9rAgQMpX74877zzjvxuhBCimLmxfTvnevcxh16v7t0JmTtHQq/IwW6D7759+6hUqZLFWE+ABg0aALB//36r25lMJg4cOEC9evVyrGvQoAGnT5/m+vXrFssXL16Mq6srBoOBatWq8e233+ZaV7ly5fD09MTd3Z2+ffty6dKlfJ6ZeBAcHBwYMWIER48e5eeff7Z1OUIIIR6Saz+t4vzLr2BKTASg5IjhBEyaiMbBbr/UFjZkt8+K6OhoAgMDcyzPWhYVFWV1u9jYWFJTU++4bdbMAU2aNKF79+6ULVuWqKgoZs+eTZ8+fYiPj+fVV181b+vt7c2QIUNo3LgxTk5O/PXXX8yePZtdu3axZ8+eHAH9djExMVy+fNli2alTp/LcRuTPgAEDGD9+PFOmTKFLly62LkcIIcQDpJTiyuezuTJ7NgAavZ7Ajz7Es3NnG1cm7JndBt/k5GScnJxyLHd2djavz2074K63/eeffyzavPDCC9StW5cxY8YwYMAA84wCb7zxhkW7Z599lgYNGtCnTx/mzJljMQOENXPmzLE6K4S4fwwGA0OGDGHixIls2bKFVq1a2bokIYQQD4BKSyN63Hjib37Dp/P0pNTsz3Gx8m2vENnZ7VAHg8FAampqjuVZ43CtTXGVffm9bAvg6OjIkCFDuHbtGnv37s2zxt69exMQEMCGDRvybAcwePBgDh06ZPFv1apVd9yuKBswYABKKfOwlIkTJ6KUuuPFg0opPv/8c6vrJkyYgFJKQq8QQhRRxoQEzr/8ijn06kNCCF2+XEKvuCt22+MbGBhIZGRkjuXRNweuBwUFWd3Ox8cHJycnc7v8bJslJCQEyHkHsdza3k07Pz8//Pz87thOCCGEENalXYgkYtBA0k5l3p7e+ZGahMyZg8Nt05QKkRu77fGtVasWJ06cICEhwWL5zp07zeut0Wq11KhRgz179uRYt3PnTsqVK4e7u3uexz5z5gwAJUuWzLOdUorw8PA7thNCCCFEwSQfPER4z57m0Overh2hS5ZI6BX5YrfBt2vXrhiNRhYsWGBelpqayqJFi2jYsKG5V/b8+fMcO3Ysx7a7d++2CL/Hjx9n06ZNdOvWzbzs9ovNAK5fv87MmTPx9fWlbt26ebadO3culy9fpkOHDvd+okIIIYTI0/VNmznXrx/GK1cA8BkwgOCZM9DevHZHiLtlt0MdGjZsSLdu3Xj77beJiYmhQoUKLFmyhPDwcItb1fbr14+tW7dazN06ePBgvvjiCzp37szIkSPR6/VMnz4df39/RowYYW43e/ZsVq1axRNPPEHp0qWJjo5m4cKFnD9/nqVLl+Lo6GhuGxoaSo8ePahRowbOzs78/ffffPfdd9SqVYuBAwc+nAdFCCGEKGZily3j0geTwWQCrRb/MWPw6dvH1mWJQspugy/A119/zbhx41i6dClxcXHUrFmT1atX06JFizy3c3d3Z8uWLQwbNoz3338fk8lEq1atmDFjhsWwhKZNm7Jt2za+/PJLrl69iqurKw0aNGDhwoW0adPGYp99+vRh27Zt/PDDD6SkpBAaGsro0aMZO3YsLi4uD+T8AbkZg3hglFJoNBpblyGEEFYpk4mYqZ8Qu2gRABqDgeBpn+B+299nIfJDoyRZ2czhw4cJCwvj0KFDVK9ePcf6s2fPkpGRQcWKFW1QnSjqTp06hU6no2zZsrYuRQghLJhSUoga/SbX168HQOfrS8jcuRhqhNm4MmFv7pSlbmfXPb7FnV6vJyUlhYyMDBzkDjTiPkpLSyM9Pf2BflshhBD3IiM2lguvDib5v/8AcCxfnpD583EsFWzjykRRYLcXtwnMd4OLiYmRIQ/ivklLSzNP7XenOw4KIcTDlHr2LOE9e5lDr0uDBpT5dpmEXnHfSDeiHXN3d8fFxYX4+HgSExPR6XQyJlPcM6UUSinS09OBzDmvXV1dbVyVEEJkStq7lwuD/w9jfDwAnk89SeB776HJdqG5EAUlwdeOaTQagoODiYuLIzExUXp9RYFoNBq0Wi0uLi54eHjg6uoqH6SEEHYhYc0aot56G5WWBoDv4MH4vjZE3qPEfSfB1845ODhQsmRJuUmGEEKIIkcpxdUvv+TytOmZCxwcCJw0Ca9nn7FtYaLIkuArhBBCiIdOZWRw8b33ubZiBQBaNzdKfToL1yZNbFyZKMok+AohhBDioTIm3iBy+DBu/PkXAA6BgYTMm4dz5Uo2rkwUdRJ8hRBCCPHQpF+6RMSgV0k9ehQAp2pVCZk7D72/n40rE8WBTGcmhBBCiIci5fgJwnv0NIde15YtKLN0qYRe8dBI8BVCCCHEA5f4zz+c692bjIsXAfDq2YOQ2bPRyrSK4iGSoQ5CCCGEeKCu/fAD0RMmQkYGAH4jR+Dz4osyXZl46CT4CiGEEOKBUEpx+dNPuTp3HgAaR0eCpnyER8eONq5MFFcSfIUQQghx35nS0oge+w4Jv/4KgM7Li1JzZuNSp46NKxPFmQRfIYQQQtxXxvh4Lrz2Okm7dgGgL12a0gvm41imjG0LE8WeBF8hhBBC3DdpFy4Q8cpA0s6cAcBQqxal5szGwcfHxpUJIbM6CCGEEOI+ST54kPAePc2h1719e0ovXiShV9gNCb5CCCGEKLDrGzdy7rl+GK9eBcDnxRcInjEdrbOzjSsT4hYZ6iCEEEKIAold+g2XJk8GpUCrxf+dsfj07m3rsoTIQYKvEEIIIe6JMhqJ+fhjYpd8DYDGYCB4+jTcW7e2cWVCWCfBVwghhBD5ZkpOJmr0aK7/sQEAXUlfQubOwxBW3caVCZE7Cb5CCCGEyJeMq1eJeHUwKQcOAOBUsQIh8+ahDw62cWVC5E2CrxBCCCHuWuqZs0S88grpFy4A4NKoEaU+nYXOw8PGlQlxZzKrgxBCCCHuStLu3YT36mUOvZ5dulB6wXwJvaLQkB5fIYQQQtxR/OrfiH77bVR6OgC+Q4bg+3+D0Wg0Nq5MiLsnwVcIIYQQuVJKcXXBF1yeMSNzgYMDge+9h9fTXWxalxD3QoKvEEIIIaxS6elcfPddrn2/EgCtuzulPvsU10aNbFyZEPdGgq8QQgghcjAmJhI5dBg3/v4bAIegQErPn49TxYo2rkyIeyfBVwghhBAW0i9eJGLgIFKPHwfAuVo1Ss2bi97Pz8aVCVEwMquDEEIIIcxSjh0jvEdPc+h1a9WK0KVfS+gVRYIEXyGEEEIAkPjX35zr05eMS5cA8O7di1Kff4bW1dXGlQlxf8hQByGEEEIQ9/33XJw4CYxGAPxGj8bn+QEyXZkoUiT4CiGEEMWYUorLM2dxdf58ADROTgRNmYJHh/Y2rkyI+0+CrxBCCFFMmdLSiB4zloTVqwHQeXtTas5sXGrXtnFlQjwYEnyFEEKIYsh47RoRQ4aQvGcvAI6hoYQsmI9jaKiNKxPiwZHgK4QQQhQzaRERRLwykLSzZwEw1KlDqdmf4+DtbePKhHiwZFYHIYQQohhJ/u8/wnv0NIde944dKL1ooYReUSxIj68QQghRTCT88QdRo0ajUlIAKPHSi5QcPhyNVvrBRPEgwVcIIYQoBmKXLOHSR1NAKdBqCRg/Du+ePW1dlhAPlQRfIYQQoghTRiOXPppC3NKlAGhcXCg1YzpuLVvauDIhHj4JvkIIIUQRZUpKInLUaBI3bgTAoWRJQubPw7laNRtXJoRtSPAVQgghiqCMK1eIeHUwKQcPAuBUsSIhC+ajDwy0cWVC2I4EXyGEEKKIST19mohXBpIeGQmAa5PGBM+ahc7d3caVCWFbchmnEEIIUYTc2LWL8F69zaHX85lnCJk/X0KvEEiPrxBCCFFkxP/6K1FjxkJ6OgAl33idEoMGodFobFyZEPZBgq8QQghRyCmluDpvHpdnfZq5QK8n6IP38XzySdsWJoSdkeArhBBCFGIqPZ3oiROJ/+FHALQeHpT67DNcGzawcWVC2B8JvkIIIUQhZbx+ncg3hnJj2zYA9EFBhCyYj1OFCjauTAj7JMFXCCGEKITSo6OJGDiI1BMnAHAOCyNk7hwcSpa0cWVC2C+Z1UEIIYQoZFKOHiW8R09z6HVr04bQr5dI6BXiDiT4CiGEEIVI4p9/cq5PXzJiYgDw7tuXUp99itbFxcaVCWH/ZKiDEEIIUUjErfgfF999F4xG0Gjwf+tNvPv1k+nKhLhLEnyFEEIIO6dMJi7PmMHVL74EQOPkRNDUj/F47DEbVyZE4SLBVwghhLBjptRUot9+m4Q1awHQ+fgQMncOhkcesXFlQhQ+EnyFEEIIO5URF8eFIa+RvHcvAI5lyhCyYD6OpUvbuDIhCicJvkIIIYQdSjt/noiXXyHt3DkADPXqEvL55+i8vGxbmBCFmMzqIIQQQtiZ5P37Ce/R0xx6PTp1ovRXX0noFaKApMdXCCGEsCMJv68navRoVGoqACVeeYWSQ99Ao5W+KiEKSoKvEEIIYQeUUsQuXkLMxx+DUqDTETBhPN7du9u6NCGKDAm+QgghhI0po5FLkz8kbtkyALQuLgTPmolb8+Y2rkyIokWCrxBCCPGQKZMJlZyMKSkJY2IiMR9PJXHzZgAc/P0JmT8P5ypVbFylEEWPBF8hhBAiD8poxJScjOlGEqakG5iSklBJSZiSkjDdyPzZ/O9GkuXPFututVVJSVaP5VS5MiHz56EPCHjIZylE8SDBVwghRJGhMjJyBlGLcGoZPnOE1duDbFISKiXlodTu2rQpwbNmonNzeyjHE6I4kuArhBDCJlRaWp6BM2fv6Y1sy7P1vGZrp9LSbHtSDg5oXV3Rurhk/sv+/7f/c731/w7+/rjUr49Gp7Nt/UIUcRJ8hRBC5EkplRlSb+QMnhY9p3fRe5r9H+npNj0vjaNjznDq6oLGIqC65gyreYRZjaOjTc9JCJE3Cb5CCFGEKKXMF03l3nt6I0c4vb3nNEdINRptel4agyH3ntNsvafm0GoRTl1z9LBqDQY0er1Nz0kI8fBJ8BVCCBtRJhOmpGRMSTcse01vD6tWe06z9bjeFlhRyqbnpXVxQeOaS4+pRVi1Ekizh1cX18x1BoMMARBC3BcSfIUQ4i6ojIzMK/stekbzuMI/r6v7b7ZVycm2PSmt1vrX9a5Wwqm1r/ytBFmNs7PcYUwIYbck+AohihyVnn6Xvad3f4V/1u1jbUany31s6W1jVC17TW/7qj9bW42TExqNxrbnJYQQD5EEXyFEoaKMRq7Mm0fKkaPZrvK/YfGVv7L1RVN6fc6v+13z+Nr/9t7T7OE0qydVr5eQKoQQBSTBVwhRqFyZPYcrc+bct/1pnJzy33Oax/hUrcEgV/YLIYSdkuArhCg0Ev/+hytz5wKg8/bGsWzZPHtPNS4u6FxdLS+Wyt7GYEDjIG+DQghRXMg7vhCiUEi/dImoUaNAKTQGA6FLv8apQgVblyWEEKIQkUtvhRB2T6WnEzl8BMa4OAACJ02U0CuEECLfJPgKIeze5VmzSN67FwCvbt3wfPJJG1ckhBCiMJLgK4Swa9c3beLql18B4FSlCv5jx9i4IiGEEIWVBF8hhN1KuxBJ1FtvA6B1daXUzBlonZ1tXJUQQojCyq6Db2pqKm+++SZBQUEYDAYaNmzIH3/8cVfbRkZG0r17d7y8vPDw8OCpp57izJkzOdppNBqr/z766KN73qcQouBMaWlEDhuGKSEBgMAP3sexTBnbFiWEEKJQs+tZHQYMGMDKlSsZOnQoFStWZPHixXTq1InNmzfTrFmzXLdLTEykdevWxMfHM2bMGPR6PTNmzKBly5bs37+fEiVKWLRv164d/fr1s1hWu3btAu1TCFEwMR9PJeXgQQC8+/bFo0MHG1ckhBCisLPb4Ltr1y6+++47pk6dysiRIwHo168fYWFhjB49mm3btuW67Zw5czh58iS7du2ifv36AHTs2JGwsDCmTZvG5MmTLdpXqlSJvn375llPfvcphLh3CevWEffNNwA416iB3+hRNq5ICCFEUWC3Qx1WrlyJTqfjlVdeMS9zdnbmxRdfZPv27UREROS5bf369c0BFaBKlSq0bduW//3vf1a3SU5OJiUl5b7uUwiRf2nh4USPfQcArYcHwTNmoJU7oQkhhLgP7Db47tu3j0qVKuHh4WGxvEGDBgDs37/f6nYmk4kDBw5Qr169HOsaNGjA6dOnuX79usXyxYsX4+rqisFgoFq1anz77bcF3uftYmJiOHz4sMW/U6dO5bmNEMWNKSWFC0OHYbpxA4Cgjz7EsVSwjasSQghRVNjtUIfo6GgCAwNzLM9aFhUVZXW72NhYUlNT77ht5cqVAWjSpAndu3enbNmyREVFMXv2bPr06UN8fDyvvvrqPe3Tmjlz5jBp0qS8TlmIYu/SB5NJPXYMAJ8XX8C9TRsbVySEEKIosdvgm5ycjJOTU47lzjenMkpOTs51O+Cut/3nn38s2rzwwgvUrVuXMWPGMGDAAAwGQ773ac3gwYPp1q2bxbJTp07RpUuXPLcToriI//lnrn3/PQCGOnXwGzrUtgUJIYQocuw2+BoMBlJTU3MszxqHazAYct0OuKdtARwdHRkyZAiDBg1i7969NGvWrMD7BPDz88PPzy/PNkIUV6mnThE9MfMbEZ23N8HTp6HR621clRBCiKLGbsf4BgYGEh0dnWN51rKgoCCr2/n4+ODk5HRP22YJCQkBMoc43K99CiGsMyUlceGNoajkZNBoCJo6FX1AgK3LEkIIca8SL0PUPltXYZXdBt9atWpx4sQJEm5OXp9l586d5vXWaLVaatSowZ49e3Ks27lzJ+XKlcPd3T3PY2fdlKJkyZL3bZ9CiJyUUlycNIm006cB8H31VdyaNbVxVUIIIfIt8TLs/gqWPAHTKsGq/7N1RVbZbfDt2rUrRqORBQsWmJelpqayaNEiGjZsaO6VPX/+PMduXgyTfdvdu3dbBNXjx4+zadMmi3G2ly9fznHc69evM3PmTHx9falbt26+9ymEuHvXVq4k/udfAHBp1Ajf/xts44qEEELctRtXYM/CW2H3t+Fw9k9QJog5DJdP2LrCHDRKKWXrInLTvXt3fvrpJ4YNG0aFChVYsmQJu3btYuPGjbRo0QKAVq1asXXrVrKfxvXr16lduzbXr19n5MiR6PV6pk+fjtFoZP/+/eae3IkTJ7Jq1SqeeOIJSpcuTXR0NAsXLuT8+fMsXbqUPn365Huf+XH48GHCwsI4dOgQ1atXL+CjJUThknL0KOE9eqLS0tCV9KXcTz/h4Otr67KEEELk5cYVOPoLHF4F4X9lhtzs3AOhWheo3gVKNQDtg+1jzW+WstuL2wC+/vprxo0bx9KlS4mLi6NmzZqsXr3aHHpz4+7uzpYtWxg2bBjvv/8+JpOJVq1aMWPGDIuA2rRpU7Zt28aXX37J1atXcXV1pUGDBixcuJA2t02jdLf7FELcmTExkQtDh6LS0kCrJXjaNAm9Qghhr25cgaO/wuGf8gi7T0H1px9K2C0Iu+7xLeqkx1cUR0opIocO4/rvvwNQctgwfAe+coethBBCPFRZYffIKjj7Fyij5Xq3gMxe3WpdIKShzcLuA+3x1Wq1aDSafBdlNBrv3EgIUSzEfbPMHHpdWzSnxMsv2bgiIYQQwN2F3ayeXRuG3YLIV/AdP358juD7008/cfjwYdq3b2++c9mxY8dYv349YWFhcoMGIYRZ8oEDXPr4YwAcAgMJmjIFTSF84xRCiCLjxlU4dnMYQ55htwuENCqUYTe7fAXfiRMnWvy8YMECYmJiOHToUI7b9R49epQ2bdrI/LZCCACM164ROXQYpKeDgwPB06fh4O1t67KEEKL4MYfdVTdnYbAWdp+82bN792H3yo1rLP5vDevPbkCr0bGu9xf3v/YCKtDFbVOnTmXIkCE5Qi9A1apVGTJkCB9//DEvv/xyQQ4jhCjklMlE1Ftvkx4VBYDfyBG41K5t46qEEKIYSYq9dYGa1bDrn9mzW60LlG4EWt1d7fZsXCRf7VvNnxc2EWc6BprMC9+U0nE1KYESLh73+UQKpkDB98KFC+jzuK2oXq/nwoULBTmEEKIIiF20iMQtWwBwe7QtPv3727YgIYQoDrLC7pFVcGar9bBb9WbP7l2GXaUUe6OPsWT/anbF/EmSJvzWypujYZXRgI+mFhHXYotW8A0LC2POnDn07t2b4OBgi3UXLlxgzpw51KhRo0AFCiEKt6S9e4mZPgMAfalSBE2efE8XyQohhLgLSbFwbHVmz26eYbcLlG58V2HXpEz8cXo3yw+t4UDc36RrYzJXZHsrV+leBDvWo33ZR+lfpzUlXF3u3zndRwUKvjNmzKB9+/ZUqlSJp59+mgoVKgBw8uRJVq1ahVKKb7755r4UKoQofDJiY4kcNhyMRjR6PcEzZ6LzsK9P/0IIUeiZw+4qOLsVTBmW6139bl2gdpdhNzUjle8Pb2HVifWcTNyBSZuQuSLbcF9NWgDlXRvRpfJjdK/RGIOjXd8eAihg8G3WrBk7d+5k3Lhx/PTTTyQnJwNgMBho3749kyZNkh5fIYopZTQSNWo0GTGZPQP+Y97GECbzVQshxH2RFAvHfrs5Zje3sPtk5pjd0CZ3FXavJSfw9X+/s/bsH1xI+Re0qZkrboZdpTQ4pJchzKspPat3pGOVGui0hesbvAJH87CwMH766SdMJhOXL18GoGTJkmgL+XQXQoiCuTJ/Pjf++QcAj86d8erZ08YVCSFEIZcVdo+sgjNbrITdkrcuULvLsBsRf4mF+1azJWITV4yHQXNzaERW2DXpMBirUL9kC56r1ZFGpcsU6uFq961PWqvV4u/vf792J4QoxG5s386Vzz4HwLFsWQImTSrUb5RCCGEzyXG3enZzC7tZY3ZDm95V2D146RSL9q1mx6UtJKgzaDQ3b+JrvjjNCU9q0jyoNc/XaU9lP7/7ekq2lK/g++677+b7ABqNhnHjxuV7OyFE4ZQeE0PkyFGgFBpn58xxvW6uti5LCCEKD3PYXQVnNhc47Cql2BL+L8sOrmH/1b9I1Uab12X1SagMd/wd6vJoaFuer/MoAR5u9/ec7ESBbmBxNyT4ClF8qIwMokaMxHj1KgAB48fjXLmSjasSQohCIDkOjq3J1rObbrnexTfbmN2moMs7wqUZ0/j52D/8cHQtx67vwKiNy1yRfSRqui9lDA15vPxj9KndDDcnx/t5RnYpX8HXZDI9qDqEEEXA5c8+J2n3bgA8n3kGr2eetnFFQghhx7LC7pFVcHpzgcNuYuoNvjnwB7+dXs+55D0obeakA9nDrjatNFU9GtOtakeeqFYLR4e7u1FFUWH/804IIQqFxK1buTp/PgBOFSsSMO4dG1ckhBB2KPkaHL/Zs5tb2K36xM1hDM3uGHYvJl5m0b61bDy3kUvpB0F7c3/mmRi0OGVUonaJpjxXszMtylUo1tdc3JfgGxkZyZ9//klMTAzPPvsspUqVwmg0Eh8fj6enJzpd8fo0IURxkx4VRdToNwHQurgQPGsWWoPBxlUJIYSdMIfdVXB6k5WwWyLbmN07h93jV8+x8N9f+Sd6C9dMJ25dnGaeiUGPu6kGjQNb8ELtToQFBt7vMyq0ChR8lVKMGDGCzz//nIyMDDQaDTVq1KBUqVIkJiZSpkwZ3n33XYYOHXqfyhVC2BuVlkbksOEY4+MBCHj3XZzKlbVxVUIIYWPJ1+D42ps9u7mF3Scybxd8h7CrlGL7hYN8/d9v/HvlL5I1EeZ1ty5Oc6WkrjatQ9rwQt3HKOXl+QBOqvArUPCdOnUqs2bN4s0336Rt27a0a9fOvM7T05NnnnmGH374QYKvEEVYzLTpJP/3HwBevXri+XhnG1ckhBA2khV2j6yCUxtzhl2Dz60xu2Wa5xl2jSYja05uY8XhdRyO30aG9krmiuyjFNK9KeXUgE7l2/FcrZZ4uTjf5xMqegoUfL/44gv69evH5MmTuXrzKu7satasydq1awtyCCGEHUv44w9ilywBwLlaNfzfesvGFQkhxEOWEp/tArVNYEyzXG/wudWze4ewm5SWzIrDm/j5xO+cSdqN0iZmrrC4TXAwldwb8UzlDjwbVh8nvQwnzY8CBd+IiAiaNGmS63pXV1cSEhIKcgghhJ1KO3+e6DFjAdC6uxM8ayZaJycbVyWEEA9BSrzlMIZcw26Xm2FXn+uuriZdY/H+taw/u4GotP2gvbmvbLcJdkwvT02fZvQK60i7ilXRFrLbBNuTAgVfPz8/IiIicl2/d+9eSpcuXZBDCCHskCk1lcihwzBdvw5A4OQPcAwJsXFVQgjxAJnD7io4vTGXsPt4tp7d3MPu2bhIFu5bzZ8XNhNrOgqam9PFmi9Oc8DVVI0Gfi14vnYn6pSS99f7pUDB95lnnmHevHkMGDAAT8/MQdRZU2SsX7+exYsXM3r06IJXKYSwK5c++oiUI0cA8OnfH49s4/uFEKLISEnI1rNrLex6Z/bsVusCZVvkGnaVUvwbfYzF+1ezO+YvbmjO3lppvk2wAR9NLVoGt+L5uh0oV8LnwZxTMVeg4Dtp0iQ2b95MrVq1aN68ORqNhilTpjBu3Di2b99O7dq1GTNmzP2qVQhhB+JX/8a15d8BYHjkEfxGDLdxRUIIcR9lhd2sC9SMqZbrDd5Q5WbPbh5h16RMbDi9m28PreFg3D+kaS9lrsg2SkFleBKkr0eHsu3oX7s1JdxcHsw5CbMCBV9PT0927NjBtGnTWLlyJc7OzmzdupXy5cszYcIERo0ahUHm8hSiyEg9c4bo8eMB0Hl5ETxzBhrHon+LSyFEEZeSACfWZfbsWgu7zl63xuyWbZlr2E3NSGXlkS38dHw9JxN3YNLevM4p+22C0wIo79qQpyo+Rs9HmmBwlHuJPUwFfrQNBgPvvPMO77wjd2kSoigzJScT+cZQVFISAEEfT0Evk6ILIQorc9hdBac25BJ2s3p2cw+715ITWHrgd9ae2UBEyr+gTclcke3iNIf0MoR5NaFH9U50qlIDnVycZjPyMUMIcVcuvvc+qSdPAlBi4EDcWrSwcUVCCJFPqdfheFbPbh5ht9rTUC73sHsh4RIL/13N5ojNXDEeAo0xc4X54jQdBmMV6pVsTr9HOtEotEyxvk2wPclX8H3hhRfQaDQsWLAAnU7HCy+8cMdtNBoNX3311T0XKISwvWs//Ej8jz8C4FK/PiVfG2LjioQQ4i5lhd0jq+DkH9bDbvYxuw7Wh28dvHSKRftXs+PiVhLU6Vu3CTZfnOaEJzVpGtSKF2t3oLK/3wM7JXHv8hV8N23aBIDJZEKn07Fp06Y7foKRTzhCFG4px09w8b33ANCVKEHQtE/QOMiXRUIIO5Z6HU78ntmzazXsekKVbGN2rYRdpRRbw/9l2cE17Lv6N6naKPO6W7cJdsffoS5tS7fhhbrtCPBwe4AnJe6HfP31Cg8Pp1GjRhw/fpywsDDCw8MfUFlCCHtgTLxB5NChqJQU0GgInvYJej/pxRBC2KHsYffUBshIsVzv7JmtZ9d62E0zpvHL8X9YeXQtxxJ2YNTGZa7IfnFaui9lnBvSuUI7+tZujpuTXOBbmOS72+bcuXPUrVuXESNGMH78eJyd5b7QQhRFSikujh9P2tnM+SZ9XxuCa6NGNq5KCCGySU3MNhtDHmG3Whco18pq2E1MvcGyg3+w+tQfnEveg9JmXsCbPexq00pTxaMx3ap24MlqtXF0kNsEF1b5Dr7Hjx/n7bff5uOPP+b7779n7ty5PProow+iNiGEDV377jsS1qwBwLVpU3wHDbJxRUIIwa2wmzVm9/aw6+R58wK1LrmG3UuJV1i4bw0bz2/iUtoB0KZnrjDPxKDFKaMitX2a0bdmJ1qWryhDN4uIfAdfDw8PZs+ezYABAxg0aBDt27end+/eTJ8+nZIlSz6IGoUQD1nyocNcmvwhAA7+/gRN/RiNVnuHrYQQ4gFJTYST2cbsWgu7VTpnjtkt19pq2D1+9RwL//2Vf6K3cs10/NbFaeaZGPS4m2rQOKAFz9fpRA2ZrrFIuucrVOrXr8/u3bv57LPPGDduHKtXryYkJOe9pDUaDf/991+BihRCPDzGhITMcb3p6aDTETx9Gg4+cutMIcRDZg67q26G3WTL9RZhtxU4OFmsVkqxI/IQX/+3mr2X/yJZE2Fed+viNFd8dbVpXaoNL9RrR4iX14M8I2EHCnRpdkZGBpcvXyY1NZUSJUpQokSJ+1WXEMIGlFJEjRlD+oULAPgNH4ZL3bo2rkoIUWzcVdjtlDmMoXzrHGHXaDKy5uR2VhxZy+Fr28jQXslckf02wenehDg1oGO5dvSr3RIvF7lWqTi55+C7YcMGBg8ezJkzZxg8eDAffPAB7u7u97M2IcRDFrtkCYkbNgLg1ro1Ps8/b+OKhBBFXtqNzNkYjqyCE+uthF2PzJ7dXMJucnoyKw5t4ueTv3P6xm6UNjFzRbbRWZq0ICq6N+bpSu3pWqM+znqZkrG4yvdv/vLlywwbNozly5dTo0YNtm3bRoMGDR5EbUKIhyhp3z5iPpkGgD4oiKAPJ8u4XiHEg3E3Ybdyp8xhDOXb5Ai7V5OusWT/Wn4P30BU6n7QpmWuyHabYH16eWr6NKVX9Y48VqkaWrlNsOAegm/lypVJS0vjo48+Yvjw4eh0MqWHEIVdRlwckcOGQ0YG6PUEz5yBTsa6CSHup7QbcHJ95jCGE7/nO+yevRbJwn9X82fkZmKNR0FjylxhvjjNAVdTVRr4taR/rY7ULRUiMzGIHPIdfBs1asScOXMoU6bMAyhHCPGwKZOJqDffJOPiRQD833wTQ82aNq5KCFEkZA+7J9dDepLlekf3bGN224D+1nhbpRT7oo+z+L/V7Ir5kxucvbWd+TbBBrw1j9AyuDXP12lPeV+51kjkLd/Bd83NeT2FEEXD1S++5MaffwHg3qED3n1627giIUShlpZ0M+z+lO+wa1ImNp7ZzbJDazgY+w9p2ks5dq/SPQnS1+Oxsm15vk5bSri5POATEkWJjO4Wohi7sWsXl2fNAkAfWprA99+TrwaFEPmXFXaPrMocxmAt7FbumHm74NvCblpGGiuPbOGn479zInEHJm1C5orslxik+VPetRFPVnyMXo80weAo8UXcG3nmCFFMZVy5QuSIEWAyoXF0pNSsWejc3GxdlhCisEhLglN/ZPbsWg27btnG7La1CLvxKddZ+t/vrDnzBxEp/4L25g0psl2c5pAeSnXPpnSv1oHOVWvioJOLbUXBSfAVohhSRiORI0dhvJw5x6X/uHdwrlLFxlUJIeyeOeyuuhl2b1iud3TL1rNrGXYjE2JYuG81m85v4orxEGiMmSvMYVeHc0Zl6vo2p98jnWhSpqx8AyXuOwm+QhRDV2bPIWnHDgA8n3oSr65dbVyREMJupSdn3kzC3LObS9it1gUqtAW9wbzqcMxpFu7/le3RW0lQp2/dJth8cZoTntSgaWArXqzTkcr+fg/nnESxJcFXiGIm8e9/uDJ3LgCOFcoTMGGC9KoIISxlhd0jq+D4Outht1KHzJ7dbGFXKcWf5/5l2YE1/Hv1L1I1UeZNbt0m2B1/h7q0Ld2G5+s8SqCn3PxKPDwSfIUoRtIvXiRq1ChQCo3BQKmZM9G6yBXRQggyw+6pDZk9u9bCrt715jCGLlDhUXPYTTOmsfrIZr4/uo6jCdsxauMy22f/PJ3uS6hzQx6v0I4+tZrj7uz4UE5JiNtJ8BWimFDp6UQOH4ExLvOPUuCkiThVqGDjqoQQNmUOu6vgxDpIS7Rcr3eFylk9u7fCbmLqDb7d8zO/nl7PuaQ9KO3NC9uyXX+mTQuhikcTulbpwFPVa+PoIDe8ErYnwVeIYiJm5kyS//0XAK9u3fB88kkbVySEsIn0lFs9u3mF3WpdoGI7c9i9lHiFRTu+Z8P5TVxKPwCa9Mz25ovTtDilV6RWiWb0qdGR1hUqyTAqYXck+ApRDFzftInYrxYC4FSlCv5jx9i4IiHEQ5UVdo+sguNrrYfdSu1v9ew6Zg6BOnH1HAv3rebvqC3Em47D7RenmfS4mcJoHNCCAbU68khw8MM7JyHugQRfIYq4tAuRRL31NgBaV1dKzZyB1tn5DlsJIQo9i7C7DtKuW67Xu9y8QK0LVGgHji4opdgReYil//3Gnst/kqyJuNXePBODC76a2rQKacOLdR8jxNvrIZ2QEAUnwVeIIsyUlkbksGGYEjLvhBT4wfs4lilj26KEEA9Oegqc3pg5Zvf42lzCblbPbmbYNZqMrDu1g+WH13Dk2jbStZnze2e/OE2le1PKqT4dyz3Gc7Vb4ONiQIjCSIKvEEVYzMdTSTl4EADvvn3x6NDBxhUJIe67uw271bpAxcfA0YWUjBRWHNrEqhO/c+bGLkzam0Mfsl2cpkkLooJbI56p3IGuNerjrJfIIAo/eRYLUUQlrFtH3DffAOBcsyb+o0fZuCIhxH2TngKnN2UOYzi2xnrYrfhYZs9uxXbg6MrVpGss2fMzv4dvICp1P2jTMttmu02wPr0cNb2b0iusE+0qVUOnlYvTRNEiwVeIIigtPJzose8AoPX0JHj6dDSOMm+mEIVaRiqc2njrArXUBMv15rDb5WbPrivh16JY+Pc3bI3cTKzxKGhMmW2zwq7JARdjVRr4taB/7U7UKxUiMzGIIk2CrxBFjCklhQtDh2G6kTn5fNBHH+JYSq60FqJQykjN7Nk9/JP1sOtggEpZPbuZYfff6OMs3jiXXTF/cYMzt9qaL04z4M0jtCjVmhfqtKe8b4mHdz5C2JgEXyGKmEsfTCb12DEASrz0Iu6tW9u4IiFEvpjD7io4vib3sFutC1Rqj0lvYOOZ3Xy7dioHYv8mTXspxy5VhieBDvVoX7YtA+q0wdfN9aGcihD2RoKvEEVI/M8/c+377wEw1K1LyTfesHFFQoi7kpEKpzff7NnNJexWbJfZs1upPWlaPT8c3cqPv0zgxPUdmLTxme2yXZxGmj/lXBryVKX29KzZBBcn+ZMvhLwKhCgiUk+dInriJAB03t4ET5+GRq+3cVVCCKuM6XDxAJzbDue3w9m/IDXeso057HaBiu1JAJb+t441P4zgfMpe0KZktssWdnVpZajm2YTu1TryeNWaOOi0CCFukeArRBFgunGDC28MRSUng0ZD0NSp6P39bV2WECJLaiJc2A3nd8D5bXBhD6Qn5Wzn4HyrZ7dieyJTk1i0bzWb9g/icsYh0Bgz25lnYtDhnFGZOr7N6fdIR5qWKScXpwmRBwm+QhRySimiJ04i7fRpAHxffRW3Zk1tXJUQxVxiTGZP7vkdmf+NPgDKaL2teyCENoHKnaBSBw7HX2LR/tVs39uPeHUKze23CTY64alq0CSoJS/U7kTVAL+Hc05CFAESfIUo5K59/z0Jv/4KgEujRvj+32AbVyREMaMUxJ7JDLhZQxdiT+fevmQVKN0ISjeG0o0xeZbi74gDfHPgN/bt/ZIUTaS5aVbnrcpww09Xl0dLt2FA3XYEebo/4JMSomiS4CtEIZZy9CiX3v8AAF1JX4I/mYpGp7NxVUIUccYMuHTwVsg9vwNuxFhvq3WAoNo3g24TCGlIkqOBjWf2suHMTg4dfIfL6SdQ2pvDHrKPUkj3pbRzAzqXb8dztVvg7ixzcQtRUBJ8hSikjNevc2HoUFRaGmi1BE+bhoOvr63LEqLoSbuROSY3a3xuxG5Iv2G9raM7hDS42ZvbCILrciElgV+Pb+OfI/9waud8bqjwWzeSAIuL07RpIVR2b8yzVdvTpVpdnPTyQVaI+0mCrxCFkFKK6HfGkX7uPAAl33gD1wYNbFyVEEXEjSu3jc/9D0wZ1tu6+ZuHLBDaGKNvFXZdOsHaE9v5d8e3RKaMJ0N7xXKbbL26Kt0Hb10lqno/Qo/q7WhdvhJauU2wEA+MBF8hCqG4b5Zx/fffAXBt0ZwSL79k44qEKKSUgrizmSH33LbM/149mXv7EhUhtLG5RzfBpSRrTu5iy7ndHD05hdiMk7emGQOL3lyldDiklyLIuSq1/WvRoUIjGoeWlSnHhHiIJPgKUcgkHzjApY8/BsAhMJCgKVPQaOUPpxB3xWSES4csx+cmXrTeVusAgY+Ye3RVSENOpiax+vh2dpzaS/j+ZSQRcWvWBbAMukYXXFV5yruH0aRUPZ6o0oBQH68HenpCiLxJ8BWiEDFeu0bk0GGQng4ODpSaMR0Hb29blyWE/UpLgsi9luNz065bb6t3tRifmxb4CH9Fn2b96R3s3/czl3ZMwai9dqu9xvJaNNJL4utQmeolHqFt2Qa0r1hT7pYmhJ2RV6QQhYQymYh6623So6IA8B81EkOtWrYtSgh7kxR7K+Se3wFR+8GUbr2tq1/mBWihTaB0I654hLD65G7+PL+bE399TrzpDGjTbrXP3ptrckBvLE1pl2rUC6hD50qNqRUULONzhbBzEnyFKCRiFy0iccsWANzbPYp3v362LUgIW1MKrp27dRHaue1w5Xju7X3Km8fnqpBGHMyA1Se2s/vcv0QcXUWqNsqyffagm+GGh6YiFT1r0KJ0PR6v0gB/d9cHc15CiAdGgq8QhUDS3r3ETJ8BgD4khMAPPpDbkorix2SEmCOW43OvR1lvq9FBYE3z+NyUwNpsiIlgw5mdHDy8gcv756C02YY8WFyEpkGbHoC/U2UeKVmbx8o3omXZyjK1mBBFgARfIexcRmwskcOGg9GIRq8neOYMdB4eti5LiAcvPeXm+NybQTdiF6QmWG+rd4FS9c3jc6O8yvLz6f/YdmEvp3YtIpEJoMk2JZnFsAVHnI1lKeNWnYZBdXi8ciOq+PnJh0shiiAJvkLYMWU0EjVqNBkxmXeF8h87BkP16jauSogHJCk2M9yax+fuA2Oa9bYuvubb/ppKN2S30Yk1p3ez9+I+osLfJ12b7U5qt+fXDE+8tJWo6l2TVqEN6Fi5Nt4uhgd2WkII+yHBVwg7dmXePG788w8AHp0749Wjh40rEuI+unbecnzu5aO5t/Uua74I7XpALdZevcqWc3s4fGoHcceX3rrlL+QYtuCQEUyQc1Vq+dWiY8XGNAmtgE4uQhOiWJLgK4SdurF9O1c+nw2AY9myBEyaJF+9isLLZMoMtlk3iTi/AxIuWG+r0UJADfP43NMeZfgl4iQ7ovZy9r+VJB2YhiaXW/4qoxOuqjzlPMJoElyXJ6s2ItTb58GemxCi0JDgK4QdSr8UQ+TIUaAUGmdngmfOROcmV5CLQiQjFSL/vXURWsQOSIm33tbBAKXqQenGZIQ04C+TK+vOHeC/y/u5GD0To+7qrbba2+fOLYGvvjLVfWrStmwDHqv4CK5Ojg/yzIQQhZgEXyHsjMrIIGrECIxXM//YB4wfj3PlSjauSog7SL5mOT438l8wplpva/AxX4QW6/8Iv8XfYMuFfRyPOEj8uZ9Am227bBMpKKXD0RhCiKEq9QLq0qlSI+oEl5ZvQoQQd02CrxB25vKnn5G0Zw8Ans88g9czT9u4IiGsiI+8NdvCue2Z04yhrLf1CoXQJqiQhhx1C+XnS9HsvriP88fXkXLyyzxv+etBRSp6hdE8pB5PVmmIn7v7Az0tIUTRZtfBNzU1lfHjx7N06VLi4uKoWbMm77//Pu3atbvjtpGRkQwbNoz169djMplo3bo1M2bMoFy5crlu8/fff9O8eXMALl++jK+vr3ndxIkTmTRpUo5tnJycSElJuYezEyKnxK1bubpgAQBOFSsSMO4dG1ckBJnjc68cvxVyz++A+PO5NNZAQBiUbkxqqQZsNrqw7uJpDl35j5gDX6F02YY76CyHLWjT/fBzqkJN30doV64RbctXR+8gc+cKIe4fuw6+AwYMYOXKlQwdOpSKFSuyePFiOnXqxObNm2nWrFmu2yUmJtK6dWvi4+MZM2YMer2eGTNm0LJlS/bv30+JEiVybGMymXjttddwdXXlxo0bue577ty5uLm5mX/W6eRNWdwf6VFRRI1+EwCtiwvBs2ahNcgUS8IGMlIzb/WbfXxucpz1tg7OEFwPSjfiUskwfknM4M+LRzgVc5DESxtBm+12wdmHLZgccDaVIdS1Gg2D6vJE5cZU9Q98oKclhBB2G3x37drFd999x9SpUxk5ciQA/fr1IywsjNGjR7Nt27Zct50zZw4nT55k165d1K9fH4COHTsSFhbGtGnTmDx5co5tFixYQEREBC+99BKzZs3Kdd9du3a16AkW4n5QaWlEDhuOMT6zNyzgvXdxKlfWxlWJYiMlHiJ2Zxufuxcycvkmy9krc+7ckIb85xrCL7HX2HP5IJHn/iL9wv9utdNg2Z2b4Y6XriJVvWvSsnR9Hq9SH0/5YCeEeMjsNviuXLkSnU7HK6+8Yl7m7OzMiy++yJgxY4iIiCAkJCTXbevXr28OvQBVqlShbdu2/O9//8sRfGNjY3nnnXd49913iYmJuX13FpRSJCQk4O7uLhdUiPsmZtp0kv/7DwDv3r3w7NzZxhWJIi0h+lbIPb8dLh0GZbLe1rM0lG5EcnA91pvc+f1qNEfiDnD15P9Al3irncVFaBocjIEEOlehjl9tOlRoRJPSldDptDn3L4QQD5HdBt99+/ZRqVIlPG67NWuDBg0A2L9/v9XgazKZOHDgAC+88EKOdQ0aNGD9+vVcv34d92wXSIwbN46AgAAGDhzIe++9l2dd5cqVIzExEVdXV7p06cK0adPw9/e/l1MUAoCEP/4gdskSAJyrV8fvrbdsXJEoUpSCKyeyjc/dDtfO5dJYA/7VoXQjLpSoxs/J8OeVM5xNOExSwjw02my3/LUYtuCIqypLOfcwGpeqy5OVG1PGR74ZE0LYH7sNvtHR0QQG5hzvlbUsKirK6naxsbGkpqbecdvKlSsDcODAAebPn8+aNWvyHK/r7e3NkCFDaNy4MU5OTvz111/Mnj2bXbt2sWfPnhwB/XYxMTFcvnzZYtmpU6fy3EYUfWnnzxM9ZiwAWnd3gmfOQOsoc5CKAshIg+j/bo3PPb8dkmOtt9U5QnBdjCGN2G0I5tfrSeyNPcHFS/swXll/q93tc+dmeOGrr0R1n0doU7YBHSrWwUWet0KIQsBug29ycjJOTk45ljs7O5vX57YdcNfbvv7663Ts2JHHHnssz3reeOMNi5+fffZZGjRoQJ8+fZgzZw5v3aGXbs6cOVZnhRDFlyk1lcihwzBdvw5A0IeTccxl+I4QuUpJgAu7bwXdC3sgw/r7I86eENKIhKC6/K7cWR8fy9H4o8RHrAFdtm0shi1ocTQGU8qlGvUCavF4pabUDiojQ72EEIWS3QZfg8FAamrOyc+zpg4z5HJRRNbyu9l2xYoVbNu2jUOHDt1Tjb1792bEiBFs2LDhjsF38ODBdOvWzWLZqVOn6NKlyz0dWxR+lz76iJQjRwDwGTAA90cftXFFolC4fvFWyD23DS4dyn18rkcpCG3MaZ+qrE7VsvVaNOeTjpBy7ttbt/zVcNuwBWc8KE9Fzxo0L12PJyo3wt/d84GflhBCPAx2G3wDAwOJjIzMsTw6OhqAoKAgq9v5+Pjg5ORkbpfXtqNGjaJbt244OjoSHh4OwLVr1wCIiIggLS0t1+NkCQkJITY2l68Rs/Hz88PPz++O7UTxEL/6N64t/w4AQ61a+I0YbuOKhF1SCq6eshyfG3c29/Z+1Ugv1ZDthiB+SzKyN+EsMdeOoxJ33mpz+9y5GSXwc6xCjZKP8FjZRrQpXwNHB7v90yCEEAVit+9utWrVYvPmzSQkJFiMn925c6d5vTVarZYaNWqw5+adr7LbuXMn5cqVM1/YFhERwbfffsu3336bo22dOnV45JFH2L9/f641KqUIDw+ndu3a+TgzUdylnjlD9PjxAOi8vAieMR2NXm/jqoRdMKbDxQO3Qu75HZB0xXpbrR6C6xAbWId1ePLHjRscSzzJ9at/o8l+y99s7/JK6XA2lc6cOzewLk9UaUxVv1IP9pyEEMKO2G3w7dq1K5988gkLFiwwz+ObmprKokWLaNiwoXlGh/Pnz5OUlESVKlUstn3rrbfYs2cP9erVA+D48eNs2rTJvC+An376Kcdxv/vuO1asWMHXX39NqVK3/iBcvnyZkiVLWrSdO3culy9fpkOHDvfvxEWRZkpOJvKNoaikJACCPp6C3sqFmKKYSE28OT53R+b0Yhf2QHqS9bZOHphKNeCET1VWZzjy142rRCSfIC1mza1b/t5+EZrRBS9dJap41aRlaD0er9wAL4Prgz4rIYSwW3YbfBs2bEi3bt14++23iYmJoUKFCixZsoTw8HC++uorc7t+/fqxdetWlLp1r/fBgwfzxRdf0LlzZ0aOHIler2f69On4+/szYsQIcztr42uzeng7duxocaOK0NBQevToQY0aNXB2dubvv//mu+++o1atWgwcOPD+PwCiSLr47nuknjwJQImBA3Fr0cLGFYmHKjHGcraF6AOgjNbbugeSUqohf7uE8HuqYs+NKK6kncycmiyLg2XQ1WX4E+hchdo3585tFloVrVbmzhVCiCx2G3wBvv76a8aNG8fSpUuJi4ujZs2arF69mhZ3CAvu7u5s2bKFYcOG8f7772MymWjVqhUzZszI0Wt7t/r06cO2bdv44YcfSElJITQ0lNGjRzN27FhcXFzuaZ+ieLn2w4/E3/yWwaV+fUq+NsTGFYkHSimIPWM5Pjf2dO7tS1YhJqAW67TebExN42jSOZKSDqJJ+fdWm+zDFkwOuFKWsu7VaBJcjyerNKaMt8wpLoQQedGo7F2l4qE6fPgwYWFhHDp0iOrVq9u6HPEApRw/Tnj3HqjUVHQlSlD2px/Ry8WORYsxAy4dtByfeyOXO0Fq9ZgCH+GQT1XWKQN/JSUQkX4Go8PFXHevMbpTwqEy1Xxq0qZsAzpWrIeLY85pG4UQojjJb5ay6x5fIYoCY+KNzHG9qamg0RA87RMJvUVB2o3MMblZ43MjdkP6DettHd1JDq7HVpcQ1hu17Em+Spw6DYlbb7WxuAhNg6MpkFKGqtQNqEPnSk2oG1Re5s4VQogCkuArxAOklOLi+PGk3Zwuz/e1Ibg2amTbosS9uXHltvG5/4Epw3pbN3+iAurwu74km9PTOZIaTYopHE3SzaEOtw+7NTnirilHRY8aNAupxxNVGhPg7v1AT0cIIYojCb5CPEDXvvuOhDVrAHBt2hTfQYNsXJG4K0plzpebdZOI8zvg6slcmxtLVOS/ElX5XePG36nJRBjPo4yHIeu6tdsuQtMavfFzrEyNEo/Qrnwj2pZ7BEcHmdJOCCEeNAm+QjwgyYcOc2nyhwA4+PsTNPVjNHKFvX0yGTPvgJZ9fG5iLuNttQ5c96/BVrcybFR69qRdI45zaNL3Z67XcNuwBS3OqhShrtVoEFiXJyo3pppf6IM+IyGEEFZI8BXiATAmJBA5dCgqPR10OoJnTMfBx8fWZYksaUkQuddyfG7adatNlaMbEf41We/kz1aj4kj6ZVIdItFkXM1scNud0DA546WtSGWvMFqGNuDxyg3xNrg/8FMSQghxZxJ8hbjPlFJEjRlD+oULAPgNH45LnTo2rqqYS4q9FXLP74Co/WBKt9o0w9WPvb7V2KDzYltGCudVNDhcAGPm7xP9bXPnGn0JdK5CrZK16VChIc1Cw9BpdQ/8lIQQQuSfBF8h7rPYJUtI3LARALfWrfF54XkbV1TMKAXXzt26CO3cdrhyPNfm8d7l2OpZjo04829GInHaSDTaM6CA2/KrUjpcVShl3avTOLguT1ZpQllvufOeEEIUFhJ8hbiPkvbtI+aTaQDog4MJ+uhDmYLqQTMZIeaI5fjc61HWm2p0nC1ZhU2GYLYqLUdNsaQ6XEKjuXk3tNt6czUmV0o4VKKaT01ahzagQ8V6uDnJDWuEEKKwkuArxH2SERdH5LDhkJEBej3BM2eg8/S0dVlFU/QBOLk+M+hG7ILUBKvN0vQu7PWtxka9N9tNGZzXxIDDdeBYZoPbxufqTQEEO1elbkBtOldsTL3gyvLBRQghihAJvkLcB8pkIurNN8m4mDkTgP+bb2KoUcPGVRVBqdfhjwmw5yurq+NcSrDVuyKbtK7sU0nE6WLQaGOAmBzDFjA54K4pRwXPMJqWyrzlb6C77wM/BSGEELYjwVeI++Dqgi+48edfALh36IB3n942rqgIOrURfn0D4iOAzCG4J71C2eRWir/Qc4x40vRXgVvDHCzmzjW5U1JfhZq+j/BouUY8Wq42jg6OD/UUhBBC2JYEXyEK6MbOXVz+9FMA9KGlCXz/Pfl6/H5Kvgbrx8K+bwCI0el4z7cMfzo6YHJIBiJybKKUBmcVRKhrNeoH1uGJSk2o5ldWfi9CCFHMSfAVogAyLl8mcuQIMJnQODpSatYsdG5uti6r6Di+DlYPhevRmID/eXgzxcuLDF06kG06MpMjnrryVPGqSYvS9elcqSElXLxsU7MQQgi7JcFXiHukjEYiR47CePkKAP7j3sG5ShUbV1VEJMXC2jfh4P8AOOfgwIiSpTnunEHWfYB9tY/QMKAJHSo0omnpGuh1cstfIYQQeZPgK8Q9ujJ7Nkk7dwLg+dSTeHXtauOKiogjP8NvI+DGZdKBr7x9mevhhkmbAYDW6MXrj7zJi3Uft22dQgghCh0JvkLcg8S//ubK3HkAOFYoT8CECTJ+tKASY2DNyMzgCxxx1DOyZAgRjhmACYAqLh2Y9/g7lDDINHFCCCHyT4KvEPmUfvEiUaNHg1JoDAZKzZyJ1kVuanDPlIKDK2HtaEiOJVmjYZZPSb51N6A0mb28elMA4xtNoEvVZjYuVgghRGEmwVeIfFDp6UQOH4ExLg6AwEkTcapQwcZVFWIJUbB6OJxYC8BOZyfe8g3iit4IKJTS0sinG592HImL3tm2tQohhCj0JPgKkQ8xM2eS/O+/AHh1747nk0/auKJCSinYvwzWjYHUeOK1Gj4q4c9qN0eyLl5zUWWZ2up9WpSpadtahRBCFBkSfIW4S9c3bSL2q4UAOFWtiv/YMTauqJC6FgG/vg6nNwHwh4uBCSX8ue6QOY4XkyPtgwbw0aOv4qCTtyghhBD3j/xVEeIupF2IJOqttwHQurpSauYMtE5ONq6qkDGZYO8i+GM8pCUSo9Mx0defv1wcyLp4zVtTnc87TqZmQDnb1iqEEKJIkuArxB2Y0tKIHDYMU0ICAIEffIBjaKiNqypkYs/AL69D+F8o4Ad3Vz7yLkmqLquX14Xe5YfwVvO+MjuGEEKIB0aCrxB3EPPxVFIOHgTA+7nn/r+9+w6Pqsr/OP6eSe+dkERAkKYBQaoiElCUjugCthX0J+gKiKGJUkyhCUgCirRdBVcFKQooNnQpNkQQAUXpIJAEMEBCAqTN3N8fgUhMAgkpkzCf1/Pk2c2de+79zuEYPrmcOQfvzp1sXFEVYrXAjwvgf7GQfZ4jjo6MCQpmh6sDl57yhjndzryuE7jRt7ptaxURkeuegq/IFZz9/HPOvPsuAK633krwqJE2rqgK+XMvfDQEjm4mB/ivjxev+/qTYzaA3I0oBt/6Ak+36GHbOkVExG4o+IoUIfPQIZLGjgPA7ONDWFwcJmdnG1dVBVhyYNPrsH4KWDL53dmJlwKDOeBiBnJDbwO3TszrPp5Ad21EISIiFUfBV6QQ1owMEiKHYT13DoDQV6bgfEOYjauqAk7sgtWDIfFnMkwm5vj5ssjHG+PitF0nSzDjWkfxYPhdtq1TRETskoKvSCFOTJpE5p49AAQMeAqvDh1sXFElZ8mGb+Lg6+lgzWaLqwtjA6uR5JSbeA3DTCvff/B611F4OLvZuFgREbFXCr4if5OyahUpy1cA4Na8OUHPP2/jiiq5xO2wegic+IWzZhNxAf584O2Z97Kb9UamtZ9A+9pNbVaiiIgIKPiK5JO5bx/HY2IBcPDzIyxuBiYnJxtXVUnlZMLGqfDtTDAs/M/djZiAQM44XpzXYHXi3pD+TLt3sDaiEBGRSkF/G4lcZD13jmORwzAuXACTidDp03EKDrZ1WZXTsa2wahAk7yHZwczEgCD+5/HXFAZfUzivd5lI0+p1bVikiIhIfgq+IoBhGCRFx5B14AAAgc8+i2fbO21cVSWUdR7WT4If5mAYVlZ6ejDNP4BzDhdft7rzUJ1BjG3XTxtRiIhIpaPgKwKkLF/O2Y8/BsD9jtsJHDzIxhVVQn98n7tiw+mDHHV0JCowiC1uf23bHOJ4O/O7TqC2nzaiEBGRyknBV+xexu+/c2LiJAAcg4IImz4dk4PDVVrZkcx0+F8M/LiAHOAdHy9m+/qRZc592WTxYVDjF/hXy542LVNERORqFHzFrlnS0jgWGYmRlQVmM2FxM3AMDLR1WZXHgfXw8VBIOcJuZydeDgzkd5e/PuxXz+1eFnR7mUAPX9vVKCIiUkwKvmK3DMMgadx4sv84AkBQZCTuLVvauKpKIiMV1o6HbW+TYTIxz8+HhT4+WC9O23W0VGNMq5fp0yjCtnWKiIiUgIKv2K0z775H2hdfAOAR0Y6AAU/ZuKJKYu9aWBMJZxPY4upCVGAAR51yf1QYhpkWvg/yRtcXtBGFiIhUOQq+Ypcu7NzJiWnTAHAMCSH0lVcwmc02rsrGzp+GL8bAjiWkmUzEBfixwtsr72VXay2mRUykQ52mtqtRRESkFBR8xe5YUlJIiBwG2dng6MgN8XE4+vnZuizb+n0NfDIc0k+wzt2NCQH+JDte/ICf1Yl7qvdj+n2DcXLQZh4iIlJ1KfiKXTGsVhJffInsxEQAgkeNxK1pU9sWZUvnkuHTUbDrQ5IdzEyuFsiXHu55L/twC693msRtodqIQkREqj4FX7Erp996i/QNGwDwurcjfv362bYgWzEM+PUD+OwFjPOnWOXpwXR/P9IcLk73sLrRp/Ygxkf010YUIiJy3VDwFbtxfutWTsbPBMCpRg1CJk2yz1CXdhw+GQG713DU0YGY6tXY7Oaa93J1h9bM7zGBOv4hNixSRESk7Cn4il3IOXWKhOEjwGLB5ORE2Mx4HLy9bV1WxTIM2LEEPn+RnIxU3vP24nU/XzLNueHfZPHhX+EjGdS6l23rFBERKScKvnLdMywWEkeNIufkSQCCx47BLTzcxlVVsNRj8HEk7P+SPc5ORIUGs8vlr+2G67p2ZEG3KII8fW1WooiISHlT8JXrXvK8eZz7fhMA3t264fvQQzauqAIZBvy0CNaOJzM7jfl+Przl443l4hQPR0s1Xmo5nr6N29u0TBERkYqg4CvXtXObNpE8+w0AnGvXpnpMjP3M6z1zGD56Dg59zVZXF2JCQzjsnLscmWGYaebTize6jsbLxf3K1xEREblOKPjKdSv7xEkSRo4Cw8Dk6krYrJk4eHrYuqzyZ7XCln/DV9Gk5VxgZoAfy/JtRFGTKXfF0rFucxsWKSIiUvEUfOW6ZOTkkDhiBJZTpwCoHhWFa/36Nq6qAiTvh4+GwJFNrHd3Y2L1EE46XvzP3OpIh+DHefW+53B21EYUIiJifxR85br052uvc37rVgB8/vEgvg/0sm1B5c1qgU1vwPpJJFuzeCUogC8ue7rtTUNeu28yzcPq2bBIERER21LwletO+saNnFqwAACX+vWpPm6cjSsqZyd/h9WDMRJ+YrWnB9P9QzjrcGm7YVf+ceOzvBzxBGaz2bZ1ioiI2JiCr1xXshMTSXxhNABmd3fCZs7E7OZm46rKiSUbvpsJG6dx1GQhtnoQP1z2XoMdWjKv+wTqBoTZrkYREZFKRMFXrhtGVhYJw4ZjSU0FIGTiBFzq1LZxVeUkaSesHoTl+C+86+3FbD8fMi4+0TVZvBl4ywieu/1BGxcpIiJSuSj4ynXj5Iw4LuzYAYDfo4/g3bWrjSsqBzmZ8PWr8G0cexxMRIcG8+tlG1HUcbmHBd2jCPb0s2GRIiIilZOCr1wXzn75JafffhsA1/Bwqr34oo0rKgcJP8GqwWQm/84CHx/e8vUm5+KaxA6WIF5oMY5Hb73bxkWKiIhUXgq+UuVlHTlC0ktjADB7eRE2Mx6zs7ONqypD2RdgwxT4/nW2OTsRHRrCocs2orjN+37e6Poi3q7aiEJERORKFHylSrNmZnIsMhJrejoAoVMm41yjho2rKkNHfoDVg0k/fYCZ/r4svWwjChdrDSa1nUCnetqIQkREpDgUfKVKOzFlCpm//Q6A/xNP4NWxo40rKiNZ5+B/EzA2z+NrNxcm3BDCiYsbURhWR9pX+ydxnYZqIwoREZESUPCVKiv14zWkvL8UALemTak2YriNKyojh76G1UM4dfYoU4P8+eyyjSi8jIbMunciLW9oYMMCRUREqiYFX6mSMg8eJCkqCgAHX1/C4uMwOVXxp58ZZ+GrKIytb/GxpwfTbggh9bKNKHrV+hcx7Z/URhQiIiLXSMFXqhzrhQskPP88xvnzAIROm4pTSIiNqyqlfV/Bx8+TcD6J2OAgvnf/ayOKauYWzO02kfqB2ohCRESkNBR8pco5HjuBzH37AQh45hk827WzcUWlcOEMfDEWy/b3WOztxethIVy4bCOK/7t5OJF3/MPGRYqIiFwfFHylSkn54ENSV64EwL1VK4KeG2Ljikph96ewZhh7M08RHRLML65/bURR2+Vu5neLIsTL34YFioiIXF8UfKXKyNizh+OxsQA4BAYS+up0TI5VcAifOwWfjybrl+Us8PXhzcDql21EEcjI5mP5Z5PrZHUKERGRSqQKpgaxR5b0cyQ8H4mRmQlmM2GvvopTtWq2Lqvkdq2ET0bys+UsUWH5N6K41asnc7u9iI+rx1UuIiIiItdCwVcqPcMwOP7yy2QdPgxA0HND8Li9tW2LKqm0E/DpSM7t/jh3IwqvYIyLT3ldLDWY2DaWzvVb2LhIERGR65uCr1R6Ke+/z9lPPwXAo21bAp55xsYVlYBhwM5lGJ+P5hsuEPu3jSjaBT1GXOehuDpeR1ssi4iIVFIKvlKpXfh1FycmTwHAMTiY0GlTMVWVdWzPJsKaYZzev5ZXAvz4zPOvqRmeRgNmdpxI6xoNbVigiIiIfVHwlUrLcvYsCZGRGNnZ4OBAWHwcjv5VYJUDw4Cf38H6xVg+ccph2g0hpFy2EcX9NZ4h5u4ncTA72LZOERERO6PgK5WSYRgkjhlD9rFjAFQbPhz3Zs1sXFUxnPkDPh5K4pFviA3w5zt337yXgszNmdt1Ig2CbrBdfSIiInZMwVcqpdOL3ib9q/8B4NmhA/7/96SNK7oKqxW2vknOV9G872ritXwbUXjxZMPcjShMFz/QJiIiIhVPwVcqnfPbfubkjBkAOIWFEfrKlModGE8dgI+eY3/ij0QF+rPzso0oajm3Z0H3GEK1EYWIiIjNKfhKpZJz5gwJw4dDTg44ORE2Mx4HHx9bl1U4qwU2zyPzfxP4j6cz/wnLvxHFiGZjeLzpvTYuUkRERC5R8JVKw7BaSXxhNDnHjwMQPHo0bo0b27iqIvy5B1YPZvufO4gKDuDgxY0oMEw08uzBvO4v4ePqadsaRUREJB8FX6k0Ti34N+e++QYAr86d8XvsURtXVAhLDnw/i/SNU3nN2533Q/7aiMLZcgMT7oyla4OWNi5SRERECqPgK5XCuc0/8udrrwHgXKsWIRMnVL55vcd/hdWD+TplNxNCAjh+cSMKrI60CXyEWV0itRGFiIhIJabgKzaX8+efJIwcAVYrJhcXwmbNxMGzEk0TyMmCb2Zw6rs4pvl58Wn1vzai8DDqE3/PJO6oqY0oREREKjsFX7Epw2IhYeQoLH8mA1B9/DhcG1aiEJn4M9ZVz/LJuT+YFhp02UYULnS/4Wkm3vOUNqIQERGpIir13q+ZmZmMHj2a0NBQ3NzcaN26NV9++WWx2iYkJNC3b198fX3x9vbm/vvv5+DBg1ds8+2332IymTCZTCQnJ5fJNeXKkt94g/ObNwPgc//9+PzjHzau6KLsDPgqhoS37mOwKZkx1QLzQm+AqRlLu61kyr1PK/SKiIhUIZX6ie8TTzzBihUriIyMpF69eixatIiuXbuyfv162rZtW2S79PR0OnToQGpqKmPGjMHJyYn4+HgiIiLYvn07AQEBBdpYrVaee+45PDw8OHfuXJlcU64s/ZtvSZ47DwDnujdRPerlyjGv9+iP5KwaxNLsJGaFVbtsIwpP+tUfxog7+1SOOkVERKREKm3w/fHHH3n//feZPn06I0eOBKBfv340atSIF154ge+//77ItnPmzGHfvn38+OOPtGyZ+wn7Ll260KhRI2bMmMHkyZMLtFmwYAFHjx5lwIABzJo1q0yuKUXLPn6cxBdeAMPA5ObGDbNmYXZ3t21RWedh3UT2/7SA6EB/dnj/telETacIFvSKJswn0IYFioiISGlU2qkOK1aswMHBgaeffjrvmKurK0899RSbNm3i6NGjV2zbsmXLvIAK0LBhQ+655x6WLVtW4PzTp08zbtw4YmNj8fX1LZNrStGM7GwSho/AcuYMACEx0bjcdJNtizr8LZlz72Du7nfoE1adHRd3X3OwBDCi8Qw+eXS2Qq+IiEgVV2mD788//0z9+vXx9vbOd7xVq1YAbN++vdB2VquVnTt30qJFiwKvtWrVigMHDpCWlpbv+Pjx46levTrPPPNMmV3z706ePMmuXbvyfe3fv/+Kba5XJ2fO5MK2bQD49u2LT8+etismMw0+GcGOJQ/wsHsGc/x8c3dfM0zc4t6D9Y+s4Ylm99muPhERESkzlXaqQ1JSEiEhIQWOXzqWmJhYaLvTp0+TmZl51bYNGjQAYOfOncyfP59PP/0UB4fCP6hU0msWZs6cOcTExBT5ur1IW7eO02++BYDLzTcTPHaM7Yo5sI701UOZ7ZjO4nwbUYQRdUcMPW9ubbvaREREpMxV2uB74cIFXFxcChx3dXXNe72odkCx2w4dOpQuXbpw331FP9Ur6TULM2jQIPr06ZPv2P79++nVq9cV211Pso4dI/HFlwAwe3hww8x4zIX0abm7kAJrx/Ht7uXEBvqT5OiVe9xw4A7/h5nVZRhuTjaoS0RERMpVpQ2+bm5uZGZmFjiekZGR93pR7YBitV26dCnff/89v/7661VrKe41i1KtWjWqVat2xXOuZ9asLBIih2E9exaAkEmTcK5Vq+IL2fsFyR8/zwzXLNZcvhGFtS6v3j2RtrXCK74mERERqRCVNviGhISQkJBQ4HhSUhIAoaGhhbbz9/fHxcUl77wrtR01ahR9+vTB2dmZw4cPA5CSkgLA0aNHycrKIjQ0tETXlMKdnDqNjIu/YPg9/jjenTtVbAHnT2P97AU+O/gJUwP8OOPgAYDJ6kznsIFM6ThQa/KKiIhc5ypt8G3atCnr16/n7Nmz+T7gtvniZgdNmzYttJ3ZbKZx48Zs3bq1wGubN2+mTp06eHnl/tP20aNHWbx4MYsXLy5wbrNmzWjSpAnbt28v0TWloLOffcaZ994DwPXWWwkeNbJiC/jtI459OoLJHgbfVPtrZQZ/mjKn60TCg23w5FlEREQqXKVd1aF3795YLBYWLFiQdywzM5OFCxfSunVratSoAcCRI0fYvXt3gbZbtmzJF1T37NnDunXr8s2zXblyZYGvhx56CID//ve/xMfHl/iakl/moUMkjRsPgNnHh7C4OEzOzhVz8/Q/yXm/H4s/e5Z/BDjzjXvudBSzxZ1/1hnLhn7/VegVERGxIybDMAxbF1GUvn37snLlSoYNG0bdunV5++23+fHHH/nf//5Hu3btAGjfvj0bN27k8reRlpbGbbfdRlpaGiNHjsTJyYm4uDgsFgvbt28nKCioyHtGR0cTExPDn3/+SWBgYJlcsyi7du2iUaNG/Prrr4SHX39zS60ZGRx+6GEy9+wB4Ia5c/Dq0KH8b2wY8MsK9q4dzQQvR7a7/vVBtRsc72J+txhq+pb8z0tEREQql5JmqUo71QFyn7qOHz+ed955hzNnznDrrbeyZs2avNBbFC8vLzZs2MCwYcOYOHEiVquV9u3bEx8ff00Btbyueb07MWlSXugNGPBUxYTes0lkfPQ8C5M38e9AH7IvLlHmaPFlSJOxPNW8c/nXICIiIpVSpX7ie727np/4pqxaRdLFpcvcWjSn1qJFmBzL8fcsw4Dti/n5q7HE+rqw/9J0CgMaenRjQfdx+Ll5lt/9RUREpMJdV098pWrK3LeP4zGxADj4+xM2Y0b5ht6Uo5xdPYS5qdt5L8grbyMKF0sw426fQK9b7ii/e4uIiEiVoeArZcp67hzHIodhXLgAJhOh06fhFBxcTjezwk8L+XpjLJN83Un0yV39w2SYaeX3MK93GY6bszaiEBERkVwKvlJmDMMgKTqGrAMHAAgcNAjPO+8sn5udPsTJlc8y88JePg76a7k7T0ttpnWYzF21G5XPfUVERKTKUvCVMpOyfDlnP/4YAPc7bidw0LNlfxOrFesPc/l00zSm+3lw2it3Iwqz1ZF7QwYy9b5ntBGFiIiIFErBV8pExu+/c2LiJAAcg4IImz4dk0MZB9DkffzxwdNMtx5lY+BfT3kDCOf1Lq/QuPqNZXs/ERERua4o+EqpWdLSOBYZiZGVBWYzYXEzcLxsDeTS3yCHnO9eZ9nWeF7z8+KcOXcjCieLK33rDmP0XY9guviBNhEREZGiKPhKqRiGQdLYcWT/cQSAoMhI3Fu2LLsbnPiN3z8YyBSHk/wc4JN3uIbDHczrOYmaflpDWURERIpHwVdK5cw775K2di0AHhHtCBjwVNlc2JLNhY3TeHvnAhb4epFtcgXAJceLZ24dx8CWXcvmPiIiImI3FHzlml3YsYMT06cD4BgSQugrr2Aym0t/4aQdbPlwAFOcz7LP7+JcXgNuduvE3O5RBHh4lf4eIiIiYncUfOWaWFJSODZsGGRng6MjN8TH4ejnV7qL5mSS+tVE5u19l8XeHlhNubuveeQEMPr2yTwQ3qYMKhcRERF7peArJWZYrSS++BI5iUkABI8aiVvTpqW76LGtrFs5kGluGST45G4tbDZMtPDpw+vdXsBdG1GIiIhIKSn4Somdfust0jdsAMDr3o749et37RfLvkDSZ+OYfWQlH3l7cGlI+lrCmNB+Ou3rNC59wSIiIiIo+EoJnd+6lZPxMwFwqlGDkEmTrnkpMeuhb/no42eJ97TkbUThZDXTofpTTL1vMI5lvQ6wiIiI2DUFXym2nFOnSBg+AiwWTM7OhM2Mx8Hb++oN/y4znQNrXiD+xFo2+rgBuQE32FqPuM5x3BpyY5nWLSIiIgIKvlJMhsVC4qhR5Jw8CUDwmDG4hYeX+Do5+9bx3mdDmOtl4pxH7kYUrhYnetUZzkvtHsVcFqtCiIiIiBRCwVeKJXnePM59vwkA7+7d8X2ob8kukJHKL6ue59XU79jm45p3+EZTU15/4FVu9Asuy3JFREREClDwlas6t2kTybPfAMC5Th1CYqJLNK/3/G+f8tZXI1jo5UCWa27o9chx5clGUTzTunu51CwiIiLydwq+ckXZJ06SMHIUGAYmV1fCZsZj9vAoXuPzp/nug2eJu7CdvT65a/KaDAh3vovXe79CoMc1zA8WERERuUYKvlIkIyeHxBEjsJw6BUD1qChc69cvVtsz25cz95vxLPVyxOqSG3p9s714vvU0ejduW241i4iIiBRFwVeK9Odrr3N+61YAfP7xIL4P9Lp6o3PJfLbs/5hl2UeCtxMADga08uhGfM8YPFy0EYWIiIjYhoKvFCptwwZOLVgAgEv9+lQfN+7KDQyDhB/f5vWtU/jE0xnMuUMrONufsR1ep8NNt5Z3ySIiIiJXpOArBWQnJJA4+kUAzO7uhM2cidnNrcjzrWeTWL60P3PNxzjlmTutwdlq4u6AR5jcdRROjhpmIiIiYntKJJKPkZXFseHDsaamAhAycQIudWoXcbLBvm/eYOau1/na3ZlLG1HUzAllUue5NA2rU0FVi4iIiFydgq/kc3LGDDJ27ATA79FH8O7atdDzcs4c4a1lj7PQOZl099ynvO4WM/fXeJYX73laG1GIiIhIpaPgK3nOrl3L6bf/C4BreDjVXnyx4EmGwU9fTWXWwUX87OoE5Abchpa6TOs1j9r+2ohCREREKicFXwEg68gRksaMBcDs5ZW7Xq+zc75zzp/cx5wP+7HEJY0s19wVG3xzHHis/ov8666HK7xmERERkZJQ8BWsmZkci4zEmp4OQOiUyTjXqHHZCVbWfTqe2YkfsM/NCTBhMgyamZsy7aE3qObpY5vCRUREREpAwVc4MWUKmb/9DoD/k0/i1bFj3mtnEnYy86OnWOV2AatL7lPeatnO/KvZJPo062yTekVERESuhYKvnUv9eA0p7y8FwK1pU6oNH5b7gtXCqpUjmHfmCxLcHQETjoZBW+e2THl4Jp4urrYrWkREROQaKPjascyDB0mKigLAwdeXsPg4TE5OHDuwibi1g/jSPQeccodIjSx3Rt41i7sb3m7LkkVERESumYKvnbJeuEDC889jnD8PQOj0aTgE+rNwyQDePv89p9xz1+R1tRrc59mFqMem4KyNKERERKQKU5KxU8djJ5C5bz8AAf96hmP+mcx4syU/uBngmBt662f5MPa+eTSr1ciWpYqIiIiUCQVfO5TywYekrlwJgFvLFizx/YH3f/w36W65a/J6WQweCHyYEd3HaCMKERERuW4o+NqZjD17OB4bC4DVx5PJTX9mk8kEptyAe1t2EC/3WEjd4Fq2LFNERESkzCn42hFL+jkSno/EyMzEMMGULufZEZgbeANz4LGazzDg3iE2rlJERESkfCj42gnDMDj+8niyDh8GYOldZnbUNmMyDNpaahLV+22CfYJsW6SIiIhIOVLwtROJby7g7KefAbC9tomVbUyEZcPTDV/gwbb9bFydiIiISPlT8LUDq/8zljrxH+IInPKCOT1MdKYB4x9bhJebl63LExEREakQCr7Xuczz5/B780McLWAxwfKujsS2nkSH5j1tXZqIiIhIhdJaVdc5F3cPLgx4mNOesOvuG5g+dqtCr4iIiNglPfG1A52eiuJo+wdpU6cRJpPJ1uWIiIiI2ISCr52ocVNjW5cgIiIiYlOa6iAiIiIidkHBV0RERETsgoKviIiIiNgFBV8RERERsQsKviIiIiJiFxR8RURERMQuKPiKiIiIiF1Q8BURERERu6DgKyIiIiJ2QcFXREREROyCgq+IiIiI2AUFXxERERGxCwq+IiIiImIXFHxFRERExC4o+IqIiIiIXVDwFRERERG74GjrAuxZZmYmAPv377dxJSIiIiJVz6UMdSlTXY2Crw0dPXoUgF69etm2EBEREZEq7OjRozRr1uyq55kMwzAqoB4pREpKChs3bqRGjRq4uLiU6732799Pr169WLVqFXXr1i3Xe9kz9XPFUD9XDPVzxVA/Vxz1dcWoyH7OzMzk6NGjRERE4Ovre9Xz9cTXhnx9fbn//vsr9J5169YlPDy8Qu9pj9TPFUP9XDHUzxVD/Vxx1NcVo6L6uThPei/Rh9tERERExC4o+IqIiIiIXVDwFRERERG7oOBrJ4KCgoiKiiIoKMjWpVzX1M8VQ/1cMdTPFUP9XHHU1xWjMvezVnUQEREREbugJ74iIiIiYhcUfEVERETELij4ioiIiIhdUPAVEREREbug4CsiIiIidkHBtwpLT08nKiqKzp074+/vj8lkYtGiRcVun5KSwtNPP01QUBAeHh506NCBbdu2lV/BVVhp+nrRokWYTKZCv44fP16+hVchW7ZsYciQIYSHh+Ph4UHNmjXp27cve/fuLVZ7jefiKU0/aywX365du+jTpw916tTB3d2dwMBA2rVrx8cff1ys9hrPxVeavtaYvnaTJk3CZDLRqFGjYp2fkJBA37598fX1xdvbm/vvv5+DBw+Wc5UFOVb4HaXMJCcnExsbS82aNWnSpAkbNmwodlur1Uq3bt3YsWMHo0aNIjAwkDlz5tC+fXt++ukn6tWrV36FV0Gl6etLYmNjqV27dr5jvr6+ZVPgdWDq1Kl899139OnTh1tvvZXjx48ze/ZsmjVrxg8//HDFH64az8VXmn6+RGP56v744w/S0tLo378/oaGhnD9/ng8++ICePXsyf/58nn766SLbajyXTGn6+hKN6ZI5duwYkydPxsPDo1jnp6en06FDB1JTUxkzZgxOTk7Ex8cTERHB9u3bCQgIKOeKL2NIlZWRkWEkJSUZhmEYW7ZsMQBj4cKFxWq7dOlSAzCWL1+ed+zkyZOGr6+v8cgjj5RHuVVaafp64cKFBmBs2bKlHCus+r777jsjMzMz37G9e/caLi4uxmOPPXbFthrPxVeaftZYLp2cnByjSZMmRoMGDa54nsZz6RW3rzWmr81DDz1k3H333UZERIQRHh5+1fOnTp1qAMaPP/6Yd+z33383HBwcjJdeeqk8Sy1AUx2qMBcXF6pXr35NbVesWEFwcDAPPvhg3rGgoCD69u3L6tWryczMLKsyrwul6evLpaWlYbFYyqCi60+bNm1wdnbOd6xevXqEh4fz+++/X7GtxnPxlaafL6exXHIODg7UqFGDlJSUK56n8Vx6xe3ry2lMF8/XX3/NihUrmDlzZrHbrFixgpYtW9KyZcu8Yw0bNuSee+5h2bJl5VBl0RR87dTPP/9Ms2bNMJvzD4FWrVpx/vz5Ys+rlOLr0KED3t7euLu707NnT/bt22frkio9wzA4ceIEgYGBVzxP47l0itvPl2gsF9+5c+dITk7mwIEDxMfH89lnn3HPPfdcsY3G87W5lr6+RGO6eCwWC8899xwDBgygcePGxWpjtVrZuXMnLVq0KPBaq1atOHDgAGlpaWVdapE0x9dOJSUl0a5duwLHQ0JCAEhMTCz2oJYrc3d354knnsj7wfrTTz8RFxdHmzZt2LZtGzVq1LB1iZXWe++9R0JCArGxsVc8T+O5dIrbzxrLJTdixAjmz58PgNls5sEHH2T27NlXbKPxfG2upa81pktm3rx5/PHHH3z11VfFbnP69GkyMzPzxu/lLh/TDRo0KLM6r0TB105duHABFxeXAsddXV3zXpey0bdvX/r27Zv3fa9evejUqRPt2rVj0qRJzJs3z4bVVV67d+9m8ODB3HHHHfTv3/+K52o8X7uS9LPGcslFRkbSu3dvEhMTWbZsGRaLhaysrCu20Xi+NtfS1xrTxXfq1Clefvllxo8fT1BQULHbXRqvlWVMa6qDnXJzcyt0nlhGRkbe61J+2rZtS+vWrUv0W7M9OX78ON26dcPHx4cVK1bg4OBwxfM1nq9NSfu5MBrLV9awYUM6duxIv379WLNmDenp6fTo0QPDMIpso/F8ba6lrwujMV24cePG4e/vz3PPPVeidpfGa2UZ0wq+diokJISkpKQCxy8dCw0NreiS7E6NGjU4ffq0rcuodFJTU+nSpQspKSl8/vnnxRqLGs8ldy39XBSN5eLr3bs3W7ZsueI8XY3nslGcvi6KxnR++/btY8GCBQwdOpTExEQOHz7M4cOHycjIIDs7m8OHDxfZX/7+/ri4uFSaMa3ga6eaNm3Ktm3bsFqt+Y5v3rwZd3d36tevb6PK7MfBgwdL9M9F9iAjI4MePXqwd+9e1qxZwy233FKsdhrPJXOt/VwUjeXiu/RPuqmpqUWeo/FcNorT10XRmM4vISEBq9XK0KFDqV27dt7X5s2b2bt3L7Vr1y7yMwJms5nGjRuzdevWAq9t3ryZOnXq4OXlVd5v4a96KuxOYjNJSUns3r2b7OzsvGO9e/fmxIkTfPjhh3nHkpOTWb58OT169Ch0Lo5cXWF9/eeffxY479NPP+Wnn36ic+fOFVlepWaxWHjooYfYtGkTy5cv54477ij0PI3n0ilNP2ssF9/JkycLHMvOzua///0vbm5ueb9saDyXXmn6WmO6eBo1asTKlSsLfIWHh1OzZk1WrlzJU089BcCRI0fYvXt3vvaXnr5fHn737NnDunXr6NOnT4W+F5NR0skvUqnMnj2blJQUEhMTmTt3Lg8++CC33XYbAM899xw+Pj488cQTvP322xw6dIgbb7wRyP3Lr23btvz666/5dgY6cuQIW7ZsqbBPV1Yl19rX9erV47bbbqNFixb4+Piwbds23nrrLUJCQtiyZQvBwcE2fFeVR2RkJLNmzaJHjx75PmxyyT//+U8AjedSKk0/aywX3wMPPMDZs2dp164dYWFhHD9+nPfee4/du3czY8YMhg8fDmg8l4XS9LXGdOm0b9+e5ORkfv3113zHNm7cmG9udVpaGrfddhtpaWmMHDkSJycn4uLisFgsbN++vWKfrlfodhlS5mrVqmUAhX4dOnTIMAzD6N+/f77vLzl9+rTx1FNPGQEBAYa7u7sRERGh3Wuu4Fr7euzYsUbTpk0NHx8fw8nJyahZs6bx7LPPGsePH7fNG6mkIiIiiuzfy39UaTyXTmn6WWO5+JYsWWJ07NjRCA4ONhwdHQ0/Pz+jY8eOxurVq/Odp/FceqXpa43p0ils57ZLP2P+7ujRo0bv3r0Nb29vw9PT0+jevbuxb9++iio1j574ioiIiIhd0BxfEREREbELCr4iIiIiYhcUfEVERETELij4ioiIiIhdUPAVEREREbug4CsiIiIidkHBV0RERETsgoKviIiIiNgFBV8RERERsQsKviIiIiJiFxR8RUTELphMJqKjo21dhojYkIKviMhFXbp0wc/PjxMnThR4LTU1lZCQEFq3bo3VarVBdcXz22+/ER0dzeHDh8v0uosWLcJkMmEymfj2228LvG4YBjVq1MBkMtG9e/drusfkyZNZtWpVKSstvu+//57o6GhSUlIq7J4iYlsKviIiF82ZM4esrCyGDRtW4LUxY8aQnJzMggULMJsr74/O3377jZiYmDIPvpe4urqyePHiAsc3btzIsWPHcHFxueZrl3fwvXDhAuPGjcv7/vvvvycmJkbBV8SOVN6f3iIiFax27dpERUWxZMkS1q5dm3d8y5YtzJs3j+HDh9OkSZNyrSEjI6NSP1Hu2rUry5cvJycnJ9/xxYsX07x5c6pXr26jygpntVrJyMgAckO7o6OjjSsSEVtS8BURuczw4cO59dZbGTRoEBkZGVgsFv71r39Rq1YtoqKi2L17N71798bf3x9XV1datGjBRx99lO8ap0+fZuTIkTRu3BhPT0+8vb3p0qULO3bsyHfehg0bMJlMvP/++4wbN46wsDDc3d05e/Ys2dnZxMTEUK9ePVxdXQkICKBt27Z8+eWXRda+aNEi+vTpA0CHDh3ypiZs2LAh75w5c+YQHh6Oi4sLoaGhDB48uERPPB955BFOnTqVr46srCxWrFjBo48+WmibV199lTZt2hAQEICbmxvNmzdnxYoV+c4xmUycO3eOt99+O6/uJ554AoAnnniCG2+8scB1o6OjMZlMBa4zZMgQ3nvvvbz3+fnnn+e9dmmOb3R0NKNGjQJyf+G5dM/Dhw8TERFR5C84DRo0oFOnTlftJxGpnPSrr4jIZRwdHVmwYAFt2rRhwoQJVKtWjW3btvH5559z6NAh7rzzTsLCwnjxxRfx8PBg2bJl9OrViw8++IAHHngAgIMHD7Jq1Sr69OlD7dq1OXHiBPPnzyciIoLffvuN0NDQfPecMGECzs7OjBw5kszMTJydnYmOjmbKlCkMGDCAVq1acfbsWbZu3cq2bdu49957C629Xbt2DB06lNdee40xY8Zw8803A+T9b3R0NDExMXTs2JFnn32WPXv2MHfuXLZs2cJ3332Hk5PTVfvnxhtv5I477mDJkiV06dIFgM8++4zU1FQefvhhXnvttQJtZs2aRc+ePXnsscfIysri/fffp0+fPqxZs4Zu3boB8M477+S916effhqAm266qTh/ZAWsW7eOZcuWMWTIEAIDAwsNzQ8++CB79+5lyZIlxMfHExgYCEBQUBCPP/44AwcO5Ndff6VRo0Z5bbZs2cLevXvzTZcQkSrGEBGRAoYMGWI4OTkZnp6exiOPPGIYhmHcc889RuPGjY2MjIy886xWq9GmTRujXr16eccyMjIMi8WS73qHDh0yXFxcjNjY2Lxj69evNwCjTp06xvnz5/Od36RJE6Nbt24lrnv58uUGYKxfvz7f8ZMnTxrOzs7Gfffdl6+22bNnG4Dx1ltvXfG6CxcuNABjy5YtxuzZsw0vL6+8mvv06WN06NDBMAzDqFWrVoG6//7esrKyjEaNGhl33313vuMeHh5G//79C9y7f//+Rq1atQocj4qKMv7+1xhgmM1mY9euXQXOB4yoqKi876dPn24AxqFDh/Kdl5KSYri6uhqjR4/Od3zo0KGGh4eHkZ6eXuDaIlI1aKqDiEghJk2aREBAAGazmfj4eE6fPs26devo27cvaWlpJCcnk5yczKlTp+jUqRP79u0jISEBABcXl7wPwFksFk6dOoWnpycNGjRg27ZtBe7Vv39/3Nzc8h3z9fVl165d7Nu3r0zez1dffUVWVhaRkZH5Ppw3cOBAvL29+eSTT4p9rb59+3LhwgXWrFlDWloaa9asKXKaA5DvvZ05c4bU1FTuuuuuQvuiLERERHDLLbdcc3sfHx/uv/9+lixZgmEYQO6f49KlS+nVqxceHh5lVaqIVDAFXxGRQnh7e9OgQQNq1KhBcHAw+/fvxzAMxo8fT1BQUL6vqKgoAE6ePAnkfqAqPj6eevXq4eLiQmBgIEFBQezcuZPU1NQC96pdu3aBY7GxsaSkpFC/fn0aN27MqFGj2Llz5zW/nz/++APInaN6OWdnZ+rUqZP3enEEBQXRsWNHFi9ezIcffojFYqF3795Fnr9mzRpuv/12XF1d8ff3JygoiLlz5xbaF2WhsP4sqX79+nHkyBG++eYbIPcXhxMnTvD444+X+toiYjua4ysiUgyXVloYOXJkkR9uqlu3LpC7LNf48eP5v//7PyZMmIC/vz9ms5nIyMhCV2z4+9NeyJ2ve+DAAVavXs3atWv5z3/+Q3x8PPPmzWPAgAFl+M6uzaOPPsrAgQM5fvw4Xbp0wdfXt9DzvvnmG3r27Em7du2YM2cOISEhODk5sXDhwkKXRSvM3z/AdonFYin0eGH9WVKdOnUiODiYd999l3bt2vHuu+9SvXp1OnbsWOpri4jtKPiKiBRDnTp1AHBycrpq+FmxYgUdOnTgzTffzHc8JSUl70NUxeHv78+TTz7Jk08+SXp6Ou3atSM6OvqKwbeokFirVi0A9uzZk/deIHdFhkOHDpU40D3wwAM888wz/PDDDyxdurTI8z744ANcXV354osv8q3xu3DhwmLX7ufnV+jKEyV5Sl2You4H4ODgwKOPPsqiRYuYOnUqq1atYuDAgTg4OJTqniJiW5rqICJSDNWqVaN9+/bMnz+fpKSkAq//+eefef/fwcEhb27oJcuXL8+bA1wcp06dyve9p6cndevWJTMz84rtLs0//XtQ7NixI87Ozrz22mv5anvzzTdJTU3NW12huDw9PZk7dy7R0dH06NGjyPMcHBwwmUz5ns4ePny40I0qPDw8Cg24N910E6mpqfmmeiQlJbFy5coS1VzY/aBgX13y+OOPc+bMGZ555hnS09P55z//War7iYjt6YmviEgxvfHGG7Rt25bGjRszcOBA6tSpw4kTJ9i0aRPHjh3LW6e3e/fuxMbG8uSTT9KmTRt++eUX3nvvvXxPWq/mlltuoX379jRv3hx/f3+2bt3KihUrGDJkyBXbNW3aFAcHB6ZOnUpqaiouLi7cfffdVKtWjZdeeomYmBg6d+5Mz5492bNnD3PmzKFly5bXFOr69+9/1XO6detGXFwcnTt35tFHH+XkyZO88cYb1K1bt8Cc5ebNm/PVV18RFxdHaGgotWvXpnXr1jz88MOMHj2aBx54gKFDh3L+/Hnmzp1L/fr1S/UBuebNmwMwduxYHn74YZycnOjRo0deIL7tttto1KgRy5cv5+abb6ZZs2bXfC8RqSRsu6iEiEjlFRERYYSHh+c7duDAAaNfv35G9erVDScnJyMsLMzo3r27sWLFirxzMjIyjBEjRhghISGGm5ubceeddxqbNm0yIiIijIiIiLzzLi1ntnz58gL3njhxotGqVSvD19fXcHNzMxo2bGhMmjTJyMrKumrd//73v406deoYDg4OBZY2mz17ttGwYUPDycnJCA4ONp599lnjzJkzV73m5cuZXUlhy5m9+eabRr169QwXFxejYcOGxsKFCwtdimz37t1Gu3btDDc3NwPIt7TZ2rVrjUaNGhnOzs5GgwYNjHfffbfI5cwGDx5caG38bTkzwzCMCRMmGGFhYYbZbC50abNp06YZgDF58uQrvm8RqRpMhvG3f48TERERIHfzjWHDhnH48GFq1qxp63JEpJQUfEVERAphGAZNmjQhICCA9evX27ocESkDmuMrIiJymXPnzvHRRx+xfv16fvnlF1avXm3rkkSkjOiJr4iIyGUOHz5M7dq18fX1ZdCgQUyaNMnWJYlIGVHwFRERERG7oHV8RURERMQuKPiKiIiIiF1Q8BURERERu6DgKyIiIiJ2QcFXREREROyCgq+IiIiI2AUFXxERERGxCwq+IiIiImIXFHxFRERExC4o+IqIiIiIXfh/WbtrC5y9cVQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = [price[0]/100]\n",
    "\n",
    "for i in range(1, len(coupon)):\n",
    "    pv_cf = np.sum(np.full(i, coupon[i]) * np.array(df))\n",
    "    df.append((price[i] - pv_cf) / (100 + coupon[i]))\n",
    "    \n",
    "df = np.array(df)\n",
    "print(\"Discount Factors = \",df)\n",
    "\n",
    "spots = df**-(1/years) - 1\n",
    "print(\"Implied Spot Rates = \",spots)\n",
    "\n",
    "par_rates = (1-df)/np.cumsum(df)\n",
    "print(\"Par Rates = \",par_rates)\n",
    "\n",
    "forwards = df[:-1]/df[1:] - 1 # Implied forward rates as ratios of consecutive discount factors.\n",
    "forwards = np.insert(forwards, 0, spots[0], axis=0)\n",
    "print(\"Implied Forwards Rates = \", forwards)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(num=0, dpi=120)\n",
    "plt.plot(years, ytm, label=\"YTM\")\n",
    "plt.plot(years, spots, label=\"Spot Curve\")\n",
    "plt.plot(years, par_rates, label=\"Par Curve\")\n",
    "plt.plot(years, forwards, label=\"IFR\")\n",
    "plt.title('Yield Curves - Benchmark Government Bonds')\n",
    "plt.xlabel('Years to Maturity')\n",
    "plt.ylabel('Yield')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "11.\tAssuming no arbitrage in the government bond market, the yield on 2-year zero-coupon bonds should be closest to:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If there are no arbitrage opportunities in the government bond market, meaning that coupon-stripping and bond reconstitution break even (or any potential profit is not sufficient to cover transactions costs), the yield on 2-year zero-coupon bonds is the 2-year bootstrapped implied spot rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spot_2y = 4.397%\n"
     ]
    }
   ],
   "source": [
    "spot_2y = spots[1]\n",
    "print(f'{spot_2y = :0.3%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spot_2y = 4.397%\n"
     ]
    }
   ],
   "source": [
    "# Method 2 \n",
    "spot_2y = zero_bond_ytm(2, price[1]-(coupon[1]*df[0]), 100 + coupon[1], 1)\n",
    "print(f'{spot_2y = :0.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "12.\tAssuming that coupon-stripping and bond reconstitution arbitrage strategies break even, the yield on 3-year zero-coupon bonds should be closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spot_3y = 4.635%\n"
     ]
    }
   ],
   "source": [
    "spot_3y = spots[2]\n",
    "print(f'{spot_3y = :0.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "13.\tThe bootstrapped 4-year implied spot rate is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "spot_4y = 4.971%\n"
     ]
    }
   ],
   "source": [
    "spot_4y = spots[3]\n",
    "print(f'{spot_4y = :0.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "14.\tAssuming no arbitrage in the government bond market, the yield to maturity on a 4-year, 6.375% annual coupon payment government bond should be closest to:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming no arbitrage, the theoretical fair price for a government bond is the present value of its cash flows using either the relevant implied spot rates or the discount factors. This assumes that the bond’s credit risk and liquidity are the same as the benchmark bonds used in the bootstrapping. Also, this neglects any tax effects, for instance, due to zero-coupon bonds being taxed differently than coupon bonds—OID versus non-OID bond taxation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The yield to maturity on a coupon bond is a “weighted average” of the spot rates, whereby the“weights” depend on the coupon rate. Given our assumption of no arbitrage—and the upward slope to the government bond yield curve—the yield to maturity is lower the higher is the coupon rate. More weight is placed on the shorter-term cash flows that have lower yields. The yield on the 0%, 4-year bond would be 4.9715%; the yield on the 5%, 4-year benchmark bond is 4.9296%. Therefore, the yield on the 6.375%, 4-year government bond must be lower than 4.9296%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gov_bond_price = 105.16981\n",
      "gov_ytm = 4.920%\n"
     ]
    }
   ],
   "source": [
    "gov_bond_cf = np.full(4, 6.375)\n",
    "gov_bond_cf[-1] += 100\n",
    "gov_bond_price = np.sum(gov_bond_cf * df)\n",
    "print(f'{gov_bond_price = :0.5f}')\n",
    "gov_ytm = coupon_bond_ytm(4, 6.375, gov_bond_price, 100, cf_freq=1, comp_freq=1)\n",
    "print(f'{gov_ytm = :0.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "15.\tBased on the information about the government bond market provided in Questions 11–14, the 3-year par yield is closest to: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The par yield is the coupon rate on a hypothetical bond that has a (flat) price equal to par value. It can be calculated from the implied spot rates or the discount factors.\n",
    "\n",
    "The 3-year, 4.75% government bond is priced at 100.375 to yield 4.6133%. The implied (i.e., no arbitrage) yield on a 3-year, 0% government bond is 4.6348%; its price would be 87.2914. Therefore, the yield on a hypothetical 3-year government bond priced at par value must be between 4.6133% and 4.6348%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "par_yield = 4.6139%\n",
      "par_rates[2] = 4.6139%\n"
     ]
    }
   ],
   "source": [
    "# Method 1\n",
    "par_yield = (1 - df[2])/np.sum(df[:3]) \n",
    "\n",
    "print(f'{par_yield = :0.4%}')\n",
    "\n",
    "# Method 2\n",
    "print(f'{par_rates[2] = :0.4%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "16.\tAn investor is choosing between (1) buying a 1-year, 3% annual coupon payment government bond and reinvesting the proceeds for the second year in another 1-year bond and (2) buying a 2-year, 5% annual coupon payment government bond. Both bonds are priced at par value. Which statement best reflects the investor’s view on the expected rate on 1-year government bonds if the first choice is preferred?\n",
    "    1. The 1-year rate one year into the future is expected to be above 3.00%.\n",
    "    2. The 1-year rate one year into the future is expected to be above 7.00%.\n",
    "    3. The 1-year rate one year into the future is expected to be above 7.04%.\n",
    "    4. **The 1-year rate one year into the future is expected to be above 7.14%.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In preferring to buy the 1-year bond and reinvest the proceeds, the investor clearly is expecting rates to rise. In particular, the investor expects the 1-year rate one year into the future to be above the 1y1y implied forward rate. That implied forward rate is the breakeven rate for the maturity choice decision.\n",
    "\n",
    "It is first necessary to get the 2-year spot rate using the bootstrapping technique to calculate the 1y1y forward. **The 1-year spot rate is 3.00% because the bond essentially has become a zero-coupon security**—it pays 103 per 100 in par value. Note that 5.00% is the yield on the 2-year coupon bond and cannot be used to calculate the implied forward rate. The 2-year spot rate is 5.0510%, obtained by solving for z."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_1y1y = 7.143%\n"
     ]
    }
   ],
   "source": [
    "spot_0y1y = 0.03\n",
    "spot_0y2y = (105 / (100 - (5/(1+ spot_0y1y))))**(1/2) - 1\n",
    "\n",
    "ifr_1y1y = ifr(spot_0y1y, 1, spot_0y2y, 2, 0, 1)\n",
    "print(f'{ifr_1y1y = :0.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Base your answers to Questions 17 and 18 on these price and yield data for zero-coupon government bonds. The prices are per 100 of par value and the yields to maturity are quoted on a semiannual bond basis.\n",
    "\n",
    "| Maturity | Price | Yield to Maturity |\n",
    "| -------- | ----- | ----------------- |\n",
    "| 1 Year   | 97.35 | 2.704%            |\n",
    "| 2 Years  | 91.68 | 4.391%            |\n",
    "| 3 Years  | 86.12 | 5.043%            |\n",
    "| 4 Years  | 80.77 | 5.411%            |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm = array([0.02703859, 0.043908  , 0.05043493, 0.05411018])\n"
     ]
    }
   ],
   "source": [
    "years = np.arange(4) + 1\n",
    "prices = np.array([97.35, 91.68, 86.12, 80.77])\n",
    "freq=2\n",
    "ytm = zero_bond_ytm(n=years, pv=prices, fv=100, freq=freq)\n",
    "print(f'{ytm = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "df = array([0.9735, 0.9168, 0.8612, 0.8077])\n",
      "df = array([0.9735, 0.9168, 0.8612, 0.8077])\n",
      "par_rates = array([0.02722137, 0.04401418, 0.05044521, 0.054029  ])\n",
      "forwards = array([0.0609178 , 0.06355138, 0.0651755 ])\n"
     ]
    }
   ],
   "source": [
    "df = 1 / (1 + ytm/freq)**(years*freq)\n",
    "print(f'{df = }')\n",
    "df = prices / 100\n",
    "print(f'{df = }')\n",
    "\n",
    "par_rates = (1 - df) / np.cumsum(df)\n",
    "print(f'{par_rates = }')\n",
    "\n",
    "forwards = ((df[:-1] / df[1:])**(1/freq) - 1) * freq\n",
    "print(f'{forwards = }')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "17. According to the expectations theory of the term structure of interest rates, the annual yield on 2-year, zero-coupon government bonds two years into the future, quoted on a semiannual bond basis, will be closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ifr_2y2y = 6.436%\n",
      "ifr_2y2y = 6.436%\n"
     ]
    }
   ],
   "source": [
    "df_t0t2 = df[1]\n",
    "df_t0t4 = df[3]\n",
    "\n",
    "ifr_2y2y = ((df_t0t2 / df_t0t4)**(1/(2*freq)) - 1) * freq\n",
    "print(f'{ifr_2y2y = :0.3%}')\n",
    "\n",
    "ifr_2y2y = ifr(ytm[1], 2, ytm[3], 4, 0, per=freq)\n",
    "print(f'{ifr_2y2y = :0.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "18. The 4-year par yield, stated on a semiannual bond basis, on a hypothetical annual coupon payment government bond is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "par_yield = 5.403%\n",
      "par_rates[3] = 5.403%\n"
     ]
    }
   ],
   "source": [
    "par_yield = (1 - df[3]) / np.sum(df) \n",
    "print(f'{par_yield = :0.3%}')\n",
    "print(f'{par_rates[3] = :0.3%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Base your answer to Question 19 on these rate data for commercial paper, which are quoted on an discount rate basis for a 360-day year.\n",
    "\n",
    "| Maturity | Commercial Paper Rate |\n",
    "| -------- | ----- |\n",
    "| 30 Days  | 3.95% |\n",
    "| 60 Days  | 4.40% |\n",
    "| 90 Days  | 4.85% |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "19. The implied forward 60-day commercial paper rate, 30 days into the future, stated on a discount rate basis for a 360-day year, is closest to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rate_30d60d = 5.32%\n"
     ]
    }
   ],
   "source": [
    "rate_t0t1 = 0.0395\n",
    "t1 = 30\n",
    "rate_t0t2 = 0.0485\n",
    "t2 = 90\n",
    "\n",
    "rate_30d60d = ifr_mm(rate_t0t1=rate_t0t1, t1=t1, rate_t0t2=rate_t0t2, t2=t2, year=360, aor=False)\n",
    "print(f'{rate_30d60d = :0.2%}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Base your answers to Question 20 on these prices and yields for annual coupon payment benchmark government bonds. The prices are percentages of par value and the yields to maturity are quoted as effective annual rates.\n",
    "\n",
    "| Maturity | Coupon Rate | Price  | YTM     |\n",
    "| -------- | ----------- | ------ | ------- |\n",
    "| 1 Year   | 0%          | 94.125 | 6.2417% |\n",
    "| 2 Years  | 5.25%       | 98.750 | 5.9311% |\n",
    "| 3 Years  | 3.75%       | 96.375 | 5.0832% |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ytm = array([0.062417  , 0.05931138, 0.05083207])\n"
     ]
    }
   ],
   "source": [
    "years = np.arange(3) + 1\n",
    "coupons = np.array([0, 5.25, 3.75])\n",
    "prices = np.array([94.125, 98.75, 96.375])\n",
    "ytm = np.vectorize(coupon_bond_ytm)(n=years, pmt=coupons, pv=prices, fv=100)\n",
    "print(f'{ytm = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "df = array([0.94125   , 0.89129157, 0.86267922])\n",
      "spots = array([0.062417  , 0.05922958, 0.05046976])\n",
      "par_rates = array([0.062417  , 0.05932113, 0.05094973])\n"
     ]
    }
   ],
   "source": [
    "df = [prices[0]/100]\n",
    "\n",
    "for i in range(1,3):\n",
    "    pv_coupon = np.sum(np.full(i, coupons[i]) * np.array(df))\n",
    "    df.append((prices[i] - pv_coupon)/(100 + coupons[i]))\n",
    "\n",
    "df = np.array(df) \n",
    "print(f'{df = }')\n",
    "\n",
    "spots = df**-(1/years) - 1\n",
    "print(f'{spots = }')\n",
    "\n",
    "par_rates = (1 - df) / np.cumsum(df)\n",
    "print(f'{par_rates = }')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1253cff9ac0>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Sbf/o0SPl5uaWYuLr6OioQkND0/w6iOcjN7eJdG/48OFMnz6de/fuMXXq1Oeqc/DgQQD27t3L0aNHk60PDg7GaDRy+fJlypcvn+p+Tpw4gVartdxE96S3YfzeSpUqpVju4OCAj48Pv//+O1u3bqVZs2aAub/buXPnaN26NVmyZLFsn9bX84MPPmDUqFEMGjSIrVu30rhxY6pXr06JEiWee6zkGTNm8OjRoyRl3t7elClT5rnq165dO8kYuA8fPuTAgQN88skn1KpVi3Xr1lnO++jRoxiNxlT7UsfHxwOk2JeyQoUKycr0ej3Zs2cnLCzMUnbx4kXCw8OpXLkyOXPmfK5zSG3/iX1an9z/s+okHjOl6z1xRJTbt2+TN29eS3lAQACTJ09m586dBAQEJOv7mVI/Y0j9ukvk5+fHtm3bKFy4MJs3byZPnjxP3T4t9uzZw7hx45KUde/eHW9vb8D8ngaoV69esro2NjbUqlWLmzdvcvLkSUtcPXr04Pfff2fhwoU0b97csv3ChQvR6/V06tTJUpb4XgkPD0/xWkrsZ5rStfSs1+1NXwuJEs/p9OnTKZ7T5cuXAfM5lShR4qVjflFjxoyxxGcymQgKCmLdunV89tlnrFu3jiNHjliO/SLXQaLnPafEYyTeV/AkNzc3ypQpw969e5OUd+7cmc8++4wSJUrQoUMHateuTfXq1cmaNevzvgziGSTxFemeVqu1jOrg4ODwXHUSb556VqIcFRX11PXh4eF4eHig1+uTrcuRI8dzxZLI09OTCxcupJosvA5Pi/HJL/PEBHDhwoWAOVF4Ulpfz7x583LkyBHGjh3Lli1bWLNmDWD+chg+fDiffPLJM2OfMWMGt27dSlKWL1++5058/ytz5sy0bNkSBwcHGjZsyNChQy3nnXh+R48eTTGxT5TS9eLu7p7itjY2NhiNRstyYhKf1mH3Utq/jY35o/vJ/T/Jzc0t1TpPW5eY4IP55sRKlSoRFhZGzZo1adSoEW5ubuh0Om7evMnChQtTvcHzWe+NgwcPEh8fT+XKlVO9MS01ie/H+Ph47t69S4ECBZKsHzt2rCX52bFjBw0bNkyyPvEGpNRGgkksf/JHV7Vq1ShSpAjr168nLCyMTJkyceLECfz9/fH29k7yIzHxWtq+fTvbt29P9TxSupae9bpZ61pIPKcnb5BMyfO+P54V86ug1WrJlSsXgwYNIigoiG+//ZYJEyYwe/Zs4MWug0TPe06Jx8iePXuKx0jp/3vYsGFkyZKFWbNm8eOPPzJjxgw0Gg21a9dm6tSpKSbdIm1kVAfxTkr8QA8PD0eZu/Sk+Ejpl/h/9xMaGprkSyDRvXv30hRTYqvxzp0701RPqzW/TVMbgD2lD+ZET2tdrVatGoULF2b9+vU8evSI+Ph4li9fTpYsWSwJYaIXeT2LFy/OihUrePjwIceOHWPSpEmYTCY+/fRT5s2b98zzvnnzZrL9v4rhxxJH07h8+bLliynx/IYOHfrU89u9e/cLHzfxy/JN/vB5GdOmTePhw4fMmzePPXv28OOPPzJ+/HjGjh1L48aNn1r3Wa36EydO5IMPPmDBggX06tUrxRElUmNjY2P5P0zrewn+//86tfdv4t38/00Ku3XrhsFgYMWKFUDqPxIT682cOfOp19KCBQuSHTutM0e+KYnndPr06aee039fi/Qi8Xo5cuSIpexFr4O0SKx7//79FNenduxu3bpx6NAhHj58yKZNm+jduzf79u2jcePGKY5MIdJGEl/xTqpSpQoA+/fvf6n9lCtXDpPJxN9//51sXVqnku3Zsyd6vZ7Vq1dz/vz5p277ZEtapkyZAAgMDEy23dWrV1MdQud5dO/endjYWFasWMGmTZt48OABnTp1StbC/TKvp42NDeXLl2fkyJGWYcHWrVv3wjG/rCf/FJmYcFWqVAmtVvvS18vTFCtWDHd3d86cOZOm4fSs5erVqwC0adMm2br//nk2rezs7PDz86Ndu3b4+vrSpUuXNM2s1adPHwB++OEHoqOj03TsxGH8Unr/JiQkWK6BcuXKJVnXrVs3tFotCxcuTPIj8cmuD/DqPnvSkzd1Tjqd7rW0Aie+55/8gfWi10FaJNZN6f0SHh7OqVOnnlrf3d2dZs2a8fvvv9OjRw9CQ0PZt2/fC8cjzCTxFe+kwYMHo9frGTp0qKX/2ZPi4uKe60O8Z8+eAHz55ZfExsZaykNDQ5kwYUKaYkqcUCEuLo7mzZunOjPbli1baNq0qWW5WLFiuLq68ueffxIcHGwpj4mJea4uA0+T+GW+aNEiFi1aBJBiq2paX8/jx4+nmJAntnw4Ojq+VNwvI3Eq7NKlS1t+VGTLlo3OnTtz7Ngxxo8fn+KX77Vr17hx48YLH1en0zFw4EBiYmIYMGBAsm4CcXFx6ao1J3Fs6P8mBlu3bmXu3LkvvX+9Xs/y5cvp0qULy5cvp3379in+ZSUlXbp0oX79+ly6dImWLVumOi1xSn8N8fb2xsPDg+XLl3Po0KEk62bMmMGNGzdo0KBBsn6duXPnpl69ehw6dIiZM2cSEhKS4o/EChUqULNmTdasWcP8+fNTjOvs2bNJ3svpXc+ePXF3d2fcuHFJWk0TmUymNDcEpCRz5syEhISkOo7wizAYDJbxb5+8L+NFr4O0aNWqFZkyZWLZsmXJPu/Hjh2b4mfk7t27LWMsPynxerHmZ+e7Qvr4indSsWLFmD9/Pr169aJkyZI0adKEIkWKEB8fT0BAAPv37ydr1qxPHUQcoGPHjqxYsYL169fj5eVFq1atiI+Px8/Pj4oVK3Lt2rU0xTVq1CgSEhIYN24cFStWpFq1alSoUMEyZfG+ffu4cuVKkn5cer2eTz/9lPHjx1O2bFlat25NQkIC27dvJ2fOnGm6Ueq/cufOTd26ddm5cyc2NjaUKlUqxYkt0vp6Ll68mNmzZ1OjRg0KFixIpkyZuHbtGhs2bMDOzo4hQ4a8cMzPK3HCkEShoaEcOHCA48eP4+DgwM8//5xk+59//pkrV67w9ddfs3jxYmrUqEH27Nm5e/cuFy5c4OjRoyxfvpz8+fO/cExjxozh8OHDbNiwgSJFitCiRQtcXFwIDAxk27ZtTJ06Nd3MJjdw4EAWLFhAu3btaNu2LTlz5sTf358tW7bg4+Nj+ZP/y9DpdCxcuBB7e3vmzp3Lhx9+iJ+fX5KZGlOrt2bNGrp168aff/5JgQIFqF27Nl5eXjg6OhISEsK5c+c4cOAAtra2SSaLcXZ2Zv78+bRr147atWvTrl078uTJw/Hjx9m2bRs5cuSw9AP9r+7du7Njxw5GjRplWU7JsmXLqFevHr179+bHH3+kcuXKuLu7c/v2bc6cOYO/vz8HDx4kW7ZsL/jKvVmZM2fGz8+P1q1bU6VKFerXr0/JkiXRaDQEBgZy8OBBHj58mKRx4EXUr1+fo0eP0qRJE2rVqoWdnR3vv/8+LVu2fK76e/bssbznlVIEBQWxefNmbt++TYECBfjyyy8t277MdfC8nJ2dmTNnDu3bt6dmzZq0b98eT09P/v77b/z9/alVq1ayFtzWrVvj7OxMlSpVyJcvH0op9u/fz9GjRylfvjwNGjR4qZgE/xm7SYh0Km/evMmGfUmU2gQWSil15swZ1b17d5UnTx5la2urMmXKpEqWLKn69eundu7cmWTblIYzU8o8bum4ceNU/vz5la2trcqbN68aNWqUio2NTdNwZk86f/68Gjx4sCpZsqRycXFRer1e5ciRQzVp0kTNnTs32RivJpNJfffdd6pAgQJKr9er3Llzq88//1w9fvz4qcOZ/Xd82ZQsXrzYMvRP4kQDqXne1/PQoUNqwIABqnTp0ipTpkzK3t5eFSxYUPXo0eO1Tl6hVOrDmdna2qr8+fOr3r17J5tYIpHBYFA//fSTqlq1qnJ1dVW2trYqd+7cql69emr69OnqwYMHyY6TlmHmlDIPlfTTTz+pihUrKicnJ+Xo6KgKFSqk+vbtq65cuWLZLnGIpt27dyfbx40bNxSgunfvnqQ8tWtYqae/T1I71j///KPq1q2r3N3dlbOzs6pevbpau3Ztquf+tOMrlfp1aTKZ1ODBgxWgGjVqlKZxnnfs2KG6du2qChYsqBwdHZVer1fZsmVTdevWVd9++22yYawSHTlyRHl7e6ssWbJY3lMDBgx46lBzjx8/Vq6urgpQXl5eT40rIiJCffvtt6pcuXLKyclJ2dvbq3z58qlmzZqp2bNnq6ioqGe+Ls+7PqXPoRf5/37WsW7cuGEZD9vOzk65uLiookWLqi5duiSbaOJpx0/t+omKilIDBgxQuXLlUjqdLsVrPCWpDWfm6OioSpcurb788ssk41o/KS3XwYuck1JKbdu2TVWvXl05ODgod3d39cEHH6gLFy6kuL9ff/1VeXt7q/z58ysHBweVKVMmVaZMGTV58uQkw2+KF6dRKoU2dSGEEEIIId4x0sdXCCGEEEJkCJL4CiGEEEKIDEESXyGEEEIIkSFI4iuEEEIIITIESXyFEEIIIUSGIImvEEIIIYTIECTxFUIIIYQQGYLM3GZFjx49Yu/eveTOnfuZMxUJIYQQQoikDAYDgYGB1K5dG3d392duL4mvFe3duxdvb29rhyGEEEII8VZbt24drVq1euZ2kvhaUe7cuQHzf1ahQoWsHI0QQgghxNvl6tWreHt7W3KqZ5HE14oSuzcUKlSIkiVLWjkaIYQQQoi30/N2GZWb24QQQgghRIYgia8QQgghhMgQJPEVQgghhBAZgiS+QgghhBAiQ5Cb24QQQgjxUhISEggLCyMqKgqllLXDEW85jUaDnZ0drq6uODk5odFoXtm+JfEVQgghxAtTSnH79m1iYmLQ6XTY2EhqIV6O0WgkPDyc8PBwPDw8yJYt2ytLfuXqFEIIIcQLi4yMJCYmBjc3Nzw9PV9p65zIuOLi4ggKCiI0NBQnJyecnZ1fyX6lj68QQgghXlhERATAK22VE8LW1hZPT0/g/6+xV0ESXyGEEEK8sPj4eGxsbKSLg3jlbG1t0ev1GAyGV7ZPSXyFEEII8cKUUmi1kk6I10Oj0bzSGyblShVCCCHES5EuDuJ1edXXliS+QgghhBAiQ5DEVwghhBBCZAiS+AohhBBCiAxBEl8hhBBCiBQ0bdqUTJkycf/+/WTrwsPD8fT0JHv27Gg0mmc+fH19ASzLffr0SfGYX375pWWbBw8evM7Ty5Bk7JEMICEhnpMX91HRq761QxFCCCHeGrNmzcLLy4uhQ4eybNmyJOtGjRrFgwcP+OqrryhYsKCl/K+//mL58uVMnz6dLFmyWMqrVatmeW5vb8/q1auZNWsWtra2Sfa7fPly7O3tiY2NfU1nlbFJ4psBrNz5I9/d86X4AR3VMtWle+OvyOSa2dphCSGEEOla/vz5GTNmDCNHjqRHjx40atQIgKNHj/Lbb78xfPhwxowZk6TOvXv3WL58Od7e3uTLly/F/TZp0oT169ezefNmWrVqZSk/cOAAN27coE2bNqxevfq1nVdGJl0dMoBdN1cBcMHOyLzoHTRdXZuBcxvw16GVmEwmK0cnhBBCpF/Dhg2jdOnSDBw4kNjYWIxGIwMGDCBv3rzJkt7nlStXLmrVqpWsFXnp0qWUKlUKLy+vVxG6SIEkvhlAj8pf0Sg+F+5Gc5L7WKthv/4+Iy+Np8W8soxb3p9bIQFWjlIIIYRIf2xsbJgzZw43btxg/Pjx/Pzzz5w4cYJff/0VR0fHF95vp06d2LBhA1FRUQAkJCSwatUqOnXq9KpCFymQrg4ZQI0yLahRpgWPH0ewfPtE9t/fxim7OEwaDYG2JgLjDvDnpmZ4xXtQv1BXOtXsiV6mnhRCCPESxm04x/m7EdYOw6JETlfGtCz5QnUrV67MwIEDmTp1KnZ2dnTs2JHGjRu/VDxt27Zl8ODBrFu3ji5durBt2zYePHhAx44dWbBgwUvtW6ROspsMxMnJlT7ek+jDJM5d2s+qf6ZyyHSVO3od8RoNJ23DOBnwIwsW/kR52/fpUmskZfPKn1uEEEKk3fm7ERy+EWrtMF6Zb7/9Fj8/P6Kjo5k+ffpL7y9Tpkw0adKE5cuX06VLF5YtW0a1atXImzfvK4hWpEYS3wyqZNGalCxak4S4GP7c/gO7Av/kiF00sVotD20U20yn2L67A4XjXajxXlv61BuIi52DtcMWQgjxliiR09XaISTxsvG4urpStGhRHjx4QPbs2V9JTJ06daJr164EBASwbt06pkyZ8kr2K1IniW8GZ2PrQJvmX9GGrwi6dZI/9kzkgOEcF+10KI2Gy7ZRXA72ZcVSX0pri9Ku8jAaFq/27B0LIYTI0F60W0FG8sEHH2BnZ0f37t0xGAz4+PhYO6R3ntzcJiw885ZlaPdVrOp9mp/e60OzGCfcjEYAHuvgoOYSw470p+nciny97muCIsOsHLEQQgjx9nJwcMDb25s9e/bQsGHDJOP+itdDWnxFcjo9dep/Sp36nxJx7xJ+OyawP+oYx+3NrcC39bHcDl/LRr+1FFN5aF56AB3KNUOn1Vk7ciGEEOKtMnz4cAoWLPjSN8uJ5yOJr3gq1xxF6dVlMb2MCZw9tJD1Z+ezzyaUu3ob4rVwlgDOnhvFnNNjKONShwF1hlA8Wx5rhy2EEEK8Fd5//33ef/99a4eRYaTrrg4Gg4GRI0eSM2dOHBwcqFy5Mtu3b3+uunfu3MHHxwd3d3dcXV1p1aoV169fT3Hb+/fv079/f3LlyoW9vT358uWjd+/eSbZZs2YN7du3p0CBAjg6OlK0aFE+++wzHj169LKn+XbQ2VCqem++HPAPG1r/xTi7KtR7nIBeKQBCbeLZFbOd9n81p9W8BszYt5iYOIOVgxZCCCGE+H8apf7NXNKhjh074ufnx5AhQyhcuDC+vr4cPXqU3bt3U6NGjVTrRUVFUa5cOcLDw/nss8/Q6/VMnz4dpRSnTp0ic+b/n643MDCQ6tWrA9C3b19y5crF3bt3OXLkCOvXr7dslyVLFnLmzIm3tzd58uTh7Nmz/PbbbxQoUIATJ07g4JD2EQ/OnTuHl5cX/v7+lCz5Ft4EYEwg4ORq1h2fxV7NPS7bJZ1v3Mmoo4RdJXpV+4Qa+WVYNCGEeBclNioVKFDAypGId9Gzrq+05lLptqvDkSNH+OOPP5g6dSrDhw8HoFu3bnh5eTFixAgOHDiQat1Zs2Zx5coVjhw5QsWKFQFo2rQpXl5e/PDDD0ycONGybf/+/bGxseHo0aNJEuL/8vPzo06dOknKypcvT/fu3Vm6dCl9+vR5ibN9S+lsyFOhPZ9UaM/gR4Hs2/k9O+9tZ6eDhkidlsc6I0cTDnJ030E8d7lT9T0fPqnZncyO6WuIGyGEEEJkDOm2q4Ofnx86nY5+/fpZyuzt7enduzcHDx4kMDDwqXUrVqxoSXoBihUrRv369Vm5cqWl7OLFi2zevJnPP/+czJkzExsbS3x8fIr7/G/SC9C6dWsALly4kNbTe+do3XNTp81Mxn90lk0VJzHckJ0KMbGW9UE2j1hzbw4NV9TAZ1Fn/Pz3kY7/2CCEEEKId1C6TXxPnjxJkSJFcHVN2jpYqVIlAE6dOpViPZPJxJkzZ6hQoUKydZUqVeLatWtERkYCsGPHDgCyZ89O/fr1cXBwwMHBgaZNm3Lz5s1nxnjv3j2A5xp+JDg4mHPnziV5XL169Zn13jpaHZlKtaR7vx0s6LyfJR4t6BphIltCAgDxWsUFdYZxxwdRa35VPl3/LddDg6wctBBCCCEygnSb+AYFBeHp6ZmsPLHs7t27KdYLDQ3FYDA8V90rV64A0K9fP2xtbVmxYgWTJk3i77//pkGDBkRHRz81xsmTJ6PT6Wjbtu0zz2fWrFl4eXkleXh7ez+z3lvNJQfvt/yOEYPOsqnGj0yIz029xzHY/NvS+8jmMbvC/qD1+ka08PXm18PriEtIucVdCCGEEOJlpds+vjExMdjZ2SUrt7e3t6xPrR7wXHWjoqIAyJEjB5s2bUKrNf8OeO+99+jYsSPLli1Lte/usmXLmDdvHiNGjKBw4cLPPJ+BAwfSrl27JGVXr15995NfAK0W+6INaVW0Ia2igrn5969subKSzfZGrtvqMWngFteYdXE0vufGU9y1PoOr9qZCrqLWjlwIIYQQ75B02+Lr4OCAwZB8OKzY2FjL+tTqAc9VN/FfHx8fS9IL0K5dO2xsbFK9gW7//v307t2bxo0b8+233z7X+WTLlo2SJUsmeRQqVOi56r5TnLORr8kYBgw6y5q6v/KzqSCtIx/jaDIBEK2L4/jjzfTc0Zb68xszYc9CIgxRVg5aCCGEEO+CdJv4enp6EhSUvO9nYlnOnDlTrOfh4YGdnd1z1U38N3v27Em20+l0ZM6cmbCw5FPynj59mg8++AAvLy/8/PywsUm3jebpm1aLrlBdavdcxzc9j7ApT3e+CIeysf9/Q1yw7i4rbn1PnWU1aLt8IH9dPiw3xAkhhBDihaXbxLdMmTJcvnyZiIiIJOWHDx+2rE+JVqulVKlSHDt2LNm6w4cPU6BAAVxcXADzcGRgnuziSXFxcTx48ICsWbMmKb927RpNmjQhW7Zs/PXXXzg7O7/QuYn/cMpClvoj6PTxGRY2ms9iTXG6h0fhYTQCEK81ciluPyMP9qHGgtoM2zKTOxEhVg5aCCGEEG+bdJv4tm3bFqPRyJw5cyxlBoOBBQsWULlyZXLnzg1AQEAAFy9eTFb36NGjSZLfS5cusWvXriT9bOvUqUO2bNlYunSppRsEgK+vL0ajkYYNG1rK7t27R6NGjdBqtWzdujVZUixeAY0GTf6alOm2kuF9jvNX4f5MCtdS53E0un9beiN0YWy/P5dma+rTdHFXfE9uIcGYYOXAhRBCCPE2SNczt/n4+LB27VqGDh1KoUKFWLhwIUeOHGHnzp3UqlULMCeve/fuTfIn8MjISMqWLUtkZCTDhw9Hr9czbdo0jEYjp06dSpK0Llq0iO7du1OxYkW6du1KQEAAM2fOpEqVKuzevRudTgeYW5hPnz7NiBEjKFWqVJI4s2fPniRJfl5v/cxtb4JSEHCI6//MYkfwftY723NLr0+yib3RidKZmzG0She8ssvMQUII8SbJzG3idXrVM7el68Q3NjaW0aNHs2TJEsLCwihdujTjx4+ncePGlm1SSnwBbt++zdChQ9m2bRsmk4k6deowffr0FG8o++OPP5g0aRIXL17E3d2ddu3aMXHiREuXCACNRpNqnLVr12bPnj1pPj9JfNMoOpSEU39w8NhctmjD2ObkSKw26R8tMlOIFoV8+KiiN062aZ9GWgghRNpI4itepwyV+L7rJPF9QUrB7aOEHJzNzts7WO9kx1n7pMPX2ZhsKexcl4/Kd6JugXJWClQIId59kviK1+lVJ77pto+vEKnSaCB3JbL6zKPDR6dZWmY4SyPs6RIegfu/N8QlaOO4EL2VT/Z3p+qCRnyx41eCHycfpUMIIYR4mrNnz9K2bVvy5s2Lvb09uXLlomHDhvz000+v9bjnz59n7NixzzWT7JNOnTpFly5dyJ07N3Z2dnh4eNCgQQMWLFiA8d/vyIxMEl/xdnNwR1O5H6UHH2Hkh2vY7FaLKSHhVI+OQfPvHzOitEFsvDOLhivr0GxZP1ac3YVJmawcuBBCiPTuwIEDVKhQgdOnT9O3b19+/vln+vTpg1arZebMma/12OfPn2fcuHFpSnznzp1LhQoV2L17N507d2bWrFl8/fXXODg40Lt3byZPnvz6An5LyCC04t2g0cB75XF+rzxNYyNo6u/HzcO/syX+Nuucnbmjt8GkNREYf5AJJw4y9WgmKmZrxrBqnSnskdva0QshhEiHvv32W9zc3Dh69Cju7u5J1gUHB1snqFQcOnSIAQMGULVqVf76668k9ykNGTKEY8eO4e/v/0qO9fjxY5ycnF7Jvt40afEV7x57V6jQi3yDDjLAZz0bsjTgt+BwmkY9xtZkbgU26ML4++FSPlzfjDqLOvLz4dUYEpLP9ieEECLjunbtGiVLlkyW9IJ5RtYnaTQaBg8ezNKlSylatCj29vaUL1+effv2Jat78uRJmjZtiqurK87OztSvX59Dhw5Z1vv6+lqGX61bty4ajQaNRvPUG+nHjRuHRqNh6dKlSZLeRBUqVKBHjx4A7NmzJ8X93bx5E41Gg6+vr6WsR48eODs7c+3aNZo1a4aLiwudO3dm8ODBODs7Ex0dnexYHTt2JEeOHEm6VmzevJmaNWvi5OSEi4sLzZs359y5c6mez+siia94t+Usi977J6p/cp4pVcawJTYTXzwIpZghzrxeAw+VP7MvjqXy4pp0WjOKQ7dfzS9iIYQQb7e8efNy/Pjx524p3bt3L0OGDKFLly588803PHz4kCZNmiSpf+7cOWrWrGkZInX06NHcuHGDOnXqWCbpqlWrFp988gkAo0aNYvHixSxevJjixYuneNzo6GjLUK958uR5ybNOLiEhgcaNG5MtWza+//572rRpQ/v27Xn8+DGbNm1KFsuGDRto27atZUjYxYsX07x5c5ydnZk8eTKjR4/m/Pnz1KhRI819mF+WdHUQGYOdM5TvTtby3ekUdJoOxxdy/twq/nTUscnJiUidFqM2hrORG+i7cwPOKh9N8nnzSeV2ZHJwtXb0QgghrGD48OE0bdqUMmXKUKlSJWrWrEn9+vWpW7cu+v+MKQ/g7+/PsWPHLDPDdujQgaJFi/L111+zZs0aAL766ivi4+P5+++/LSMVdOvWjaJFizJixAj27t1LgQIFqFmzJj/++CMNGzakTp06T43z6tWrxMfHJ5tn4FUxGAy0a9eO7777zlKmlCJXrlysWLEiyeRgmzZt4vHjx7Rv3x6AqKgoPvnkE/r06ZNkUrLu3btTtGhRJk6cmKT8dZPEV2Q8nu+jbTENr0bj8Tq3lk+PzGfvwwusdXHmsIM9AFGam/jdmsHqGz+Tz7E6fcu0p0WRGk8dz1kIIcQTNv8P7p21dhT/L0cpaDopTVUaNmzIwYMH+e6779i6dSsHDx5kypQpZM2alblz5/LBBx8k2b5q1aqWpBcgT548tGrVig0bNlj+7L9t2za8vb2TDM/l6elJp06d+P3334mIiMDVNW0NLhEREQApdnF4VT766KMkyxqNhnbt2jF79myioqJwdnYGYMWKFeTKlYsaNWoAsH37dh49ekTHjh158OCBpb5Op6Ny5crs3r37tcWcEkl8RcZl6wRlu+BctgvN7/nT7Lgvt/xXstEO1rk4cd/GBqVN4EbsXkYd2svYA9mo6dmcYVU7ksfN09rRCyFE+nbvLNz629pRvLSKFSuyZs0a4uLiOH36NGvXrmX69Om0bduWU6dOUaJECcu2hQsXTla/SJEiREdHExISApi7AhQtWjTZdsWLF8dkMhEYGJjmsf0TE+XIyMg01XteNjY2vPfee8nK27dvz4wZM1i/fj2dOnUiKiqKv/76i/79+1saiq5cuQJAvXr1nhr7myKJrxAAObzQNP+efA2/YfD5P+l3bD5H7p1hjYszux0dSNBoiNMGs/P+Anau9SWbTRk6lmhLt/ebYKuztXb0QgiR/uR4PX92f2EvGY+trS0VK1akYsWKFClShJ49e7Jq1SrGjBnzigJ8cYUKFcLGxoazZ5+vhT21v16mNs6vnZ0dWm3y28KqVKlCvnz5WLlyJZ06dWLDhg3ExMRYujkAmEzm4UMXL15Mjhw5ku3DxubNpqKS+ArxJFtHKNMR2zIdqRF8gRrHFxJy5g826xNY6+LEVVtb0CiCjSeZefYkP52eRFmPBgyp1Jkynsl/wQshRIaVxm4Fb5MKFSoAEBQUlKQ8sXXzSZcvX8bR0ZGsWbMC4OjoyKVLl5Jtd/HiRbRaLblzm4fYTEvXOkdHR+rVq8euXbsIDAy07CM1mTJlAuDRo0dJym/duvXcx0zk4+PDzJkziYiIYMWKFeTLl48qVapY1hcsWBAwj4LRoEGDNO//VZNRHYRITbbi0HQSWYddpFuDafjp8rPszj3aRkTi9O8vWJM2kuOP1tJ1W1uqL/qQyX8vIsrw2MqBCyGEeBV2796N+ncypCf99ddfAMm6LBw8eJATJ05YlgMDA/nzzz9p1KgROp0OnU5Ho0aN+PPPP5OMZnD//n2WLVtGjRo1LH/6Txwn97/JaWrGjBmDUoquXbsSFRWVbP3x48dZuHAhYB6tQqfTJRtqbdasWc91rCe1b98eg8HAwoUL2bJlCz4+PknWN27cGFdXVyZOnEh8fHyy+oldQN4UafEV4ln09lDaB11pH0qFXKbUiYV8dmoZO3UG1rg4ccLefENchLrCkmtTWXplJoWdazKgfEca5K8kN8QJIcRb6uOPPyY6OprWrVtTrFgx4uLiOHDggKVls2fPnkm29/LyonHjxnzyySfY2dlZEslx48ZZtpkwYQLbt2+nRo0aDBw4EBsbG2bPno3BYGDKlCmW7cqUKYNOp2Py5MmEh4djZ2dHvXr1ko0fnKhatWr88ssvDBw4kGLFitG1a1cKFy5MZGQke/bsYf369UyYMAEANzc32rVrx08//YRGo6FgwYJs3LjxhSblKFeuHIUKFeLLL7/EYDAk6eYA5j68v/76K127dqVcuXJ06NCBrFmzEhAQwKZNm6hevTo///xzmo/7wpSwGn9/fwUof39/a4ci0io+Vqkzq5RpQXN1Y7yHmj4jt6ozt7jy8vVK8ii/oKEasW2muhsZbO2IhRDitbh27Zq6du2atcN4LTZv3qx69eqlihUrppydnZWtra0qVKiQ+vjjj9X9+/eTbAuoQYMGqSVLlqjChQsrOzs7VbZsWbV79+5k+z1x4oRq3LixcnZ2Vo6Ojqpu3brqwIEDybb7/fffVYECBZROp1NAivv6r+PHj6tOnTqpnDlzKr1erzJlyqTq16+vFi5cqIxGo2W7kJAQ1aZNG+Xo6KgyZcqk+vfvb8lLFixYYNmue/fuysnJ6anH/PLLLxWgChUqlOo2u3fvVo0bN1Zubm7K3t5eFSxYUPXo0UMdO3bsqft+1vWV1lxKo1QKbfjijTh37hxeXl74+/un+Q5OkY48uAonFhJ3ahkH1GPWuDixz9EB45MtvUpLLtsKdC/lg0/JBui0OuvFK4QQr9D169cBkgzPlRFpNBoGDRr0ZlsvM4BnXV9pzaWkj68QLytLIWg0HtthF6jT4ld+dPZiR+AdhoaGkS/u3/5MGhN34o8w8cRwyi+sQ/+N47nw4LpVwxZCCCEyGunjK8SrYmMLJVtDydZkCb1OrxOL6XFyCacSQlnj4sQ2J0ditFqM2kcceLiSA5tWkklbnDaFP6Rf+VY46B2sfQZCCCHEO01afIV4HTwKQIMxaIedp1yruUxwK8uugLuMDXlI6ViDZbMw0wXmXvqWyktq03HN5+wPOJHiHcRCCCGEeHnS4ivE66TTQ4kPoMQHOIfdos3JxXx4YjHXHgSx1sWJDc5OhOl0KG0M/pFbGLh7C47kpnGeD/iksg9ZHD2sfQZCCCGegzRavB2kxVeINyVTXqj3FZqh5yjUZiGfZ67EjoC7TLsfQs3oGLT/fmhGE8jagF+ou7IeLf7oz9oLuzApk5WDF0IIId5+0uIrxJums4FizaFYc2wfBdLw5BIanFjE/Qd3We/sxFoXJ27r9aAxcstwgK+PHGD8YQ+qZ2/K0CqdKZDp6TPyCCGEECJl0uIrhDW554a6X6AZcpYcPsvol706G+/cZ17QfZpHPcbu3xni4jWh7AleSqs/m1NvaSfmHF+DIcHwjJ0LIYQQ4knS4itEeqCzgaJNoGgTdOF3qHRqKZVOLCLi4W02OzmxxsWJ83Z2oFGEJJzlJ/+z/HJmCu9nqscnlTpTIaeMAy2EEEI8i7T4CpHeuOWC2iPg09O4dlxF+1x1+CPoAX53gugUHomr0QiASfuYk+Eb6Lm9A1UXteTb/fN4FBtu5eCFEEKI9EsSXyHSK60OCjeEDkvRDDtP0Rr/4wuTC7sC7zAl+AFVY2LQ/HtDXJS6yR/XZ1Dzj7q0XjWYzVf/ljuMhRBCiP+QxFeIt4FLDqg1HD45jV3nNTTN04DZwWFsvn2Xj8LC8UxIMG+niedq9F5G/PMRFRc24PPt07gdEWTd2IUQQoh0Qvr4CvE20WqhUH0oVB9NVDC5Ti1l4PGF9A+8wWEHe9Y4O7HLyZF4jQaDJpgtdxewZY0vnrZl6VqyLR28mqDX6a19FkIIIYRVSIuvEG8r52xQYyh8fAJdtz+pVqAp3z+MYFfAHUY+DKNwXJx5O40iKP4EU06NouLi2vTZ8DX+wZetG7sQQghhBZL4CvG202qhQB1o5wufXcS9/ji62GRj9Z17/HHnHj4RkTj/OyyaURPJ4dC1dNzchpqLP2TaocVExUVZNXwhhEivfH190Wg0loe9vT1FihRh8ODB3L9//43FsXbtWpo2bUqWLFmwtbUlZ86c+Pj4sGvXrjcWw7tCujoI8S5xygLVP4FqH6O5+TclTyyk5Pk/GR76iB1ODqxxduaYgz0Aj0xXWHBpCr4XZ1DMpSYfle9InbyV0Gg0Vj4JIYRIX7755hvy589PbGwsf//9N7/++it//fUX/v7+ODo6vrbjKqXo1asXvr6+lC1blmHDhpEjRw6CgoJYu3Yt9evX559//qFatWqvLYZ3jSS+QryLNBrIX9P8aDIZhzN/0PK4Ly3vXSbAxoa1Lk786exEiI0NShPHhaidfLJ3Jw540ih3Sz6p3JFsTlmsfRZCCJEuNG3alAoVKgDQp08fMmfOzLRp0/jzzz/p2LHjC+/XZDIRFxeHvb19iut/+OEHfH19GTJkCNOmTUvSMPHll1+yePFibGxePpVTShEbG4uDg8NL7yu9k64OQrzrnDJD1UEw6Aj03EKeEm35NCKWbYF3+eVeMPUfR2Pz79BnMQTxZ+Ac6q+qT7M/erPq/FYSTAlWPgEhhEhf6tWrB8CNGzcA+P7776lWrRqZM2fGwcGB8uXL4+fnl6yeRqNh8ODBLF26lJIlS2JnZ8eWLVtSPEZMTAzfffcdxYoV4/vvv0/xr3Fdu3alUqVKAIwdOzbFbRK7a9y8edNSli9fPlq0aMHWrVupUKECDg4OzJ49Gy8vL+rWrZtsHyaTiVy5ctG2bdskZTNmzKBkyZLY29uTPXt2+vfvT1hY2FNeOeuTxFeIjEKjgbxV4cPZ8NlFbJpMppZzfmYEP2B7wB0+exhG/rj4f7c1EWg4wjdHh1NxUR0GbR7P5YfXrRu/EEKkE9euXQMgc+bMAMycOZOyZcvyzTffMHHiRGxsbGjXrh2bNm1KVnfXrl0MHTqU9u3bM3PmTPLly5fiMf7++29CQ0Pp1KkTOp3ulZ/DpUuX6NixIw0bNmTmzJmUKVOG9u3bs2/fPu7du5cslrt379KhQwdLWf/+/fn888+pXr06M2fOpGfPnixdupTGjRsTHx//yuN9VaSrgxAZkaMHVBkAlftD4BGynFhID/81dI8I4rSdLWtdnNns5EiMVkuCJpx9wSvZt3ElmXXF8Cnahp5lW+Fg8+7/SUwI8eImH5nMxdCL1g7DophHMUZWGvlCdcPDw3nw4AGxsbH8888/fPPNNzg4ONCiRQsALl++nKSbwODBgylXrhzTpk2jefPmSfZ16dIlzp49S4kSJZ56zAsXLgBQqlSpF4r5Wa5evcqWLVto3LixpSxnzpx8/fXX+Pn5MXjwYEv5ihUrcHZ2tpzL33//zdy5c1m6dCmdOnWybFe3bl2aNGnCqlWrkpSnJ5L4CpGRaTSQp7L50XgimrOrKHPclzL3/Rn5MIytTo6scXHmlL0dAA+NF/n1/Lf8du4HSrvXYXCFzlTO9b7cECeESOZi6EWO3T9m7TBeiQYNGiRZzps3L0uXLiVXrlwASZLesLAwjEYjNWvWZPny5cn2Vbt27WcmvQAREREAuLi4vEzoqcqfP3+SpBegSJEilClThhUrVlgSX6PRiJ+fHy1btrSc56pVq3Bzc6Nhw4Y8ePDAUr98+fI4Ozuze/duSXyFEOmcgztU6gsV+8CdEzgeX0Br/9W0jrrPdb0Na52dWe/sRKiNDqWJ5XT4Fvru3IKzJjdN833AoAo+ZHb0sPZZCCHSiWIexawdQhIvE88vv/xCkSJFsLGxIXv27BQtWhSt9v97i27cuJEJEyZw6tQpDAaDpTylRoH8+fM/1zFdXV0BiIyMfOG4nya1ONq3b8+oUaO4c+cOuXLlYs+ePQQHB9O+fXvLNleuXCE8PJxs2bKluI/g4ODXEvOrIImvECIpjQbeK29+NJ4IZ1dR4Lgvn907wydhj9jn6MBaF2f2O9hj0miIUoGsuvELq67/RgHHyvQp04FmhWqh0776PmlCiLfHi3YrSI8qVapkGdXhv/bv388HH3xArVq1mDVrFp6enuj1ehYsWMCyZcuSbf+8IycUK2ZO1M+ePYu3t/czt0/tL29GozHF8tTiaN++PV988QWrVq1iyJAhrFy5Ejc3N5o0aWLZxmQykS1bNpYuXZriPrJmzfrMeK1FEl8hROrsXaFib/Pj7kn0x32pf9aP+vdDCNbpWO/sxFoXJwL0etAYuR5zgFEHDzD2gAe1cjbl08qdyOeWx9pnIYQQr83q1auxt7dn69at2NnZWcoXLFjwUvutUaMGmTJlYvny5YwaNeqZN7hlypQJgEePHuHu7m4pv3XrVpqOmz9/fipVqmTp7rBmzRq8vb2TnFvBggXZsWMH1atXf+uGQJNRHYQQzydnWWg5Ez67CC1nki17afqER7DxdhDzg+7TMvIxdibzsGhxmlB2BC2l5brmNFjWiQWn1mAwGp5xACGEePvodDo0Gk2SltWbN2+ybt26l9qvo6MjI0eO5MKFC4wcORL177CTT1qyZAlHjhwBzMkowL59+yzrHz9+zMKFC9N87Pbt23Po0CHmz5/PgwcPknRzAPDx8cFoNDJ+/PhkdRMSEnj06FGaj/mmSIuvECJt7FygfA/zI+g0muMLqXhmJRUfPOSLh6FsdnZijbMT5/69Ie5+/FmmnT7LjFOTKZ+5Ph9X7EzZHCWtegpCCPGqNG/enGnTptGkSRM6depEcHAwv/zyC4UKFeLMmTMvte/PP/+cc+fO8cMPP7B7927atm1Ljhw5uHfvHuvWrePIkSMcOHAAgEaNGpEnTx569+7N559/jk6nY/78+WTNmpWAgIA0HdfHx4fhw4czfPhwPDw8kt3cV7t2bfr37893333HqVOnaNSoEXq9nitXrrBq1SpmzpyZZMzf9EQSXyHEi/N8H1pMg0bjwX8NLsd98blzDJ/IKC7r9ax1cWK9szMROi0mTTRHQzfQbesGXLX5aFXQm/7l2uJm72btsxBCiBdWr1495s2bx6RJkxgyZAj58+dn8uTJ3Lx586UTX61Wy6JFi2jVqhVz5szh+++/JyIigqxZs1KrVi2mTJlC1apVAdDr9axdu5aBAwcyevRocuTIwZAhQ8iUKRM9e/ZM03Hfe+89qlWrxj///EOfPn3Q6/XJtvntt98oX748s2fPZtSoUdjY2JAvXz66dOlC9erVX+q8XyeNSqntXLwR586dw8vLC39/f0qWlBYw8Y645w8nFsLpFWAIJw7Y5eTIOmcnDjg4oJ68/0LpKepSlf5lO1I/fzW0Gul9JcTb5vp18+Q2BQoUsHIk4l30rOsrrbmUtPgKIV6tHF7QbCo0GAfn12F7fCFNAg/R5HE0QTod61ycWO3syn29FjTxXIrax7D9+7Dfn5X677Xg40odyeXiae2zEEII8Q6S5hUhxOth6whlOkHvrTDwEFT+CE+9Cx89imDb7dvMCbpP06jH2JjMm8cSwqbbC2iyujFN/ujKcv8NxBvT77SXQggh3j6S+AohXr9sxaHpJPOIEB/+jjZvdarGGpgS8pA9gbf54kEohQ0J5m01ijuGU0w8PoqKi2sx4K8xnAu5ZN34hRBCvBOkq4MQ4s3RO0BpH/Mj5DKcWIjbqWV0igylU2QU5231rHFxZr2TCzE6MGqi+CdkDf/8tQYPXSHaFmlDzzLeONs6W/tMhBBCvIWkxVcIYR1Zi0Djb2HYBWgzD/LVpERcPF89DGNfYCDfBT+gXMz/d3UINV5lzoXJVFtWm45rh7Av8HCK41oKId48eS+K1+VVX1vS4iuEsC69PZRqa348uAonFmJ/aiktHj+kxeNoAm1sWOvihJ+zG2E2oDRx+EfsZNCunThqctAk7wcMrtiBrI7pd4pMId5lWq2WuLg4lFKpTpsrxItQSmE0GlMcTu1FSYuvECL9yFLIPCbwsIvQzhcK1CF3QgKfhIWzOzCAWfeCqfPYgPbfBoBodY81N+dQb2UDWq7sxZqLW4k3yQ1xQrxJdnZ2GI1GgoODpeVXvDIJCQkEBQVhNBpxdn513dukxVcIkf7Y2ELJ1uZH6HU4sQjdyaXUfBxMzZhYQrVaNjg7sdzFgzu2CjQmbsYcZczho0w47EaNHI35uGJnCnvIuKJCvG7Zs2fHYDAQGhpKeHi4ZQpfIV6EUgqTyURCgvmGZ0dHRzJlyvTK9i8TWFiRTGAhRBoY4+HSZjjuC9d2AQoFnLGzZZWzG385OxKvTfpxllVfjI7F29LZqyWOekdrRC1EhmAymbh//z4GgwGTyWTtcMRbTqPRoNfrcXV1xcXF5ak/pNKaS0nia0WS+ArxgsJuwonFcHIJRN0DIFqjYZuTI0ucM3PJIenmWmXH+x51GVShI5U8y0prlBBCvCPSmktJH18hxNsnUz6oPxqGnoMOy6BwIxwVeEc9xu9eAOtv36VreDROCToATBoDJ8O20Gd7d6otacp3//zGw5iH1j0HIYQQb5wkvkKIt5fOBoo1h86rYMgZqD0SXHKSPz6BEaEP2B94gx/vh1DhMWiUuZU3ynSHZVd/oc6K+rT268/mq7sxmoxWPhEhhBBvgiS+Qoh3g3seqDsKhpyFjiugSFP0Gi11o2NYEBzAzsBABodG4RH377A4GiNXHx9gxD+fUGlxPT7fMZmA8EDrnoMQQojXKl0nvgaDgZEjR5IzZ04cHByoXLky27dvf666d+7cwcfHB3d3d1xdXWnVqhXXr19Pcdv79+/Tv39/cuXKhb29Pfny5aN3794vtU8hhJXobKBoE+j0BwzxhzqjwC03WY0m+oeHsufONXzv3qdeFOhM5o/AOELZcmcJzdc1o9Hyjiw+u5bYhFgrn4gQQohXLV3f3NaxY0f8/PwYMmQIhQsXxtfXl6NHj7J7925q1KiRar2oqCjKlStHeHg4n332GXq9nunTp6OU4tSpU2TOnNmybWBgINWrVwegb9++5MqVi7t373LkyBHWr1//Qvt8XnJzmxBviMloHgniuK95ZAhl7toQpdGw0dmNhc5ZuG0fl6SKTjlSMWt9BlfsxPvZvKwQtBBCiGd5Z0Z1OHLkCJUrV2bq1KkMHz4cgNjYWLy8vMiWLRsHDhxIte6UKVMYOXIkR44coWLFigBcvHgRLy8vRowYwcSJEy3bNmvWjIsXL3L06NGnJq9p2efzksRXCCuICIJTS+HEQngUYCm+otez0NWTzY564mySToLhrsvHh4Vb06tMG9zs3N50xEIIIVLxziS+I0aMYNq0aYSGhuLq6mop/+677xg1ahQBAQHkzp07xbqVKlUCzMnzkxo3bsy1a9e4evUqYE5cixcvzqxZs/joo4+IjY1Fp9OlODXe8+4zLSTxFcKKTCa4vvvfVuC/wGQeLD0e2OHkwlxnTy47xMITI59plA3FXKsxoFxH6uSthlaTrnuLCSHEO++dGc7s5MmTFClSJEnSC/+fgJ46dSrFeiaTiTNnzlChQoVk6ypVqsS1a9eIjIwEYMeOHYB51pn69evj4OCAg4MDTZs25ebNmy+0z9QEBwdz7ty5JI8XSZaFEK+IVguF6kP7xTD0PNQfA5nyoQeaPo5k9f3LbA+8Q7dwhVOcPQBKk8CFyH18uvcjKi9uwFd7pnE38q51z0MIIcRzS7eJb1BQEJ6ensnKE8vu3k35yyY0NBSDwfBcda9cuQJAv379sLW1ZcWKFUyaNIm///6bBg0aEB0dneZ9pmbWrFl4eXkleXh7ez+1jhDiDXHJDjWHwccnoduf5qmStXpyGI18HhrIgTuXmX3vIWUfO6L594a4WBXCn7cW0Hh1E5qt6MrKCxuIM8Y940BCCCGsycbaAaQmJiYGOzu7ZOX29vaW9anVA56rblRUFAA5cuRg06ZNaLXmL7T33nuPjh07smzZMvr06ZOmfaZm4MCBtGvXLknZ1atXJfkVIj3RaqFAHfMjKgROL4fjvmhDr1Et5jHVYi4SrtWwwjUXSxxcCbOPAo0iMPYU44+c4rsjE6mWvRGDK3SieJai1j4bIYQQ/5FuW3wdHBwwGAzJymNjYy3rU6sHPFfdxH99fHwsSS9Au3btsLGxsdxAl5Z9piZbtmyULFkyyaNQoUJPrSOEsCLnrFD9E/j4OHTfCF5tQWeLm0nR79Ft9gWd54+7wdSKdEZntAUggSj23V+Dz6a21Fnqza/HFxMZ9/RuUEIIId6cdNvi6+npyZ07d5KVBwUFAZAzZ84U63l4eGBnZ2fZ7ml1E//Nnj17ku10Oh2ZM2cmLCwszfsUQrxjNBrIX9P8ePwQzvxhviHuwWVKGmL5xXAegwbWub7HPPtMBDmGA/Aw4Rqz/Kfw69nplM5Ui4/Kd6RarkpoNJqnH08IIcRrk25bfMuUKcPly5eJiIhIUn748GHL+pRotVpKlSrFsWPHkq07fPgwBQoUwMXFBYDy5csDJEuw4+LiePDgAVmzZk3zPoUQ7zCnzFB1EAw6Aj03Q+n2oLPDTkH78Ntsu3+Wv27fp0WkK/p4RwCUJp7Tj3YyYGcfqi5pyIS/f+b+4/tWPhEhhMiY0m3i27ZtW4xGI3PmzLGUGQwGFixYQOXKlS1DmQUEBHDx4sVkdY8ePZokUb106RK7du1K0s+2Tp06ZMuWjaVLl1q6LAD4+vpiNBpp2LBhmvcphMgANBrIWw0+nAOfXYQmkyFrMQByxxv47oE/R29f5PsHCRR4nBmU+aP2sek+K67NpsGqhrRa1Yv1V7YSb4p/2pGEEEK8Qul2HF8w971du3YtQ4cOpVChQixcuJAjR46wc+dOatWqBZiT17179/LkaURGRlK2bFkiIyMZPnw4er2eadOmYTQaOXXqlKUlF2DRokV0796dihUr0rVrVwICApg5cyZVqlRh9+7d6HS6NO/zeck4vkK8Q5SCwCPmbhDn1sATUx4/1OmZ7V6cdXaKGLvwJNX0uFI7Z1MGV+hEwUwF3nDQQgjxdntnJrAA841jo0ePZsmSJYSFhVG6dGnGjx9P48aNLduklPgC3L59m6FDh7Jt2zZMJhN16tRh+vTpKd5Q9scffzBp0iQuXryIu7s77dq1Y+LEicm6L6Rln89DEl8h3lExj+DsKji2AILPWYoVcMTZk5kO73HWIQx0SYc/y25blM4l2tG+REsc9Y5vNmYhhHgLvVOJ77tOEl8h3nFKwZ3jcHwB+K+B+GjLqmitjgWZvFiqtyHSISRJNa2yo3yWOnxUvhMVcpSVG+KEECIVac2l0u2oDkII8dbTaOC9CuZH4+/MrcDHF8C9sziajAx6eJpBwAXHHExzys9hu0co/WNMGgNHH27l6LatuOpy4V2oNb3eb0tmh8zWPiMhhHirpdub24QQ4p1i7woVe0P//dB3N5TvAbbOABSPvsfvIQc5fvsi/4vwIMvjXKh/b4iLMN5h0aWfqbOiHm3X9GPrjd0kmBKseCJCCPH2khZfIYR4kzQayFXO/Gg0AfxXm2+Iu3sSPYrOD0/RGbjtkJVpzsXYqY/AZBcGGhOXIg8yfN9B7DSZaJi7GQPKdSSvW15rn5EQQrw1JPEVQghrsXMxt/yW7wFBp+H4QjizEuIieS8mhGkxIZjQsDlzGX7WuhLoeAeNNg6DCmNjwFI2Biwll31Junn50LpoUxxsnj6DpBBCZHTS1UEIIdIDz/ehxTTzuMAf/Ay5KgCgRdH84Uk2h+xlX/Aj2j4uhE2Mp6XandhzfHdsDFWX1mbA5lGcCfFPNsqNEEIIM0l8hRAiPbFzhnJdoe9OGPAPVOoHdm4AeMQ8YEzwLk7eO8xvEVkoHFUUleAEgJEY/gneQOe/OlJ7WUt+OjqfR7GPrHgiQgiR/kjiK4QQ6VUOL2g21dwK7P0r5K5sWVX94QnWhGznSEgwvaOLYfc4P0qZhz0LS7jFnPPTqfVHXTquG8SegP2YlMlaZyGEEOmG9PEVQoj0ztYRynQyP4IvmPsCn14OsY9wjH3IkNhtDAHOZSnPZK0nJ/S30diGojQJ+Ifv4+Pd+3DQZKFZvpb0K9eBnM45rX1GQghhFdLiK4QQb5NsxaHpJHMrcOs5kKeaZVXJB8dZFLyREw9v8VmMFy5RxVEmc/tGjHrA6hsLaOzXhBarurL64kYMRoO1zkIIIaxCZm6zIpm5TQjxSoRcghOL4NRSiAlLsupmlnJ8b5OP3dxF63A3yTobnKjp2YiPynWieJZibzJiIYR4JdKaS0mLrxBCvO2yFoXG38Kwi9BmHuSraVmV78EJfr63hrNhF5kQ9z5ZosqiEhwBSOAxu4PW4rOpHXWXeTPn5GIi4iKsdRZCCPHaSeIrhBDvCr09lGoLPTbC4ONQ7RNwNE9zrDU8otWdDewO+ZNdMQ60NFSDxwUtN8Q9iL/GT2emUGNZHbptGMKBO4fkhjghxDtHujpYkXR1EEK8dgkGuLjJPDvcjb1JVpnsXNmftR5T4uy5qT+P1vZRkvXO2ux4F2rNpxV7Y29j/+ZiFkKI5yRdHYQQQvw/Gzvw+hC6r4dPTkKNoeCUFQCtIYLat9exKfgPDsVp6ZpQF11UKZRJB0CU6T5LLv/Gh2v6yI1wQoh3giS+QgiRUXgUgAZjYeh58FkEBesD5q4OLiGnGBG4kJMR+1hMWYrHNMBoyAZAYMxpOqz7iHhjvPViF0KIV0ASXyGEyGhsbKFEK+i6Bj49BTWHg3MOADSGSMreWsPKe/P5O85AlhgPAK5GHaXbhk9JMCVYMXAhhHg5kvgKIURGlikf1B8NQ/2h/VIo3IjEVmCPB2fZeP80eWJtAfAP30/fvz6Xm96EEG8tSXyFEEKATg/FW0DnVTDkDNQeCS6eOCnF8vvXyGawA+DYwx18vG00cl+0EOJtJImvEEKIpNzzQN1R8NEByFIUV5Ni1b1ruBscANh3bz2f75ogya8Q4q0jia8QQoiUOXqY+wG7voeHycSa+1dwijMnv1tvr2Ts/h+sHKAQQqSNJL5CCCFS5/YedF0LDh5kNZpYc+8advHm5HfNjYVMOTTLygEKIcTzk8RXCCHE02UtAp39QO9ETmMCq+7fxCbBnPwuvvQrvxxfYOUAhRDi+UjiK4QQ4tneKw8dloBWT/54A8uD76JNMM/m9pv/NHzPrLBygEII8WyS+AohhHg+BevBh7MBDcUMkfg+eIDGaB7t4YcT37Lywp/WjU8IIZ5BEl8hhBDPz6sNNJsKQNmYUGY9jASjHjSK8Ye/ZuPVrVYOUAghUieJrxBCiLSp1Bdq/w+AGo/v8X1oAphsQGPii79HsuvmPisHKIQQKZPEVwghRNrV+R9U7ANA46hbfB1mgzLpQGNkyJ4hHLhz2MoBCiFEcpL4CiGESDuNBppOgZKtAWgXcZmhj5xRSovSxPPRjkEcv3fSykEKIURSkvgKIYR4MVodtJ4NBeoA0Dv8LD0eZUEpDSYM9Nk6gHMh56wboxBCPEESXyGEEC/Oxg7aL4GcZQEY/ugYrR/lBiCBaLpt7suVsCvWjFAIISwk8RVCCPFy7FzME1xkLgzA+Ed/U/tRIQDiVCSdN/biVsQta0YohBCAJL5CCCFeBacs0HUNuOQE4OewXZR5VAyAGNMjOqzvwd2ou9aMUAghJPEVQgjxirjnMSe/9u4ALHq0g0LhJQGIMj6g/foeBEcHWzFAIURGJ4mvEEKIVydbcei8CvSOaJQJv/Bd5Aj3AuBRfBAd1vcgNDbUykEKITIqSXyFEEK8Wrkrgc8i0NqgMxrYHLkP93+T3xBDIB3W9yTcEG7lIIUQGZEkvkIIIV69wg3B+1cAbOKj2BF9GIeIEgAExVyny8a+PI5/bM0IhRAZkCS+QgghXo/SPtBkEgB2sQ/ZGXsOm0jzDW83oy7QbVN/YhJirBmhECKDkcRXCCHE61PlI6j5GQAujwPZEX8ToszDnl0OP02fzYOJM8ZZMUAhREYiia8QQojXq95oKNcdgMzhl9liDMMUVQCAM6FH+GjbEOJN8daMUAiRQUjiK4QQ4vXSaKDFdCjeEoBcoSdYhxFjdF4AjgTvZ8jOkRhNRmtGKYTIACTxFUII8fppdfDhXMhXE4DCIftZrHHBGPMeAPvubmfk3tGYlMmaUQoh3nGS+AohhHgz9PbQYRnkKA1A+Xt/8ZMmD8bYHABsDdjAmL8noJSyZpRCiHeYJL5CCCHeHHtX6LIaPMx9fOsH/cE3mtIYDVkBWHd9FZOP/CDJrxDitZDEVwghxJvlnA26rgXn7AC0vTuXIVTHFOcBwNKLC/np5CxrRiiEeEdJ4iuEEOLNy5QPuqwBOzcA+gb9QhdTI0zx5uXfz/7GvLMLrBigEOJdJImvEEII68jhBZ1WgI09GmXkfyE/0iK+NaYEZwBmnJjGsvPLrRykEOJdIomvEEII68lbFdr5gkaHJiGWSY9mUCO2PSrBEYDvjk5k7ZV1Vg1RCPHukMRXCCGEdRVtCq1+BkBjiODX6F8oFd0ZZbQD4OsDX7P5+mZrRiiEeEdI4iuEEML6ynSCRhMA0D4OZolxPnkjuqJMekAxcv8X7A7Ybd0YhRBvPUl8hRBCpA/VPobqnwKge3SDdbaryPqoG8pkg8LIkN3DOHD3gJWDFEK8zSTxFUIIkX40GAdlugCgDz7LZuetuIR2RSkdJhIYtONjjt8/buUghRBvK0l8hRBCpB8aDbScCUWbAWB/5wDbsxxB/6ATSmlIUHH02/YRZ0POWjlQIcTbSBJfIYQQ6YvOBtrOhzzVAHC+sZmd711HE9IepTTEmWLovbU/l0IvWTlQIcTbJl0nvgaDgZEjR5IzZ04cHByoXLky27dvf666d+7cwcfHB3d3d1xdXWnVqhXXr19Ptp1Go0nxMWnSpGTb7tixg7p165IlSxbc3d2pVKkSixcvfunzFEII8R96B+i4HLJ7AeBxcTnbCkZhCvkQgBhjJD029+H6o+Sf60IIkRobawfwND169MDPz48hQ4ZQuHBhfH19adasGbt376ZGjRqp1ouKiqJu3bqEh4czatQo9Ho906dPp3bt2pw6dYrMmTMn2b5hw4Z069YtSVnZsmWTLK9fvx5vb2+qVq3K2LFj0Wg0rFy5km7duvHgwQOGDh366k5cCCEEOLhDl9UwrxE8uoXnmVlsLP8VzS+2xCbbBqISHtF9c2+WNV9Ebtfc1o5WCPEW0CillLWDSMmRI0eoXLkyU6dOZfjw4QDExsbi5eVFtmzZOHAg9Tt7p0yZwsiRIzly5AgVK1YE4OLFi3h5eTFixAgmTpxo2Vaj0TBo0CB+/vnnp8bTqFEjzp07x/Xr17GzM48tmZCQQLFixXBycuL06dNpPsdz587h5eWFv78/JUuWTHN9IYTIEB5eg/lN4HEwAGcqTaXd+cvYZt0KQBb7HCxvsZgcTjmsGaUQwgrSmkul264Ofn5+6HQ6+vXrZymzt7end+/eHDx4kMDAwKfWrVixoiXpBShWrBj169dn5cqVKdaJiYkhNjY21X1GRESQKVMmS9ILYGNjQ5YsWXBwcEjLqQkhhEiLzAWhix/YuQJQ+tgXLPAqT9yDOgA8iL1Ht7968SDmgRWDFEK8DdJt4nvy5EmKFCmCq6trkvJKlSoBcOrUqRTrmUwmzpw5Q4UKFZKtq1SpEteuXSMyMjJJua+vL05OTjg4OFCiRAmWLVuWrG6dOnU4d+4co0eP5urVq1y7do3x48dz7NgxRowY8czzCQ4O5ty5c0keV69efWY9IYQQgOf70GEZ6OzAlEC1Y0OZWaIBcaHmG+CCogPpsbkPj2IfWTdOIUS6lm77+AYFBeHp6ZmsPLHs7t27KdYLDQ3FYDA8s27RokUBqFatGj4+PuTPn5+7d+/yyy+/0LlzZ8LDw/noo48sdUePHs2NGzf49ttvmTDBPLuQo6Mjq1evplWrVs88n1mzZjFu3LhnbieEECIV+WuaR3tY2RUSYmhy+hPGl5rD6Cvx2GY6yq3Ia/Ta0peFzebjYuti7WiFEOlQum3xjYmJSdKtIJG9vb1lfWr1gOeu+88///Dpp5/ywQcfMGDAAI4fP46XlxejRo1Ksp2dnR1FihShbdu2LF++nCVLllChQgW6dOnCoUOHnnk+AwcOxN/fP8lj3bp1z6wnhBDiCcVbmMf5BYh9hM/FIQzL34X48DIAXAm/SN+tA4iOj7ZejEKIdCvdtvg6ODhgMBiSlSf2w02tX21i+YvUBbC1tWXw4MGWJDhx9IjBgwdz6NAhTpw4gVZr/r3g4+NDyZIl+fTTTzl8+PBTzydbtmxky5btqdsIIYR4DuW6weMHsHMcRN6lX8DnPMo1jQV3f0Xveo5zoWf4aPsgZjf6FXsbe2tHK4RIR9Jti6+npydBQUHJyhPLcubMmWI9Dw8P7OzsXqhuoty5zcPihIaGAhAXF8e8efNo3ry5JekF0Ov1NG3alGPHjhEXF/ccZyWEEOKVqDEUqgwCQPPwKiMejqFN1kEkRJm7sZ0IOcanu4YSb4y3ZpRCiHQm3Sa+ZcqU4fLly0RERCQpT2xZLVOmTIr1tFotpUqV4tixY8nWHT58mAIFCuDi8vS+X4kTXWTNmhWAhw8fkpCQgNFoTLZtfHw8JpMpxXVCCCFeE40GGk2A0u3Ni3dPMsEwlfoun5DwuAAAB4L+ZvjeESSYEqwZqRAiHUm3iW/btm0xGo3MmTPHUmYwGFiwYAGVK1e2tMoGBARw8eLFZHWPHj2aJPm9dOkSu3btol27dpaykJCQZMeNjIxkxowZZMmShfLlywPmbgru7u6sXbs2SctuVFQUGzZsoFixYjKkmRBCvGlaLbT6BQo3AkBzYy8z7eZRyX4Ixug8AOwK3MGXf3+FSZmsGakQIp1It318K1euTLt27fjiiy8IDg6mUKFCLFy4kJs3bzJv3jzLdt26dWPv3r08OQ/HwIED+f3332nevDnDhw9Hr9czbdo0smfPzmeffWbZ7pdffmHdunW0bNmSPHnyEBQUxPz58wkICGDx4sXY2toCoNPpGD58OF999RVVqlShW7duGI1G5s2bx+3bt1myZMmbe2GEEEL8P50e2i2Exd4QeBjdhXXMK+dBh7tDOR/zPTqHO/x1YxMONg6Mqfo1Go3G2hELIawo3Sa+AIsWLWL06NEsXryYsLAwSpcuzcaNG6lVq9ZT67m4uLBnzx6GDh3KhAkTMJlM1KlTh+nTp1u6LwBUr16dAwcOMHfuXB4+fIiTkxOVKlVi/vz51KtXL8k+v/zyS/Lnz8/MmTMZN24cBoOB0qVL4+fnR5s2bV7L+QshhHgOto7Q8Q9Y0AxCLmBzYj7LamThw0tDuR47FZ39fVZf8cPBxp4RFUdI8itEBpZupyzOCGTKYiGEeIUi7sK8xhAeAEB0g0l8cOw9ghynobUzz+rWt1RfPin3iTWjFEK8Qu/MlMVCCCFEmrjmhK5rwTEzAI47vmB19SgyR32CKc4dgN/P/s7vZ363YpBCCGuSxFcIIcS7I0sh6OwHts6Awm3zx6ypb49L2GBM8a4A/HjyRxafX2zdOIUQViGJrxBCiHdLrnLQYSnobMEUT5aNvVndPBd2DwZiSnACYMrRKfhd9rNyoEKIN00SXyGEEO+eAnXgw98BDcQ/JtfGrqz6oDi6+wNQRvNsbt8c/IYN1zZYNUwhxJslia8QQoh3U0lvaP6D+XlMKAW3dGWZd0VUUF+U0RaF4qu/v2LHrR1WDVMI8eZI4iuEEOLdVbE31P3S/DziNl67euLbuh4Jd3uhTHpMmBi+93P23d5n3TiFEG+EJL5CCCHebbU+h0r9zc8fXKLiP/35zbsZcXe6oUw6jCqBIbuHcjjosHXjFEK8dpL4CiGEeLdpNNBkEni1NS/fOUadk58xvYU3hrudUUpLvCmOQTs/5lTwKauGKoR4vSTxFUII8e7TasH7Vyj476yc13bS/Op4vm3oQ+yd9iilwWCMof/2AZx7eM66sQohXhtJfIUQQmQMNrbgsxhyVTAv+/vh8+AXvqjVgdgg89Tz0QmP6bu1H1fCrlgxUCHE6yKJrxBCiIzDzhk6r4IsRc3LR2bTW63mk0qdiL3XCoDI+Ah6b+3DzfCb1otTCPFaSOIrhBAiY3H0gK5rwDWXeXnXBD523U/PUp2Jvd8UgDBDKL229uFO1B0rBiqEeNUk8RVCCJHxuL0HXdeCgwcAmk3D+CLvJdoW6oohpAEAITH36bWlD/cf37dmpEKIV0gSXyGEEBlT1qLQ2Q/0ToBCs6YvE95/SJNcXYl7WAuAu49v02dbXx7GPLRurEKIV0ISXyGEEBnXe+Wh/WLQ6sEYh25FZ36oCTUy9yAutCoANyNu0HdbP8IN4VYOVgjxsiTxFUIIkbEVqg+tfwM0EBeFflk7ZjV2pbxLD+IflQfgyqPL9N/en6i4KOvGKoR4KZL4CiGEEKXaQtMp5ufRD7Bb3pa53rkpru9NfHhpAM49PMegnYOIjo+2YqBCiJchia8QQggBULkf1B5pfh4egONKH3w7FiO/6kt8ZHEATgSfYMjuIRiMBisGKoR4UZL4CiGEEInqfAEVepmfB5/HbU0XFnd7H09DXxKiCgNwMOggw/cMJ94Ub8VAhRAvQhJfIYQQIpFGA82+hxLmySwIPESWv/qzrGdlMkX2I+FxfgD23N7DF/u/wGgyWjFYIURaSeIrhBBCPEmrgw9/h/y1zctXtuK553OW96mO86N+GGNyA7D15la+PvA1JmWyYrBCiLSQxFcIIYT4Lxs76LAUPMuYl8/8Qd7jk1jaqxb6B/0wxnoCsP7aeiYenohSynqxCiGemyS+QgghRErsXKDLashcyLx88GeKXJ3H4h510N7rh9GQFYAVl1Yw7fg0SX6FeAtI4iuEEEKkximLeWpjF3MLLzvGUjp4PfO71cN0tx+mOPOUx77nfPn19K9WDFQI8Twk8RVCCCGexj2POfm1dzcvb/iUSrEH+K1jPeJv98UU7wbAr6d/ZYH/AuvFKYR4Jkl8hRBCiGfJVhw6rQQbB1Am8OtFHbvLzGxbn9iAvpgSXACYdnwayy8ut3KwQojUSOIrhBBCPI88lcFnEWh0YDTA8o40zRLC5Fb1ibnVB1OCIwATD09k7ZW1Vg5WCJESSXyFEEKI51WkEXj/25fXEAFL2tA2fxxjmtQjJrA3ymgPwJgDY9h8Y7MVAxVCpCRNia9Wq0Wn06X5IYQQQrwz3m8Pjb8zP38cDItb072UA5/Vrkd0YE+UyRaF4n/7v2BXwC7rxiqESMImLRt//fXXaDSaJGVr167l3LlzNG7cmKJFiwJw8eJFtm3bhpeXF97e3q8sWCGEECJdqDoQHofA39Mg7CYsacOgHhuJMtRjzpEEHHIvwKRNYPje4fxU7yeq56pu7YiFEKQx8R07dmyS5Tlz5hAcHIy/v78l6U104cIF6tWrR86cOV86SCGEECLdqf81RD+AE4vg/ln4oxMjOvsRFVuPZWcTcMi9iHhTPJ/uHsJvDX6lQo4K1o5YiAzvpfr4Tp06lcGDBydLegGKFy/O4MGDmTJlysscQgghhEifNBpoPh2KtTAv3/oHzeo+jGtRlFZF6hF7pyNKaTEYYxm0cxBnQs5YN14hxMslvrdv30av16e6Xq/Xc/v27Zc5hBBCCJF+6WygzTzIW8O8fGkT2k1DmNKmFPXz1Cf2bjuU0hCdEM2AHQO4GHrRuvEKkcG9VOLr5eXFrFmzuHPnTrJ1t2/fZtasWZQqVeplDiGEEEKkb3p76LgMcvz7fXdyCTa7v+HHjmWpmr0hhnutAYiMi6Tvtn5ce3TNisEKkbGlqY/vf02fPp3GjRtTpEgRWrduTaFC5vnMr1y5wrp161BKsWTJklcSqBBCCJFu2btBlzUwrxGE3YB/ZmDnlIXZXT+i+3wjp+7FY59jA48MYfTd1hffJr7kcc1j7aiFyHBeKvGtUaMGhw8fZvTo0axdu5aYmBgAHBwcaNy4MePGjZMWXyGEEBmDczbz1MbzG0PUfdj2FY6OWZjXoy2dfzdxKTgOu2xbCYkJoc+2PixsshBPZ09rRy1EhvLSE1h4eXmxdu1aIiMjCQoKIigoiMjISNasWSNJrxBCiIzFI7+55dfOzbz85yBcb+1kYa9K5NW1xPCgLgBBj4Pos60PIdEhVgxWiIznlc3cptVqyZ49O9mzZ0erlQnhhBBCZFA5vKDTH2BjD8oIq7rj8eA4S/pUJrvRm7iH5jF9AyID6LutL2GxYVYOWIiMI01dHb755ps0H0Cj0TB69Og01xNCCCHeWnmrQTtf+KMzJMTC8vZk77mZZX2q0PY3E4/CErDNdJhr4dfov70/cxvPxdXW1dpRC/HO0yil1PNu/CItuRqNBqPRmOZ6GcG5c+fw8vLC39+fkiVLWjscIYQQr9rJpfDnQPNz5xzQextX4zPTbvY/xLguRe9+EoD3s77PnIZzcNQ7WjFYId4+ac2l0pTJmkymND8k6RVCCJFhle0MDf/9a2nUPVjsTSHHGBb3qoI+rAPxEeZ7YU6HnGbwrsHEJsRaMVgh3n3SGVcIIYR4nap/CtU+Nj8PvQ5L2+CVWYNvzypogjuREFkMgKP3jjJkzxDijHFWDFaId9srSXzv3LnD8uXLmTlzpmWmNqPRSGhoqLT4CiGEEA3HQ5nO5udBp+GPTpTP6cjv3apgvNeVhMcFAfjnzj+M2DeCBFOCFYMV4t31UomvUophw4aRP39+OnfuzLBhw7h8+TIAUVFR5MuXj59++umVBCqEEEK8tTQaaPkjFGliXr65H9b0oUbBTPzcsRJxd7pjjM4LwM6AnXz595cYTdJwJMSr9lKJ79SpU5k5cybDhw9n+/btPHmfnJubGx9++CGrV69+6SCFEEKIt57OxjzSQ56q5uULG2DTMBqVyM4PbSsRc7snxphcAPx14y/GHxpPGu4/F0I8h5dKfH///Xe6devGxIkTKVOmTLL1pUuXtrQACyGEEBme3gE6/gHZ/r37/Lgv7P4W77K5mPBBBaIDe2GMzQ7A6iurmXx0siS/QrxCL5X4BgYGUq1atVTXOzk5ERER8TKHEEIIId4tDu7QdQ245zEv75sKh36jc+W8jGpcnpiAPpgMWQBYemEpM0/MlORXiFfkpRLfbNmyERgYmOr648ePkydPnpc5hBBCCPHucckBXdeBU1bz8paRcGYV/WoV5OPaZYkO6IspLhMA8/znMefMHOvFKsQ75KUS3w8//JDffvuN69evW8o0Gg0A27Ztw9fXl3bt2r1chEIIIcS7KHNB6LIabF3My+sGwJUdDG1YhB6V3yc6oA+mePNsbj+f+plF5xZZMVgh3g0vlfiOGzcOT09PypQpQ7du3dBoNEyePJkaNWrQtGlTSpcuzahRo15VrEIIIcS7xfN96LgcdLZgSoCVXdHcPsbo5iVo9/775m4PCU4ATD02lZWXVlo5YCHebi+V+Lq5uXHo0CFGjBjBnTt3sLe3Z+/evTx69IgxY8awf/9+HB1l+kUhhBAiVflrQpt5oNFCfDQsa4f2wSW++7A0TYuak19ldABgwqEJbLi2wcoBC/H20ijpMW81aZ1fWgghxDvsuC9s+NT83DUX9NpKnHMu+i8+xt5bJ3DMMxeNzoBWo2Vqrak0ytfIquEKkR6kNZeSKYuFEEKI9KB8D6j/tfl5xB1Y3BpbQxi/dilPRc/3iQnsiTLpMSkTI/eNZN/tfVYNV4i3kU1aNu7VqxcajYY5c+ag0+no1avXM+toNBrmzZv3wgEKIYQQGUaNYfD4ARyaBQ+vwNK22HffwLweFek814R/YDccci8kQZvA0N1D+aXBL1TxrGLtqIV4a6SpxXfXrl3s3LkTk8lkWd69e/czHy/KYDAwcuRIcubMiYODA5UrV2b79u3PVffOnTv4+Pjg7u6Oq6srrVq1SjL6RCKNRpPiY9KkSSnud8WKFVStWhUnJyfc3d2pVq0au3bteuFzFEIIISw0Gmj0LZTyMS/fPQEruuCsM7KwZ0UKuZQj5k5nlNISZ4rj410fc+L+CevGLMRbJE0tvjdv3qRKlSpcunQJLy8vbt68+ZrCMuvRowd+fn4MGTKEwoUL4+vrS7Nmzdi9ezc1atRItV5UVBR169YlPDycUaNGodfrmT59OrVr1+bUqVNkzpw5yfYNGzakW7duScrKli2bbL9jx47lm2++oW3btvTo0YP4+Hj8/f25c+fOqzlhIYQQQqsF71kQEwZXt8P13bB2AO5t5rK4TyV8fjNy+0489rmWE5sQy8CdA5nXaB4ls8i9IkI8k0qjHDlyKFtbW/XFF1+omJiYtFZ/bocPH1aAmjp1qqUsJiZGFSxYUFWtWvWpdSdPnqwAdeTIEUvZhQsXlE6nU1988UWSbQE1aNCgZ8Zz8OBBpdFo1LRp09J4Jqnz9/dXgPL3939l+xRCCPGOMEQp9XsDpca4mh8bP1PKZFKBoY9V1Yk7VMGJ45SXr5fy8vVS1ZdXV5dCL1k7YiHeuLTmUmm+ue3SpUv06dOHKVOmUKpUKXbs2PGKU3EzPz8/dDod/fr1s5TZ29vTu3dvDh48+NQZ4/z8/KhYsSIVK1a0lBUrVoz69euzcmXKYyDGxMQQGxub6j5nzJhBjhw5+PTTT1FKERUV9QJnJYQQQjwnWyfotAKyFjMvH/0d9k7hvUyOLOlTGXdjVWKDvAEIN4TTd1tfboTfsF68QrwF0pz4urq68ssvv3Dw4EFcXV1p3LgxXbt2JSQk5JUGdvLkSYoUKYKrq2uS8kqVKgFw6tSpFOuZTCbOnDlDhQoVkq2rVKkS165dIzIyMkm5r68vTk5OODg4UKJECZYtW5as7s6dO6lYsSI//vgjWbNmxcXFBU9PT37++efnOp/g4GDOnTuX5HH16tXnqiuEECKDcvSALmvALbd5ec9EODqXAlmdWdy7Mg6xNYi93xyA0NhQ+mzrw+3I21YMWIj0LU19fJ9UsWJFjh49yk8//cTo0aPZuHEjuXPnTradRqPh9OnTad5/UFAQnp6eycoTy+7evZtivdDQUAwGwzPrFi1aFIBq1arh4+ND/vz5uXv3Lr/88gudO3cmPDycjz76CICwsDAePHjAP//8w65duxgzZgx58uRhwYIFfPzxx+j1evr37//U85k1axbjxo17/hdACCGEAHDLBV3XwvzGEP0QNg0HBw+Ke33Iwl6V6DxXYdDGYZd1O8HRwfTZ1gffJr7kcMph7ciFSHdeOPEFSEhIICQkBIPBQObMmZPdNPYyYmJisLOzS1Zub29vWZ9aPeC56/7zzz9JtunVqxfly5dn1KhR9OjRAwcHB0u3hocPH/LHH3/Qvn17ANq2bUupUqWYMGHCMxPfgQMH0q5duyRlV69exdvb+6n1hBBCCLIUhs5+sLAlxEXBmn7gkImyBesyt3sFeiwwYdDEYZdlL3ei7tB3W18WNFlAFocs1o5ciHTlhSew2LFjB15eXkyaNIn+/ftz6dKlVzqcmYODAwaDIVl5Yj9cBweHVOsBL1QXwNbWlsGDB/Po0SOOHz+eZHu9Xk/btm0t22q1Wtq3b8/t27cJCAh46vlky5aNkiVLJnkUKlToqXWEEEIIi1zloP0S0OrBFA9/dIY7x6lWMAu/di6P6WFT4kKrAXAz4ib9tvfjUewj68YsRDqT5sQ3JCSELl260LhxYxwdHTlw4AA//vgjLi4urzQwT09PgoKCkpUnluXMmTPFeh4eHtjZ2b1Q3USJXTZCQ0Mt+7S3tydz5szodLok22bLlg0wd4cQQgghXquCdaHN74AG4h/DkrYQcpn6xbMzvX1Z4oJbEPfIfI/LlbArDNgxgMi4yKfvU4gMJM2Jb9GiRVm3bh2TJk3i+PHjlpvNXrUyZcpw+fJlIiIikpQfPnzYsj4lWq2WUqVKcezYsWTrDh8+TIECBZ6ZpCdOdJE1a1bLPsuUKUNISAhxcXFJtk3sa5y4rRBCCPFalWwNzb83P48JhSUfQvgdWr6fk0kfvo8h6EPiw98H4NzDcwzaOYjo+GgrBixE+pHmxLdKlSr4+/vz+eefJ2v9fJXatm2L0Whkzpw5ljKDwcCCBQuoXLmypVU2ICCAixcvJqt79OjRJMnvpUuX2LVrV5J+timNRBEZGcmMGTPIkiUL5cuXt5S3b98eo9HIwoULLWWxsbEsXbqUEiVKPLMVWQghhHhlKvaBOqPMz8MDzclvdCjtK+ZhdAsvYu/6EB9ZAoCTwSf5dPenGIzJuwAKkdFolFLK2kGkxsfHh7Vr1zJ06FAKFSrEwoULOXLkCDt37qRWrVoA1KlTh7179/LkaURGRlK2bFkiIyMZPnw4er2eadOmYTQaOXXqlKV1duzYsaxbt46WLVuSJ08egoKCmD9/PgEBASxevJjOnTtb9hkTE0PFihW5fPkyn376KXny5GHx4sWcOHGCDRs20LRp0zSf37lz5/Dy8sLf35+SJWXGHSGEEGmgFPz1uXl8X4D3KkK3P8HWiZk7rjB953kc3luEjfNlAGq/V5vpdaaj1+mtGLQQr1Zac6mXGtXhdVu0aBGjR49m8eLFhIWFUbp0aTZu3GhJelPj4uLCnj17GDp0KBMmTMBkMlGnTh2mT5+epEtC9erVOXDgAHPnzuXhw4c4OTlRqVIl5s+fT7169ZLs08HBgV27djFixAjmz5/P48ePKVOmDJs2baJx48av5fyFEEKIVGk00HSKeYizc2vg9lFY2Q06/sEn9QsRZYjn97+74JB7ATZON9h7ey//2/8/JteajI02XX/9C/HapOsW33edtPgKIYR4aQlxsLw9XNtlXi7lA61nozQaRq09y/JjV3HMPQ+do3n0oQ8KfsD46uPRal54YCch0o205lJy1QshhBBvMxtb8FkMuf69L+XsStg6Cg0wwbsUH5TKT3RgT4yx5kmc1l9bz7eHvkXavURGJImvEEII8bazc4ZOqyBLEfPy4V9h/w/otBp+8HmfBkXzEhPQG6PBPATnyssr+f7Y95L8igxHEl8hhBDiXeCUGbqsAddc5uVd4+G4L3qdlp87laNa/rzEBPTBFGeeZXXR+UX8cuoXKwYsxJsnia8QQgjxrnDPbU5+HTKZlzcOhfPrsdfrmNO1AmVz5iH6Vh9M8W4AzD4zm3ln51kxYCHeLEl8hRBCiHdJtmLmbg96R1AmWN0bbuzDyc6GBT0rUTxrXqJv9cUUb57MacaJGSy9sNTKQQvxZkjiK4QQQrxrclc03/CmtQFjHCzvBHdP4eagZ1HvSuR3/7fbQ4ITAJOOTGLtlbVWDlqI108SXyGEEOJdVLgBtJ5tfh4XCUvawMNrZHG2Y2mfyng65iMmoBfKaA/AmANj+Ov6X1YMWIjXTxJfIYQQ4l1Vqi00mWx+Hv0AFntDRBCebg4s61uZLLYFiA7ohTLaolCM+nsUO2/ttGrIQrxOkvgKIYQQ77IqA6DW5+bnjwLMLb8xYeTN7MSSPpVx1RYk5nYPlMkGozIyfN9w/r7zt3VjFuI1kcRXCCGEeNfV/RLK9zQ/Dz4HyzpAXDRFsruwqFclHIxFiLndFaV0JJgSGLJ7CEfvHbVuzEK8BpL4CiGEEO86jQaa/wDFPzAvBx4Cv55gjKf0e+7M71ERfVxxYm93QiktBqOBQTsHcTrktHXjFuIVk8RXCCGEyAi0OmgzF/LXMi9f3gLrPwGlqJTfg9+6lEcT40XsXR+U0hCTEMNH2z/iwsML1o1biFdIEl8hhBAio7Cxg/ZLwfN98/LpZbB9NAB1imbjxw5lMUWWITboQwAi4yPpv70/V8OuWitiIV4pSXyFEEKIjMTeFTqvBo+C5uUDP8E/MwFoWsqTKW3fJyG8IrH3zN0iwgxh9N3el1sRt6wVsRCvjCS+QgghREbjnBW6rgXnHObl7V/DySUAtC3/HuM+KEl8WDUMwU0AeBDzgD7b+nA36q61IhbilZDEVwghhMiIMuU1J7/2bubl9Z/ARfMEFt2r5ePzxkWJe1gHQ0g9AO49vkefbX0Ijg62VsRCvDRJfIUQQoiMKnsJ6LQSbBxAGc0jPdz8B4BBdQvxUZ2CxD1oSNzDGgAERgbSd1tfQmNDrRm1EC9MEl8hhBAiI8tTBXwWgkYHCbGwvCPcOwvAiMZF6VolH4bg5sSFVQbgevh1+m/vT7gh3JpRC/FCJPEVQgghMroijaHVL+bnhnDz7G6hN9BoNIz7oCQfln0Pw71WxD8qB8DF0IsM3DGQx/GPrRi0EGknia8QQgghoExHaPSt+XnUfVjcGiLvo9VqmNK2NI1LehIb1Ib4iFIAnHlwhsE7BxOTEGPFoIVIG0l8hRBCCGFWbTDUGGp+HnYDlraB2HBsdFp+7FiWmoWzE3unPQmRxQA4dv8YQ3YPIc4YZ8WghXh+kvgKIYQQ4v/VHwNlu5if3zsLyztBfCx2Njpmdy1PxXxZibnTmYSoQgAcuHuA4XuHE2+Kt2LQQjwfSXyFEEII8f80GmgxE4o2Ny/f+htW9wZjAo62NszrURGvnJmJud2NhOh8AOwO3M2X+7/EaDJaL24hnoMkvkIIIYRISmcDbedB3urm5YsbYeMQUApXez2LelWmcFYPYgJ7YIx5D4DNNzcz7uA4TMpkvbiFeAZJfIUQQgiRnN4BOi6H7Oab2Ti5GHZ+A4CHky1L+lQmj7sH0QG9MMaaZ4Bbe3Utk45MQillraiFeCpJfIUQQgiRMns36LIaMuUzL/89DQ6ahz3L7mrP0j6Vye6ciZiAPhgNWQFYfnE5M07MkORXpEuS+AohhBAidS7ZzVMbO2UzL28dBaf/ACC3hyNL+1Qmk70HMQF9MMV5ADDffz6zz8y2VsRCpEoSXyGEEEI8nUcB6LoG7FzNy+sGwuWtABTK5sKiXpVwtslMdEAfTPFuAPxy6hcWnltorYiFSJEkvkIIIYR4thyloOMfoLMDZYSV3SHgMABeudxY0KMi9mQlOqAPKsEZgO+Pfc+KiyusGbUQSUjiK4QQQojnk686tFsAGi0kxMCydnD/PAAV8nkwp1t59Mbs5uTX6AjAhMMT+PPqn9aMWggLSXyFEEII8fyKNYeWP5qfx4bDkg8h7BYANQtn5adOZdHEexId0Atlsgfg6wNfs+XmFmtFLISFJL5CCCGESJtyXaHBOPPzyCBY3BqiQgBoXDIH37crjTK8R0xADzDZYlImvtj3BXsC91grYiEASXyFEEII8SKqfwpVB5ufh16DpW3BEAlA67LvMb6VF8aYfEQHdgNlQ4JKYNieYRy8e9CKQYuMThJfIYQQQqSdRgMNx8P7Hc3LQafgj06QYACgS5W8fNG0GMboQkTf7gJKR7wpnk93f8rx+8etF7fI0CTxFUIIIcSL0Wrhg5+gSBPz8o19sKYvmIwA9K9dkI/rFcIYVYyYOx1AaYhJiGHQzkGcDTlrxcBFRiWJrxBCCCFenE4PbRdA7irm5fN/wqbP4N+Z24Y1LEKPavlIiCxFzN12oDQ8jn/MgB0DuBR6yYqBi4xIEl8hhBBCvBxbR+j0B2QrYV4+vgD2fAeARqPh6xYlaFf+PRIiyhF7zxuAiLgI+m3vx/Xw61YKWmREkvgKIYQQ4uU5ZIIua8A9j3l572Q4bJ62WKvVMKlNaZqX8iT+UWVi77UAIDQ2lL5b+xIYGWitqEUGI4mvEEIIIV4NV0/oug4cs5iXN4+As34A6LQaprf/v/buOz6qKv3j+Gdm0hshECChhyqEDokiEpAugoD0XkIRWQRB2UX90dQVWWV1EezA0hSCoIuNIrAu0pHeewudhATS5/7+GBkdJ4FAQhKS7/v1mpf3nvucO889jseH4cy9tWlaJZCU641IutQSgEsJlxi8cjAXbl7IpaSlIFHhKyIiItmnSAXovRTcfG37y4bC0dUAuLmYmdW7HuHlA0i++iRJV5oAcC7+HINXDuZKwpVcSloKChW+IiIikr2Ca0OPhWBxA2sqfNkHzm4DwMPVwmf9G1CrtD/Jl1uRfK0hACdvnGTwysHEJMbkXt6S76nwFRERkexXvjE8+xmYzJByy/aAi8u2uzj4uLswd0ADqhT3I+liO5KvNwDgaMxRhq4eSlxyXG5mLvmYCl8RERF5MKq1h7bv2rYTrtsebRx7FgB/LzfmRYZRrog3SRc6khJbG4D9V/czfPVwbqXcyqWkJT9T4SsiIiIPTv0B8OSrtu0b52zF761rABTz9WB+ZDjBhbxIPN+FlBvVAdh5eScjfxpJYmpibmUt+ZQKXxEREXmwnhgL4cNs21cO25Y9JMUDUKqwF/Mjwynq40ni+R6kxlcBYPOFzby47kVS0lJyK2vJh1T4ioiIyINlMkGrv0ONLrb9c9thcR9ITQYgJNCHeYPC8XP3IOFsb1JvhgDw87mfGffzOFKtqbmVueQzKnxFRETkwTOb4ZmZULG5bf/YT7B8GFitADwS5MfcgWF4uXqQcKYfaQm2B2GsOrWK1za8htWw5lbmko+o8BUREZGc4eIGXf8NpWx3cWDvUvhhHBgGAHXKFObTfvVxs3hy6/QArIklAVhxfAVTNk3B+C1O5H6p8BUREZGc4+YNPRdDYFXb/paP4b/T7IcbVijKrF51ccGLW6cHYiQXByDqcBRvb31bxa9kiQpfERERyVleAdD7K/ArZdtf+wZs/cx+uNkjxZnerTZYvbl5ahCk2B6BPP/AfP71679yIWHJL1T4ioiISM4rVBL6LAPPANv+t2Ng33L74Xa1gnmrUw2MVD/iT0ZCamEAPtnzCZ/u+TQXEpb8QIWviIiI5I7AytArCly9AQO+GgzH19kPd2tQhteeroaR6k/8yUhMaYUAeG/He8zfPz93cpaHmgpfERERyT2l6kH3+WB2hbRk+KIXnNthPzyoUXlGN6+MkVKE+JODMFl9AJi6dSpLDy/NrazlIZWnC9+kpCTGjRtHcHAwnp6ehIeHs2rVqkz1PXfuHF27dsXf3x8/Pz+eeeYZjh8/7hRnMpnSfb311lt3PH+LFi0wmUyMGDHivq5NREREflPhSej0MWCC5HjbAy6uHLUfHtmsIoOfKI81uRjxJwdisnoCMGnjJFYcX5FLScvDyCW3E7iT/v37ExUVxahRo6hUqRJz5szhqaeeYu3atTRq1CjDfvHx8TRt2pTY2FjGjx+Pq6sr06dPJyIigp07d1KkSBGH+BYtWtC3b1+Htjp16mR4/q+++oqNGzdm7eJERETkd6Gd4NZV+G6s7Z/zOsKgH8EvGJPJxPinHiE+KZVFWyD+1AB8yn2GYUri1f+9iofFg+Zlm+f2FchDIM8Wvlu2bOGLL75g2rRpjB07FoC+ffsSGhrKyy+/zC+//JJh35kzZ3LkyBG2bNlCgwa2ewW2adOG0NBQ3nnnHd58802H+MqVK9O7d+9M5ZWYmMiYMWMYN24c//d//3efVyciIiJOwgbbit51f4fY0zCvEwz4DrwCMJlMvN6hBjeT0vhmF9w81Q/vsrNJI4WX/vsS7zV9j8alGuf2FUgel2eXOkRFRWGxWBgyZIi9zcPDg0GDBrFx40bOnDlzx74NGjSwF70AVatWpVmzZixevDjdPgkJCSQmJt41r7fffhur1WovxkVERCQbRYyDBpG27csHYGE3SL4FgMVs4p2utWj+SDHSEkK4eaYPJsOFVGsqL657kS3RW3IxcXkY5NnC99dff6Vy5cr4+fk5tIeFhQGwc+fOdPtZrVZ2795N/fr1nY6FhYVx7Ngx4uLiHNrnzJmDt7c3np6eVKtWjYULF6Z77tOnT/PWW28xdepUPD097+l6Ll26xL59+xxeR48evXtHERGRgsRkgjZvQ/WOtv2zW2BJP0hLAcDVYmZGz7o0rFCEtJuVuXm2JyYsJKUlMeKnEey8tDP3cpc8L88WvtHR0QQFBTm13247f/58uv2uXbtGUlJSpvs2bNiQN954g+XLlzNr1iwsFgu9evVi1qxZTv3HjBlDnTp16N69+z1fz8yZMwkNDXV4dejQ4Z7PIyIiku+ZLdDxIwhpYts/shK+fh6sVgA8XC180rc+dcr4kxZfjVtnuwImElITeG71c+y/uj/XUpe8Lc+u8U1ISMDd3d2p3cPDw348o35Apvtu2LDBIWbgwIHUq1eP8ePH079/f/s3u2vXrmXp0qVs3rz5Pq4Ghg8fTpcuXRzajh49quJXREQkPS7u0G0+zG0P53fA7i/Bqwi0ehNMJrzdXZjTP4zun2ziQHQtEs6n4BkcRXxKPENXDeXzVp9TqXCl3L4KyWPy7De+np6eJCUlObXfXoeb0VKD2+330xfAzc2NESNGEBMTw/bt2wFITU1l5MiR9OnTx2Hd8L0oVqwY1atXd3hVrFjxvs4lIiJSILj7Qq8lUOS3AnbTTPjfdPvhQl6uzBsURkigN6mx9Um88AwAMUkxDF45mJOxJ3MhacnL8mzhGxQURHR0tFP77bbg4OB0+wUEBODu7n5ffW8rXbo0YFs2AfDvf/+bQ4cOMXToUE6ePGl/AcTFxXHy5Elu3bqVuQsTERGRzPMuCn2+At/f/t+9ZhJsn2s/XNTHnfmDwinp70nK9cdIvNgGgKuJV4lcGcm5+HO5kbXkUXm28K1duzaHDx/mxo0bDu23lxrUrl073X5ms5kaNWqwbds2p2ObN28mJCQEX1/fO7737QddBAYGArYftaWkpPD4449Tvnx5+wtsRXH58uVZuXLlPV2fiIiIZJJ/GVvx6+Fv218xCg78x3442N+TBZHhBPq6k3ItgqTLzQC4eOsikT9GcvHmxZzPWfKkPFv4du7cmbS0ND7++GN7W1JSErNnzyY8PNz+rezp06c5ePCgU9+tW7c6FL+HDh3ip59+clhne/nyZaf3jYuL45///CdFixalXr16AHTv3p1ly5Y5vQCeeuopli1bRnh4ePZdvIiIiDgq9oht2YOrFxhWiBoEJ362Hy5X1Jv5g8Lx93Il+Upzkq/a7ul7Nv4sg1cN5mrC1dzKXPIQk2EYRm4nkZGuXbuybNkyRo8eTcWKFZk7dy5btmxhzZo1NG5s+0A3adKE9evX88fLiIuLo06dOsTFxTF27FhcXV159913SUtLY+fOnfZvcidOnMjy5ctp164dZcqUITo6ms8//5zTp08zb948evXqdcf8TCYTzz//PDNmzLiv69u3bx+hoaHs3buX6tWr39c5RERECpQjq2BRd7CmgpsvDPgWgmrZD+86E0OvTzcTn5SCR4lvcC1se9JqlcJV+KzVZxRyL5RbmcsDcK+1VJ79xhdsywhGjRrFvHnzGDlyJCkpKaxYscJe9GbE19eXdevW0bhxY15//XVee+01atWqxfr16+1FL8Djjz9OsWLF+PTTT3n++eeZPn06VapUYfXq1XctekVERCQXVGoBHX675WhyHMx/Fq4esx+uVdqfz/rVx93FQuKFdqTF2u7rf+j6IZ5b/RzxyfG5kbXkEXn6G9/8Tt/4ioiI3KdNH8IP42zb/mVh0ErwLWE/vO7QJQb/exspaWl4l/oSs+8uAOoWq8uHLT7E0+XeHkQleVO++sZXREREJF2PDoMnxtq2Y07ZvvlNiLEfblKlGO91r4PZZObm2a5w01YU7bi0gxd+eoGkNOfbnkr+p8JXREREHk5Pvgp1+9m2L+6FRT0g5feHVD1VI4ipz9YELMSd6Y4poTIAG6M3MnbdWFKsKbmQtOQmFb4iIiLycDKZ4Onp8Eg72/7pXyBqIKSl2kO61C/NxHbVwHDlxqnemJNCAFh3dh3jfx5PmjUtNzKXXKLCV0RERB5eZgt0+hTKPWHbP/Qd/Gck/OEnTP0fL89LraqA4Ubsyb5YUsoC8MPJH5jwywSshjU3MpdcoMJXREREHm6uHtB9IZSoadvfuQBWT3AIGd6kAsMiKoDVg5jj/XBJLQnA18e+5s3Nb6Lf+hcMKnxFRETk4efhB72XQoBtKQMb3oMN79sPm0wmxrWuQu9Hy4DVi5jjA3BJKw7Al4e+ZPr26Sp+CwAVviIiIpI/+BSDPsvA57fbmq16DXYutB82mUxMbh9KpzolMdJ8iDk+EFdrUQBm75vNh7s+zI2sJQep8BUREZH8o3A56PMVePz2hLavR8Ch7+2HzWYTb3euSavqxTFSC3H9+EBcjQAAZu6ayey9s3MhackpKnxFREQkfyleHXp8CS4eYKTBkv5waqP9sIvFzPs96vBEpaIYKQFcPz4AV/wAeHf7uyw6uCiXEpcHTYWviIiI5D9lH4Muc8FkgdREWNgNLuy1H3Z3sfBRn3o0KFcYIznQtuwBHwDe3Pwmy44sy63M5QFS4SsiIiL5U5XW8MwHtu2kWJjfCa6ftB/2cnPhs/4NCC3phzWpBDEnBuCCFwATN07khxM/5ELS8iCp8BUREZH8q3YPaPm6bTv+IszrCPGX7If9PFz598BwKhXzwZpYktiT/XAxuWM1rPzt57+x9vTaXEpcHgQVviIiIpK/NfwLPP6CbfvacZj/LCTesB8O8HZjfmQ4ZQK8sCaU5cbJvlhMbqQaqYxZP4Zfzv2SS4lLdlPhKyIiIvlf80lQp7dt+8Ju+KInpCTaDxf382BBZDjF/dxJu1WBuFO9MONCijWFF9a+wLYL23IpcclOKnxFREQk/zOZ4On3oMpTtv2TP8PSQWBNs4eUDvBiQWQ4Ad5upN2sws2z3TFhJjEtkefXPM/uy7tzKXnJLip8RUREpGCwuEDnz6FMQ9v+wRWwYjT84YltFYv58u+BYfh6uJAaF0rC+S6YMHEr9RbDVg/j4LWDuZS8ZAcVviIiIlJwuHpCj0VQvIZtf8dc+Ol1h5DQkoWY3b8Bnq4WUmLrkHyxIwBxyXEMWTmE4zHHczprySYqfEVERKRg8fSH3kttT3kD+PkfsGmWQ0j9cgF83LcebhYzidfCSL3cHoDrSdeJXBnJmRtncjZnyRYqfEVERKTg8S0OfZaBdzHb/g9/hd2LHUKeqBTIv3rWwWI2kXClIca1NgBcTrhM5MpIouOjczprySIVviIiIlIwBYTYvvl1tz2umOXPwZFVDiGtqpfgH11qYjJB/MUITLHNATh/8zyDVw3mSsKVnM5askCFr4iIiBRcQTVta34t7mBNhS/7wJktDiEd65RiyjOhANw43wxLXGMATt04xeCVg7meeD3H05b7o8JXRERECrZyjWx3ezCZITUBFnSBSwccQno/Wpa/takKmIg52wbXm7Y7QxyNOcrQVUO5kXwjnRNLXqPCV0REROSRp6Hde7btxBiY1wliTjuEDI2owF+erAiYuHb6adwTGwBw4NoBhq8ezq2UWzmbs9wzFb4iIiIiAHX7QrMJtu248zCvI9x0XMP7YovK9G9YDjBz5UQHPJPrALDr8i7+8tNfSExNRPIuFb4iIiIitzUaDY+NsG1fPQoLOkNSnP2wyWTi/56uRpd6pQALl449i1eq7Z7AWy5sYfS60SSnJedC4pIZKnxFREREbjOZoMUUqNndtn/+V/iiF6Qm2UPMZhNvPVuTtjWCABcuHu2Kt7UqAP879z/G/XccqdbUXEhe7kaFr4iIiMgfmc3wzAyo1NK2f2I9fDUErGn2EIvZxPRutWlSJRAMVy4c7oEPFQFYfXo1r254lbQ/xEveoMJXRERE5M8srtBlLpQOt+3vXw7fvwyGYQ9xczHzYe96hJcPAMOd6EO98TWVA+Db498yZdMUjD/ES+5T4SsiIiKSHjcv6PklFKtm29/6Kax7yyHEw9XCp/3qU6tUIbB6cP5QH3zNpQBYemQpU7dOVfGbh6jwFREREcmIZ2Hb090KlbHtr38LtnziEOLr4cqcAWFUKe4Lad5EH+yHrzkIgAUHFvD+r+/ndNaSARW+IiIiInfiFwx9loFXUdv+dy/B3qUOIYW93Zg3KIxyRbww0nyJPtQPH0sxAD7d8ykf7/44p7OWdKjwFREREbmbohWhdxS4+QAGfDUUjq5xCCnm58H8yHCCCnlgpPpz4VA/fCxFAPjXr/9i3v55uZC4/JEKXxEREZHMCK4D3ReCxQ2sKfBlHzi73SGkVGEvFkSGU9THDSOlCBcP98PLUgiAt7e+zZLDS3Ijc/mNCl8RERGRzAqJgE6fACZIuWl7wMXlw44hgT78e2A4fh4uWJOLceVofzwtPgBM2TiF/xz7Ty4kLqDCV0REROTeVO8AT79r2064Znu0cew5h5BqwX7MGRiGl5uFtMQgrh/vj7vZCwODVze8ysqTK3M+b1HhKyIiInLP6g+Epq/atm+ctRW/t645hNQtU5hP+9bHzcVMyq1SxJ3qh6vZHathZdx/x/Hfs//NhcQLNhW+IiIiIvej8VgIG2rbvnIIFnSB5JsOIQ0rFmVmz7q4mE0kxZcl8WxfXEyupBqpjF47mk3Rm3Ih8YJLha+IiIjI/TCZoPVbENrZtn9um+0Hb6nJDmHNqxXn3W61MZngVmwFUqN7YzFZSLYmM/Knkfx66ddcSL5gUuErIiIicr/MZugwCyo0s+0fWwPLnwOr1SGsfa1g/t6xBgBx16tgutwLM2YSUhMYvno4+67sy+nMCyQVviIiIiJZ4eIG3eZByfq2/b1R8MNf4U+PKu4eVoZX2z4CwPXL1XC73h2A+JR4hq4eyuHrjneHkOynwldEREQkq9y8odcSKFrFtr/lI/j5H05hkU+EMKp5JQAuX6iJd1wXAGKTYhmycggnY0/mVMYFkgpfERERkezgFQB9vgK/Urb9n16HbbOdwl5oVonIRuUBuHC2Hn63OgJwNfEqkSsjORt3NsdSLmhU+IqIiIhkl0KloM8y8Ayw7X/7Iuz/2iHEZDLxSttH6BFWGoBzp8IpnPQ0ABdvXSRyZSQXbl7I0bQLChW+IiIiItkpsDL0igJXbzCssDQSjq93CDGZTLzeoQbtawUDcPr44xRJbQ3AufhzDF45mCsJV3I89fxOha+IiIhIditVz/aDN7MrpCXDFz3hvONtyyxmE+90rUXzR4oBJk4eiaCYYbs7xMkbJxmyagixSbG5kHz+pcJXRERE5EGo2Aw6fQSYIDke5neGq8ccQlwtZmb0rEvDCkUAE8cONqO4qTEAR64fYdiqYcQnx+d87vmUCl8RERGRByX0WWjztm371hWY1wFuRDuEeLha+KRvfeqU8QfMHN3fmiDLYwDsvbqX59c8z62UWzmadn6lwldERETkQQofAhHjbNsxp2F+J0i47hDi7e7CnP5hPBLkB5g5vPdpglxt9wXecWkHL6x9gaS0pBxOPP9R4SsiIiLyoDX5G9QfaNu+tB8Wdodkx29xC3m5Mm9QGCGB3oCFw3s6EOxeG4BN0ZsYs24MKWkpOZt3PqPCV0RERORBM5ngqX9AtQ62/TObYEl/+FMhW9THnfmDwinp7wmGC4d2dSLYvToA68+u568//5VUa2rO5p6PqPAVERERyQlmC3T6GMpH2PaP/AhfjwCr1SEs2N+TBZHhBPq6g+HGod1dCfKwPRFu5amVTPhlAlbD+uezSyao8BURERHJKS7u0H0BBNex7e/+Ala9BobhEFauqDfzB4Xj7+UKVneO7O5OCY8QAL459g1vbHoD40995O5U+IqIiIjkJHdf2wMuilS07W+cARvecwqrUsKXuQPC8HF3wUjz5PjeXhT3KAvA4sOLeWfbOyp+75EKXxEREZGc5l3U9mhj3yDb/uoJsGOeU1it0v581q8+7i5m0lK8Ob2vD4Eetqe9zd0/l5m7ZuZk1g+9PF34JiUlMW7cOIKDg/H09CQ8PJxVq1Zlqu+5c+fo2rUr/v7++Pn58cwzz3D8+HGnOJPJlO7rrbfecoj76quv6NatGyEhIXh5eVGlShXGjBlDTExMdlyqiIiIFDT+ZWzFr4e/bf8/I+HACqew8JAifNSnHq4WE8nJPkQf7E+AezEAPtz1IZ/t+SwHk364mYw8/B15jx49iIqKYtSoUVSqVIk5c+awdetW1q5dS6NGjTLsFx8fT926dYmNjWXMmDG4uroyffp0DMNg586dFClSxB5rMplo0aIFffv2dThHnTp1qF69un2/aNGiBAcH06FDB8qUKcOePXv48MMPCQkJYceOHXh6et7z9e3bt4/Q0FD27t3r8F4iIiJSgJzeDP9+BlITwOJuK4bLPe4U9t2eaEYs3IHVAF/vGPwrfkJM8lUA/hr2V3o90iunM89191pLueRATvdly5YtfPHFF0ybNo2xY8cC0LdvX0JDQ3n55Zf55ZdfMuw7c+ZMjhw5wpYtW2jQoAEAbdq0ITQ0lHfeeYc333zTIb5y5cr07t37jvlERUXRpEkTh7Z69erRr18/FixYQGRk5H1cpYiIiBR4ZcKh2zxY1B3Skmz/7P8tBNV0CHuqRhBTn63JS1G7ibvpj8upQfiW+Yi4lFje2vIWXi5edKzUMZcu4uGQZ5c6REVFYbFYGDJkiL3Nw8ODQYMGsXHjRs6cOXPHvg0aNLAXvQBVq1alWbNmLF68ON0+CQkJJCYmZnjOPxe9AB072j5cBw4cuNvliIiIiGSsUgt45rf1ukk3YP6zcM15iWaX+qWZ2K4aANdjAkg5F4m3iw8AE36ZwHfHv8uxlB9Gebbw/fXXX6lcuTJ+fn4O7WFhYQDs3Lkz3X5Wq5Xdu3dTv359p2NhYWEcO3aMuLg4h/Y5c+bg7e2Np6cn1apVY+HChZnK8cKFC4BtGcTdXLp0iX379jm8jh49mqn3ERERkQKgVjdo9Xfb9s1LMK8jxF10Cuv/eHleamW7r+/lq4GYLg3G08ULA4Px/xvPmtNrcjLrh0qeLXyjo6MJCgpyar/ddv78+XT7Xbt2jaSkpEz3bdiwIW+88QbLly9n1qxZWCwWevXqxaxZs+6a49SpU7FYLHTu3PmusTNnziQ0NNTh1aFDh7v2ExERkQLkseHwxBjb9vWTtm9+E2OdwoY3qcCwiAoARF8sjsfVwbiZ3Ukz0nhp/UtsOLchB5N+eOTZwjchIQF3d3endg8PD/vxjPoBme67YcMGXnjhBdq3b8+wYcPYvn07oaGhjB8/PsP3AFi4cCGfffYZY8aMoVKlSne9nuHDh7N3716H1/Lly+/aT0RERAqYJ1+Dur/96P7iHljUA1IcaxKTycS41lXo/WgZAE6fD8I/LhIXswsp1hReWPsCWy9szenM87w8W/h6enqSlJTk1H57HW5Gd1G43X4/fQHc3NwYMWIEMTExbN++Pd2Yn3/+mUGDBtGqVSveeOONO1/Ib4oVK0b16tUdXhUrVsxUXxERESlATCZoOx2qPm3bP7UBogZBWuqfwkxMbh9KpzolATh2ujTFEgZjMVlISktixJoR7Lq8K6ezz9PybOEbFBREdHS0U/vttuDg4HT7BQQE4O7ufl99bytdujRgWzbxZ7t27aJ9+/aEhoYSFRWFi0uevTGGiIiIPKwsLvDsZ1DuCdv+oW9hxQtOjzY2m0283bkmraoXt4UdL0up1IGYMHEr9RbPrXqOA1f1I/zb8mzhW7t2bQ4fPsyNGzcc2jdv3mw/nh6z2UyNGjXYtm2b07HNmzcTEhKCr6/vHd/79oMuAgMDHdqPHTtG69atKVasGN999x0+Pj6ZvRwRERGRe+PqAd0XQonfbmv263xYM8kpzMVi5v0edXiiku3H9nsPVyDE1B+AuJQ4hq4ayrGYYzmVdZ6WZwvfzp07k5aWxscff2xvS0pKYvbs2YSHh9u/lT19+jQHDx506rt161aH4vfQoUP89NNPdOnSxd52+fJlp/eNi4vjn//8J0WLFqVevXr29gsXLtCyZUvMZjM//vijU1EsIiIiku08/KD3Uihc3rb/v+nwywynMHcXCx/1qUf9soUB2Lm/ClVcbOuEryddZ/DKwZy+cTrH0s6r8vST27p27cqyZcsYPXo0FStWZO7cuWzZsoU1a9bQuHFjwHZ/3fXr1/PHy4iLi6NOnTrExcUxduxYXF1deffdd0lLS2Pnzp32onXixIksX76cdu3aUaZMGaKjo/n88885ffo08+bNo1ev35+AUrt2bXbt2sXLL79MjRo1HPIsXrw4LVq0uOfr05PbREREJFOunYDPW0H8b7c36/Ah1O7hFHYjMYWen2xi7znb35iH19nF/sRFAAR5BzGn9RyCfe685PNhcq+1VJ4ufBMTE3nttdeYP38+169fp2bNmkyZMoVWrVrZY9IrfAHOnj3L6NGjWblyJVarlSZNmjB9+nSHH5StWrWKadOmsWfPHq5evYq3tzdhYWGMGzeOJ5980uF8JpMpwzwjIiJYt27dPV+fCl8RERHJtAt7YfZTkBQLJgv0WASVWzmFXY1PotvHmzh6KR6AhvW3sufmUgDK+JZhTus5BHrlj7+5zleFb36nwldERETuyalfbA+2SE0EF0/ouxzKPOoUdiE2kS4f/cKZawmAweNhG9kd9w0AFQpV4PPWnxPgEZCzuT8A91pL5dk1viIiIiLyJ2UbQpc5tm98UxNgYVe4uM8prEQhDxYMepTifu6AiQ1bHqNWoTYAHIs9xtBVQ4lNcn4wRn6nwldERETkYVKlDbT/l207MRbmdYLrp5zCyhTxYv6gcAK83QAT/9v0BLX8mwFw8NpBhq8ezs2UmzmYeO5T4SsiIiLysKnTC1pMsW3HX7Atf4h3vltVpeK+/HtgGL7uLoCZXzY9SU1/2w0Cdl/ZzYg1I0hIzfhJtfmNCl8RERGRh9HjI6HhSNv2tWOw4FlIvOEUFlqyELMHNMDT1YLVsLBlSytC/W3rgrdd3MbotaNJTkvOycxzjQpfERERkYdVi8lQ+7fbr0bvgi96QkqiU1j9cgF83LcebhYzKWkWft3ejkf8bc8r2HB+Ay+tf4kUa0pOZp4rVPiKiIiIPKxMJmj3PlS2/XCNkz/DV4PBmuYU+kSlQN7vUQeL2URisoX9v3aiSiHbU+F+OvMTr/zvFdLS6ZefqPAVEREReZhZXKDLbCjzmG3/wDfw7YuQzh1rW4eW4B9dbMVufKKFI3u6UcGvKgDfn/ieyZsmYzWsOZZ6TlPhKyIiIvKwc/WEHl9Asd/uZbt9Dqx9I93QjnVKMaVDKACxNy2cPdCbcr4VAPjqyFdM3TLV6cFg+YUKXxEREZH8wNMf+nwF/mVt+/+dBps+TDe0z6Nl+Wsb2ze9V264cOVof0r52PotPLiQf+74Z74sflX4ioiIiOQXviWgzzLw/u2RxD+Mg91L0g0dFlGBvzxZEYDoa67cOj2IIK+SAHy+93M+2v1RjqSck1T4ioiIiOQnRSpA76Xg5mvbXz4MjqxON/TFFpXp37AcAKcuumFcGEoxz+IAfLDzA+bum5sTGecYFb4iIiIi+U1QLeixCCxuYE2FxX3gzFanMJPJxP89XY0u9UoBcOScGx5Xn6OwewAA/9j2DxYfWpyjqT9IKnxFRERE8qPyT0Dnz8FkhpRbsLALXDroFGY2m3jr2Zq0rREEwL5THhSN/wuF3AoBMGXTFL459k2Opv6gqPAVERERya8eaQdP/9O2nXAd5neCmDNOYRaziendatOkim1t8I6jnpRKHomPqw8Ar214jR9P/phTWT8wKnxFRERE8rN6/aDZ/9m2b5yDeR3h5lWnMDcXMx/2rkd4edsyh00HvKlkjMLD4oHVsPLX//6VdWfW5VzeD4AKXxEREZH8rtGL8Ohw2/bVI7CgMyTFO4V5uFr4tF99apWyLXP47x4faruNxs3sRqqRyovrXmTj+Y05mXm2UuErIiIikt+ZTNDyDajZzbZ/fgd82RtSk51CfT1cmTMgjCrFbXeFWLWjEOHeo3Exu5BiTeGFtS+w4+KOnMw+26jwFRERESkIzGZ45gOo2MK2f3wtLBsK1jSn0MLebswbFEa5Il4AfLelMBH+ozCbzCSkJjB8zXD2Xtmbk9lnCxW+IiIiIgWFxRW6zoVSYbb9fV/B9+Mgnae0FfPzYH5kOEGFPABYvqEozYuOxISJmyk3GbpqKIeuHcrJ7LNMha+IiIhIQeLmDT2/hMBHbPtbP4H1b6cbWqqwFwsiwynq4wbA0v+WoHWJ5wG4kXyDIauGcDz2eI6knR1U+IqIiIgUNF4B0OcrKFTatr/uTdj6abqhIYE+/HtgOH4eLgAsWVeKp4KHAnAt8RqDVw7mTJzzLdLyIhW+IiIiIgWRXzD0WQZeRWz7346FvV+lG1ot2I85A8PwcrNgGLB0bQhPlewPwKVblxi8cjAXbl7IocTvnwpfERERkYKqaCXoFQVuPoABXw2BY2vTDa1bpjCf9q2Pm4uZVKvBsnWP0LpUTwDOxZ9j8MrBXEm4koPJ3zsVviIiIiIFWcm60H0BWNzAmgJf9IJz29MNbVixKDN71sXFbCI51eDb9bVpUepZAE7eOMnglYOJSYzJweTvjQpfERERkYIupAl0+hgwQcpNWNAFLh9ON7R5teK82602JhPcSray6udHebJkOwCOxhxl6OqhxCXH5Vzu90CFr4iIiIhA9Y7Q9h+27VtXYX4niD2Xbmj7WsH8vWMNAOIS0/jfpggaB7cEYP/V/Ty/5nlupdzKkbTvhQpfEREREbFpEAlNxtu2Y8/Yit9b19IN7R5Whlfb2m6JdjU+lR3bWtGwRBMAfr30K+vPrs+JjO+JCl8RERER+V3EyxA2xLZ9+SAs7AbJN9MNjXwihFHNKwEQHZvCwd3tCC/+OH8L+xttyrfJqYwzTYWviIiIiPzOZILWUyHU9qM1zm6Bxf0gLSXd8BeaVSKyUXkATl1N4fSB7jxVtnNOZXtPVPiKiIiIiCOzGTp8CBWetO0fXQXLh4PV6hRqMpl4pe0jdG9gexjG4Ys36ff5FuKTUnMy40xR4SsiIiIizlzcoOs8KFnPtr9nMfw4HgzDKdRkMvFGxxq0qxUMwK6zsaw7dCkns80Ul9xOQERERETyKHcf6LkEZreGK4dh8yzwCYQnxjiFWswm3u1ai8SUNJ6sWoynawbnQsJ3pm98RURERCRj3kWg91fgV9K2v2YybJ+TbqirxczHferRI6xMzuV3D1T4ioiIiMid+ZeGPsvAs7Btf8Vo2P9NuqEmkykHE7s3KnxFRERE5O4Cq0CvKHD1AsMKSwfBif/mdlb3RIWviIiIiGROqfrQbR6YXSAtGRb1hPM7czurTFPhKyIiIiKZV7E5dPzItp0cB/OfhavHcjenTFLhKyIiIiL3pkZnaPO2bfvWFZjXAW5E52pKmaHCV0RERETuXfhQaPyybTvmtO2b34SYXE3pblT4ioiIiMj9aToe6g2wbV/aB4u6Q/Kt3M3pDlT4ioiIiMj9MZmg7TtQ7Rnb/umNEDUA0lJyN68MqPAVERERkftntkCnT6B8Y9v+4R/gm5HpPto4t6nwFREREZGscXGH7gshqLZtf9dC2LUoV1NKjwpfEREREck6d1/bAy4CKkCdPlCja25n5MQltxMQERERkXzCJxAiV9sebZwHH12swldEREREso9XQG5nkCEtdRARERGRAkGFr4iIiIgUCCp8RURERKRAUOErIiIiIgWCCl8RERERKRBU+IqIiIhIgaDCV0REREQKhDxd+CYlJTFu3DiCg4Px9PQkPDycVatWZarvuXPn6Nq1K/7+/vj5+fHMM89w/PhxpziTyZTu66233rrvc4qIiIhI3pOnH2DRv39/oqKiGDVqFJUqVWLOnDk89dRTrF27lkaNGmXYLz4+nqZNmxIbG8v48eNxdXVl+vTpREREsHPnTooUKeIQ36JFC/r27evQVqdOnSydU0RERETyljxb+G7ZsoUvvviCadOmMXbsWAD69u1LaGgoL7/8Mr/88kuGfWfOnMmRI0fYsmULDRo0AKBNmzaEhobyzjvv8OabbzrEV65cmd69e98xn3s9p4iIiIjkLXl2qUNUVBQWi4UhQ4bY2zw8PBg0aBAbN27kzJkzd+zboEEDe4EKULVqVZo1a8bixYvT7ZOQkEBiYmK2nlNERERE8o48W/j++uuvVK5cGT8/P4f2sLAwAHbu3JluP6vVyu7du6lfv77TsbCwMI4dO0ZcXJxD+5w5c/D29sbT05Nq1aqxcOHCLJ/zzy5dusS+ffscXkePHr1jHxERERHJPnl2qUN0dDRBQUFO7bfbzp8/n26/a9eukZSUdNe+VapUAaBhw4Z07dqV8uXLc/78eT744AN69epFbGwszz333H2dMz0zZ85k0qRJd7pkEREREXmA8mzhm5CQgLu7u1O7h4eH/XhG/YBM992wYYNDzMCBA6lXrx7jx4+nf//+eHp63vM50zN8+HC6dOni0Hb06FE6dOhwx34iIiIikj3ybOHr6elJUlKSU/vtdbienp4Z9gPuqy+Am5sbI0aMYNiwYWzfvp1GjRpl+ZwAxYoVo1ixYneMEREREZEHJ8+u8Q0KCiI6Otqp/XZbcHBwuv0CAgJwd3e/r763lS5dGrAtcciuc4qIiIhI7sqz3/jWrl2btWvXcuPGDYcfuG3evNl+PD1ms5kaNWqwbds2p2ObN28mJCQEX1/fO7737YdSBAYGZts503P7G2T9yE1ERETk3t2uodL7W/l0GXnUpk2bDMCYNm2avS0xMdGoWLGiER4ebm87deqUceDAAYe+b731lgEYW7dutbcdPHjQsFgsxrhx4+xtly5dcnrfGzduGBUqVDCKFi1qJCUl3fM578Xy5csNQC+99NJLL7300kuvLLyWL1+eqdrLZBiGQR7VtWtXli1bxujRo6lYsSJz585ly5YtrFmzhsaNGwPQpEkT1q9fzx8vIy4ujjp16hAXF8fYsWNxdXXl3XffJS0tjZ07d9q/yZ04cSLLly+nXbt2lClThujoaD7//HNOnz7NvHnz6NWr1z2f817ExMSwfv16Spcune4P57LT7R/SLV++nIoVKz7Q98rrNBaONB6ONB6/01g40ng40nj8TmPhKCfHIykpiTNnzhAREYG/v//dO9zXV5U5JCEhwRg7dqxRokQJw93d3WjQoIHxww8/OMREREQY6V3GmTNnjM6dOxt+fn6Gj4+P8fTTTxtHjhxxiFm5cqXRokULo0SJEoarq6vh7+9vtGzZ0lizZk26+WTmnHnV3r17DcDYu3dvbqeS6zQWjjQejjQev9NYONJ4ONJ4/E5j4Sgvj0eeXeMLtluFTZs2jWnTpmUYs27dunTbS5UqxZIlS+54/hYtWtCiRYtM55OZc4qIiIhI3pRn7+ogIiIiIpKdVPiKiIiISIGgwreACAwMZMKECff1I7z8RmPhSOPhSOPxO42FI42HI43H7zQWjvLyeOTpuzqIiIiIiGQXfeMrIiIiIgWCCl8RERERKRBU+IqIiIhIgaDCV0REREQKBBW+IiIiIlIgqPB9SMTHxzNhwgRat25NQEAAJpOJOXPmZLp/TEwMQ4YMITAwEG9vb5o2bcqOHTvSjf3mm2+oW7cuHh4elClThgkTJpCamppNV5I9sjIea9asYeDAgVSuXBkvLy9CQkKIjIwkOjraKbZJkyaYTCanV+vWrbP5iu5fVsZizpw56V6fyWTiwoULTvH5/bOR0b9vk8mEq6urQ2y5cuXSjRs2bNgDuKr7s3XrVkaMGEH16tXx9vamTJkydO3alcOHD2eqf36bN7IyHvlt3sjKWOTHeSMr45Hf5g2Affv20aVLF0JCQvDy8qJo0aI0btyY//znP5nqn5fnjjz9yGL53ZUrV5g8eTJlypShVq1aGT6qOT1Wq5W2bduya9cuXnrpJYoWLcrMmTNp0qQJ27dvp1KlSvbY77//ng4dOtCkSRP+9a9/sWfPHl5//XUuXbrErFmzHsCV3Z+sjMe4ceO4du0aXbp0oVKlShw/fpwZM2awYsUKdu7cSYkSJRziS5Uqxd///neHtuDg4Oy4jGyRlbG4bfLkyZQvX96hzd/f32G/IHw2XnnlFSIjIx3abt68ybBhw2jZsqVTfO3atRkzZoxDW+XKle8r7wdh6tSpbNiwgS5dulCzZk0uXLjAjBkzqFu3Lps2bSI0NDTDvvlx3sjKeOS3eSMrY3Fbfpo3sjIe+W3eADh16hRxcXH069eP4OBgbt26xdKlS2nfvj0fffQRQ4YMybBvnp87DHkoJCYmGtHR0YZhGMbWrVsNwJg9e3am+n755ZcGYCxZssTedunSJcPf39/o0aOHQ2y1atWMWrVqGSkpKfa2V155xTCZTMaBAweyfiHZJCvjsX79eiMtLc2pDTBeeeUVh/aIiAijevXq2ZLzg5KVsZg9e7YBGFu3br1rbEH4bKRn3rx5BmAsWLDAob1s2bJG27Zts5LqA7dhwwYjKSnJoe3w4cOGu7u70atXrzv2zY/zRlbGI7/NG1kZi/w4b2RlPNLzMM8bGUlNTTVq1aplVKlS5Y5xeX3u0FKHh4S7u7vTNwqZFRUVRfHixenUqZO9LTAwkK5du/L111+TlJQEwP79+9m/fz9DhgzBxeX3vwwYPnw4hmEQFRWVtYvIRlkZj8aNG2M2m53aAgICOHDgQLp9UlNTiY+Pv6/3e9CyMhZ/FBcXR1paWrrHCspnIz0LFy7E29ubZ555Jt3jycnJ3Lx5M9veLzs1bNgQNzc3h7ZKlSpRvXr1DD/rt+XHeSMr45Hf5o2sjMUf5Zd5I7vG47aHed7IiMVioXTp0sTExNwxLq/PHSp8C4Bff/2VunXrOk3aYWFh3Lp1y76G6ddffwWgfv36DnHBwcGUKlXKfjw/io+PJz4+nqJFizodO3z4MN7e3vj6+lKiRAlee+01UlJSciHLB6dp06b4+fnh5eVF+/btOXLkiMPxgvrZuHz5MqtWraJDhw54e3s7Hf/pp5/w8vLCx8eHcuXK8d577+VClvfGMAwuXryY7mf9jwrKvJHZ8UhPfps37nUs8vu8cb+fjfw0b9y8eZMrV65w7Ngxpk+fzvfff0+zZs3u2Cevzx1a41sAREdH07hxY6f2oKAgAM6fP0+NGjXsP9K43f7n2PPnzz/YRHPRP//5T5KTk+nWrZtDe4UKFWjatCk1atTg5s2bREVF8frrr3P48GG+/PLLXMo2+3h5edG/f3/7/8C2b9/Ou+++S8OGDdmxYwelS5cGKLCfjS+//JLU1FR69erldKxmzZo0atSIKlWqcPXqVebMmcOoUaM4f/48U6dOzYVsM2fBggWcO3eOyZMn3zGuoMwbmR2P9OS3eSOzY1FQ5o37/Wzkp3ljzJgxfPTRRwCYzWY6derEjBkz7tgnz88dD2QBhTxQ97pu0Ww2G88995xT+5o1awzAWLZsmWEYhjF58mQDMC5evOgU+8QTTxi1atXKQtYPTlbXca5fv95wcXExunbtmqn4wYMHG4CxcePG+3q/Byk71rT+/PPPhslkMoYOHWpvK6ifjccee8wIDAx0WH+WEavVarRq1cpwcXExzpw5c1/v96AdOHDA8PPzMx577DEjNTX1jrH5fd4wjHsbjz/LT/OGYWRtLAwjf80bhpG18chP88aBAweMVatWGXPnzjXatm1rdOzY0bhw4cId++T1uUNLHQoAT09P+5qaP0pMTLQf/+M/M4q9fTw/OXjwIB07diQ0NJRPP/00U31u/xp39erVDzK1XNOoUSPCw8Mdrq8gfjaOHz/Oxo0b6datm8P6s4yYTCZGjx5Namrqfd1Z40G7cOECbdu2pVChQkRFRWGxWO4Yn9/njXsdjz/Kb/NGVsbitvw0b2RlPPLbvFG1alWaN29O3759WbFiBfHx8bRr1w7DMDLsk9fnDhW+BUBQUFC695q83Xb7Fju3/7oho9i8dCue7HDmzBlatmxJoUKF+O677/D19c1Uv9t/jXft2rUHmV6uKl26tMP1FbTPBth+nAKk+9eVGcmrn43Y2FjatGlDTEwMP/zwQ6b+feXneeN+xuO2/DZvZGUs/iw/zBtZHY/8NG+kp3PnzmzduvWO9zfO63OHCt8CoHbt2uzYsQOr1erQvnnzZry8vOz3D6xduzYA27Ztc4g7f/48Z8+etR/PD65evUrLli1JSkrixx9/THeNUUaOHz8O2H6lml8dP37c4foK0mfjtoULF1KhQgUeffTRTPfJi5+NxMRE2rVrx+HDh1mxYgXVqlXLVL/8Om/c73hA/ps3sjIW6XnY543sGI/8Mm9kJCEhAbD9ASEjeX7ueCALKOSButO6xfPnzxsHDhwwkpOT7W1ffPGF0z31Ll++bPj7+xvdunVz6F+1alWjVq1aDmuaXn31VcNkMhn79+/P/ovJBvc6HvHx8UZYWJjh6+trbNu2LcPzxsbGGomJiQ5tVqvV6NatmwEY27dvz7ZryC73OhaXLl1yivv2228NwBg5cqRDe0H4bNy2Y8cOAzBee+21dM979epVp3V/ycnJxuOPP264ubnZ7yOc21JTU4327dsbLi4uxrfffpthXEGZN7IyHvlt3sjKWOTHeSMr43Fbfpk3DMNId91tcnKyUbduXcPT09OIi4szDOPhnDt0V4eHyIwZM4iJibH/0vE///kPZ8+eBeAvf/kLhQoV4m9/+xtz587lxIkTlCtXDrD91cSjjz7KgAED2L9/v/0pKmlpaUyaNMnhPaZNm0b79u1p2bIl3bt3Z+/evcyYMYPIyEgeeeSRHL3eu7nf8ejVqxdbtmxh4MCBHDhwwOEejT4+PnTo0AGAHTt20KNHD3r06EHFihVJSEhg2bJlbNiwgSFDhlC3bt0cvd47ud+xaNiwIXXq1KF+/foUKlSIHTt28Pnnn1O6dGnGjx/v8B4F4bNx24IFC4CM/7rym2++4fXXX6dz586UL1+ea9eusXDhQvbu3cubb76ZrfcRzooxY8bwzTff0K5dO65du8b8+fMdjvfu3RugwMwbWRmP/DZvZGUs8uO8kZXxuC2/zBsAQ4cO5caNGzRu3JiSJUty4cIFFixYwMGDB3nnnXfw8fEBHtK544GU0/JAlC1b1gDSfZ04ccIwDMPo16+fw/5t165dMwYNGmQUKVLE8PLyMiIiIjJ86s6yZcuM2rVrG+7u7kapUqWMV199Nd0/3ea2+x2PO/UrW7asPe748eNGly5djHLlyhkeHh6Gl5eXUa9ePePDDz80rFZrzl7sXdzvWLzyyitG7dq1jUKFChmurq5GmTJljOeeey7DX+3m98+GYRhGWlqaUbJkSaNu3boZnn/btm1Gu3btjJIlSxpubm6Gj4+P0ahRI2Px4sUP8KruXURERIbj8Mfpv6DMG1kZj/w2b2RlLPLjvJHV/1by07xhGIaxaNEio3nz5kbx4sUNFxcXo3Dhwkbz5s2Nr7/+2iHuYZw7TIZxh5/miYiIiIjkE/pxm4iIiIgUCCp8RURERKRAUOErIiIiIgWCCl8RERERKRBU+IqIiIhIgaDCV0REREQKBBW+IiIiIlIgqPAVERERkQJBha+IiIiIFAgqfEVERESkQFDhKyIiBYLJZGLixIm5nYaI5CIVviIiv2nTpg2FCxfm4sWLTsdiY2MJCgoiPDwcq9WaC9llzv79+5k4cSInT57M1vPOmTMHk8mEyWTif//7n9NxwzAoXbo0JpOJp59++r7e480332T58uVZzDTzfvnlFyZOnEhMTEyOvaeI5C4VviIiv5k5cybJycmMHj3a6dj48eO5cuUKH3/8MWZz3p069+/fz6RJk7K98L3Nw8ODhQsXOrWvX7+es2fP4u7uft/nftCFb0JCAq+++qp9/5dffmHSpEkqfEUKkLw7e4uI5LDy5cszYcIEFi1axMqVK+3tW7du5cMPP+TFF1+kVq1aDzSHxMTEPP2N8lNPPcWSJUtITU11aF+4cCH16tWjRIkSuZRZ+qxWK4mJiYCtaHdxccnljEQkN6nwFRH5gxdffJGaNWsyfPhwEhMTSUtLY9iwYZQtW5YJEyZw8OBBOnfuTEBAAB4eHtSvX59vvvnG4RzXrl1j7Nix1KhRAx8fH/z8/GjTpg27du1yiFu3bh0mk4kvvviCV199lZIlS+Ll5cWNGzdISUlh0qRJVKpUCQ8PD4oUKUKjRo1YtWpVhrnPmTOHLl26ANC0aVP70oR169bZY2bOnEn16tVxd3cnODiY559//p6+8ezRowdXr151yCM5OZmoqCh69uyZbp9//OMfNGzYkCJFiuDp6Um9evWIiopyiDGZTNy8eZO5c+fa8+7fvz8A/fv3p1y5ck7nnThxIiaTyek8I0aMYMGCBfbr/OGHH+zHbq/xnThxIi+99BJg+wPP7fc8efIkERERGf4Bp0qVKrRq1equ4yQieZP+6Csi8gcuLi58/PHHNGzYkClTplCsWDF27NjBDz/8wIkTJ3j88ccpWbIkf/3rX/H29mbx4sV06NCBpUuX0rFjRwCOHz/O8uXL6dKlC+XLl+fixYt89NFHREREsH//foKDgx3ec8qUKbi5uTF27FiSkpJwc3Nj4sSJ/P3vfycyMpKwsDBu3LjBtm3b2LFjBy1atEg398aNGzNy5Ejef/99xo8fzyOPPAJg/+fEiROZNGkSzZs357nnnuPQoUPMmjWLrVu3smHDBlxdXe86PuXKleOxxx5j0aJFtGnTBoDvv/+e2NhYunfvzvvvv+/U57333qN9+/b06tWL5ORkvvjiC7p06cKKFSto27YtAPPmzbNf65AhQwCoUKFCZv6VOfnpp59YvHgxI0aMoGjRoukWzZ06deLw4cMsWrSI6dOnU7RoUQACAwPp06cPgwcPZu/evYSGhtr7bN26lcOHDzsslxCRh4whIiJORowYYbi6uho+Pj5Gjx49DMMwjGbNmhk1atQwEhMT7XFWq9Vo2LChUalSJXtbYmKikZaW5nC+EydOGO7u7sbkyZPtbWvXrjUAIyQkxLh165ZDfK1atYy2bdvec95LliwxAGPt2rUO7ZcuXTLc3NyMli1bOuQ2Y8YMAzA+//zzO5539uzZBmBs3brVmDFjhuHr62vPuUuXLkbTpk0NwzCMsmXLOuX952tLTk42QkNDjSeffNKh3dvb2+jXr5/Te/fr188oW7asU/uECROMP/9vDDDMZrOxb98+p3jAmDBhgn1/2rRpBmCcOHHCIS4mJsbw8PAwxo0b59A+cuRIw9vb24iPj3c6t4g8HLTUQUQkHW+88QZFihTBbDYzffp0rl27xk8//UTXrl2Ji4vjypUrXLlyhatXr9KqVSuOHDnCuXPnAHB3d7f/AC4tLY2rV6/i4+NDlSpV2LFjh9N79evXD09PT4c2f39/9u3bx5EjR7LlelavXk1ycjKjRo1y+HHe4MGD8fPz49tvv830ubp27UpCQgIrVqwgLi6OFStWZLjMAXC4tuvXrxMbG8sTTzyR7lhkh4iICKpVq3bf/QsVKsQzzzzDokWLMAwDsP17/PLLL+nQoQPe3t7ZlaqI5DAVviIi6fDz86NKlSqULl2a4sWLc/ToUQzD4LXXXiMwMNDhNWHCBAAuXboE2H5QNX36dCpVqoS7uztFixYlMDCQ3bt3Exsb6/Re5cuXd2qbPHkyMTExVK5cmRo1avDSSy+xe/fu+76eU6dOAbY1qn/k5uZGSEiI/XhmBAYG0rx5cxYuXMhXX31FWloanTt3zjB+xYoVPProo3h4eBAQEEBgYCCzZs1KdyyyQ3rjea/69u3L6dOn+fnnnwHbHxwuXrxInz59snxuEck9WuMrIpIJt++0MHbs2Ax/3FSxYkXAdluu1157jYEDBzJlyhQCAgIwm82MGjUq3Ts2/PnbXrCt1z127Bhff/01K1eu5NNPP2X69Ol8+OGHREZGZuOV3Z+ePXsyePBgLly4QJs2bfD390837ueff6Z9+/Y0btyYmTNnEhQUhKurK7Nnz073tmjp+fMP2G5LS0tLtz298bxXrVq1onjx4syfP5/GjRszf/58SpQoQfPmzbN8bhHJPSp8RUQyISQkBABXV9e7Fj9RUVE0bdqUzz77zKE9JibG/iOqzAgICGDAgAEMGDCA+Ph4GjduzMSJE+9Y+GZUJJYtWxaAQ4cO2a8FbHdkOHHixD0XdB07dmTo0KFs2rSJL7/8MsO4pUuX4uHhwY8//uhwj9/Zs2dnOvfChQune+eJe/mWOj0ZvR+AxWKhZ8+ezJkzh6lTp7J8+XIGDx6MxWLJ0nuKSO7SUgcRkUwoVqwYTZo04aOPPiI6Otrp+OXLl+3bFovFvjb0tiVLltjXAGfG1atXHfZ9fHyoWLEiSUlJd+x3e/3pnwvF5s2b4+bmxvvvv++Q22effUZsbKz97gqZ5ePjw6xZs5g4cSLt2rXLMM5isWAymRy+nT158mS6D6rw9vZOt8CtUKECsbGxDks9oqOjWbZs2T3lnN77gfNY3danTx+uX7/O0KFDiY+Pp3fv3ll6PxHJffrGV0Qkkz744AMaNWpEjRo1GDx4MCEhIVy8eJGNGzdy9uxZ+316n376aSZPnsyAAQNo2LAhe/bsYcGCBQ7ftN5NtWrVaNKkCfXq1SMgIIBt27YRFRXFiBEj7tivdu3aWCwWpk6dSmxsLO7u7jz55JMUK1aMv/3tb0yaNInWrVvTvn17Dh06xMyZM2nQoMF9FXX9+vW7a0zbtm159913ad26NT179uTSpUt88MEHVKxY0WnNcr169Vi9ejXvvvsuwcHBlC9fnvDwcLp37864cePo2LEjI0eO5NatW8yaNYvKlStn6Qdy9erVA+CVV16he/fuuLq60q5dO3tBXKdOHUJDQ1myZAmPPPIIdevWve/3EpE8IndvKiEikndFREQY1atXd2g7duyY0bdvX6NEiRKGq6urUbJkSePpp582oqKi7DGJiYnGmDFjjKCgIMPT09N4/PHHjY0bNxoRERFGRESEPe727cyWLFni9N6vv/66ERYWZvj7+xuenp5G1apVjTfeeMNITk6+a96ffPKJERISYlgsFqdbm82YMcOoWrWq4erqahQvXtx47rnnjOvXr9/1nH+8ndmdpHc7s88++8yoVKmS4e7ublStWtWYPXt2urciO3jwoNG4cWPD09PTABxubbZy5UojNDTUcHNzM6pUqWLMnz8/w9uZPf/88+nmxp9uZ2YYhjFlyhSjZMmShtlsTvfWZm+//bYBGG+++eYdr1tEHg4mw/jT38eJiIgIYHv4xujRozl58iRlypTJ7XREJItU+IqIiKTDMAxq1apFkSJFWLt2bW6nIyLZQGt8RURE/uDmzZt88803rF27lj179vD111/ndkoikk30ja+IiMgfnDx5kvLly+Pv78/w4cN54403cjslEckmKnxFREREpEDQfXxFREREpEBQ4SsiIiIiBYIKXxEREREpEFT4ioiIiEiBoMJXRERERAoEFb4iIiIiUiCo8BURERGRAkGFr4iIiIgUCCp8RURERKRAUOErIiIiIgXC/wMACjR1+altLgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(num=0, dpi=120)\n",
    "plt.plot(years, ytm, label=\"YTM\")\n",
    "plt.plot(years, spots, label=\"Spot Curve\")\n",
    "plt.plot(years, par_rates, label=\"Par Curve\")\n",
    "plt.title('Yield Curves - Benchmark Government Bonds')\n",
    "plt.xlabel('Years to Maturity')\n",
    "plt.ylabel('Yield')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "20. Assuming that there are no opportunities for coupon-stripping and bond reconstitution in the government bond market, the yield on a 3-year, 5% annual coupon payment government bond should be closest to:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 3-year, 3.75% coupon government bond has a yield of 5.0832%, while a 3-year, zero-coupon government bond has a yield of 5.0470%. The lower yield on the zero-coupon government bond is due to the downward-sloping yield curve. Therefore, the 5% coupon payment government bond with its higher coupon rate than its 3.75% coupon counterpart, will have a yield higher than 5.0832%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yield_to_mat = 5.094%\n"
     ]
    }
   ],
   "source": [
    "cf = np.full(3, 5)\n",
    "cf[-1] += 100\n",
    "price = np.dot(cf, df)\n",
    "yield_to_mat = coupon_bond_ytm(n=3, pmt=5, pv=price, fv=100, cf_freq=1, comp_freq=1, beg=False)\n",
    "print(f'{yield_to_mat = :0.3%}')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "fin",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}