{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Replication of Ben S. Bernanke, Jean Boivin and Piotr Eliasz QJE 2005\n", "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive(FAVAR) Approach. The Quarterly Journal of Economics, Vol. 120, No. 1 (Feb., 2005), pp. 387-422\n", "- Francesco Franco, NOVA SBE Empirical Macroeconomics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# PART 1" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "'''Importing packages and functions''' \n", "\n", "import os # operating system\n", "import pandas as pd # pandas\n", "import numpy as np # numpy\n", "from numpy import linalg as LA\n", "from numpy.linalg import inv, multi_dot # linear algebra from numpy for PCA\n", "import matplotlib.pyplot as plt # figures\n", "%matplotlib inline " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "RangeIndex: 511 entries, 0 to 510\n", "Columns: 120 entries, 0 to 119\n", "dtypes: float64(120)\n", "memory usage: 479.1 KB\n" ] }, { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
0123456789...110111112113114115116117118119
00.013400.008610.007320.005230.009520.01330.018800.031200.045000.01740...0.004730.000000.000000.004360.000000.000000.000000.003480.0046295.8
10.006020.004920.000000.01940-0.004750.01070.013900.025600.038700.01490...0.00471-0.003010.005240.000000.000000.000000.00000-0.003480.0091796.4
20.014300.014500.015700.006400.016500.02580.016000.027300.029700.03050...0.000000.000000.000000.004340.003450.000000.000000.006940.0045696.9
30.008290.009560.004760.020100.000000.03190.005640.025400.034100.00892...0.004680.003010.002610.004320.003440.000000.000000.006900.0000097.5
40.007040.00714-0.004760.00746-0.007030.02330.00337-0.00659-0.00736-0.00301...0.004660.000000.000000.000000.003430.003250.003370.003430.0045497.2
\n", "

5 rows × 120 columns

\n", "
" ], "text/plain": [ " 0 1 2 3 4 5 6 7 \\\n", "0 0.01340 0.00861 0.00732 0.00523 0.00952 0.0133 0.01880 0.03120 \n", "1 0.00602 0.00492 0.00000 0.01940 -0.00475 0.0107 0.01390 0.02560 \n", "2 0.01430 0.01450 0.01570 0.00640 0.01650 0.0258 0.01600 0.02730 \n", "3 0.00829 0.00956 0.00476 0.02010 0.00000 0.0319 0.00564 0.02540 \n", "4 0.00704 0.00714 -0.00476 0.00746 -0.00703 0.0233 0.00337 -0.00659 \n", "\n", " 8 9 ... 110 111 112 113 114 \\\n", "0 0.04500 0.01740 ... 0.00473 0.00000 0.00000 0.00436 0.00000 \n", "1 0.03870 0.01490 ... 0.00471 -0.00301 0.00524 0.00000 0.00000 \n", "2 0.02970 0.03050 ... 0.00000 0.00000 0.00000 0.00434 0.00345 \n", "3 0.03410 0.00892 ... 0.00468 0.00301 0.00261 0.00432 0.00344 \n", "4 -0.00736 -0.00301 ... 0.00466 0.00000 0.00000 0.00000 0.00343 \n", "\n", " 115 116 117 118 119 \n", "0 0.00000 0.00000 0.00348 0.00462 95.8 \n", "1 0.00000 0.00000 -0.00348 0.00917 96.4 \n", "2 0.00000 0.00000 0.00694 0.00456 96.9 \n", "3 0.00000 0.00000 0.00690 0.00000 97.5 \n", "4 0.00325 0.00337 0.00343 0.00454 97.2 \n", "\n", "[5 rows x 120 columns]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "'''Load data set'''\n", "\n", "#Change to your directory and put csv in it\n", "os.chdir(r\"C:\\Users\\ffranco\\Dropbox\\Work\\Teaching\\Empirical\\Class6_2018\\data\")\n", "\n", "df = pd.read_csv(\"nsbalpanel.csv\",header=None) #load data\n", "df.info()\n", "df.head()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "'''\n", " Data Description in Appendix1 page 416-420\n", " The transformation codes are:\n", " 1:no transformation\n", " 2:first difference\n", " 4:logarithm\n", " 5:first difference of logarithm.\n", " An asterisk *, next to the mnemonic, denotes a variable assumed to be slow-moving in the estimation\n", "'''\n", "\n", "# let us keep the indexes of the slow-moving variables\n", "slowindex = list(range(0,53))+list(range(102,119)) # remember that index in python starts with 0, therefore\n", " # need to take out 1 from numbers in appendix\n", " # furthermore range is closed on the left and open on the right\n", " \n", "xindex = [15,107,77,80,95,92,73,101,16,48,50,25,47,117,53,61,70,119]\n", "\n", "data_dict = {0:'IPP',\n", " 1:'IPF',\n", " 2:'IPC',\n", " 3:'IPCD',\n", " 4:'IPCN'}" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "'''Transforming the data'''\n", "\n", "stdffr = df.loc[:,76].std() # keep std of the ffr\n", "df = df.apply(lambda x: (x-x.mean())/x.std())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the case where you observe one factor without error $Y_t=ffr_t$\n", "$$\\mathcal{X}_{t}=\\Lambda\\left[\\begin{array}{c}\n", "Y_{t}\\\\\n", "F_{t}\n", "\\end{array}\\right]+\\left[\\begin{array}{c}\n", "0\\\\\n", "e_{t}\n", "\\end{array}\\right]$$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "'''Specification: what is observable'''\n", "\n", "#df = df.rename(columns=data_dict) \n", "\n", "observables = [76] #[\"ffr\"]\n", "Y = df.loc[:,observables]\n", "X = df.loc[:,df.columns.difference(observables)]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "''' Parameters '''\n", "\n", "num_factors = 3 # Change to increase number of factors to be extracted\n", "N = X.shape[1] # number of series \n", "T = X.shape[0] # number of observations\n", "M = Y.shape[1] # number of series considered observables factors\n", "K = num_factors\n", "# number of periods for IRFS \n", "num_impulses = 40\n", "num_lags = 13\n", "nrep1 = 1\n", "nrep2 = 100\n", "nsteps = 48" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PCA computing the eigenvalues and eigenvectors\n", "This is the Linear Algebra algorithm that is widely used because numerically stable. In the notes we have that • The estimators of $F_{t}$ and $\\Lambda$ solve the minimization problem$$\\min_{\\left\\{ F_{i}\\right\\} _{i=1}^{T},\\Lambda}\\left(NT\\right)^{-1}\\sum_{t=1}^{T}\\left[\\mathcal{X}_{t}-\\Lambda F_{t}\\right]'\\left[\\mathcal{X}_{t}-\\Lambda F_{t}\\right]$$subject to $N^{-1}\\Lambda'\\Lambda=I_{r}.$\n", "\n", "Under our simplified assumptions $\\hat{F}_{t}=N^{-1}\\hat{\\Lambda}'\\mathcal{X}_{t}$ and $\\hat{\\Lambda}$ is the matrix of eigenvectors (multiplied by $\\sqrt{N}$) of the sample variance matrix of $\\mathcal{X}_{t}.$ \n", "Remember that a square matrix can be decomposed as $$\\mathcal{X}'\\mathcal{X}=VSV^{-1}$$ where $V$ are the eigenvectors and $S$ the eigenvalues. Now our covariance matrix is $$\\frac{\\mathcal{X}'\\mathcal{X}}{N}$$ therefore $\\Lambda=\\sqrt{N}V$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def extract_eig(x,nf):\n", " \n", " # Compute the factors with the eigenvalues eigenvectors decomposition\n", " # Inputs: x the data\n", " # nf number of factors\n", " # Outputs: lam the factor loadings\n", " # fac the factors \n", " x=np.array(x)\n", " xx=x.T@x \n", " s, V = LA.eig(xx)\n", " W = V[:,:3]\n", " lam = W*np.sqrt(x.shape[1])\n", " fac = x@lam/x.shape[1]\n", " return fac, lam " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PCA using the SVD decomposition\n", "The SVD decomposition is practical because always exists and says that $\\mathcal{X}=VSU'$ where $V$ and $U$ are orthonormals. Therefore $$\\mathcal{X}'\\mathcal{X}=VSU'USV'=VS^{2}V'$$ and we can see that $V$ is our $\\Lambda$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def extract_svd(x,nf):\n", " \n", " # Compute the factors with the SVD\n", " # Inputs: x the data\n", " # nf number of factors\n", " # Outputs: lam the factor loadings\n", " # fac the factors \n", " \n", " x = np.array(x)\n", " U, s , V = LA.svd(x)\n", " W = V.T[:,:nf]\n", " lam = W*np.sqrt(x.shape[1])\n", " fac = x@lam/x.shape[1]\n", " \n", " return fac, lam " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Slow-R-Fast identification scheme\n", "the Bernanke, Boivin, and Eliasz (2005) implementation of the slow-R-fast identification scheme starts from \n", "$$\\mathcal{X}_{t}=\\Lambda F_{t}+e_{t}$$\n", "and divide the factors into slow-moving and fast-moving\n", "$$\\begin{bmatrix}\\mathcal{X}_{t}^{s}\\\\\n", "\\mathcal{X}_{t}^{f}\n", "\\end{bmatrix}=\\begin{bmatrix}\\Lambda_{ss} & 0 & 0\\\\\n", "\\Lambda_{fs} & \\Lambda_{fr} & \\Lambda_{ff}\n", "\\end{bmatrix}\\begin{bmatrix}F_{t}^{s}\\\\\n", "R_{t}\\\\\n", "F_{t}^{f}\n", "\\end{bmatrix}+e_{t}$$\n", "or $$\\mathcal{X}_{t}^{s}=\\Lambda_{ss}F_{t}^{s}+e_{t}^{s}$$ $$\\mathcal{X}_{t}^{f}=\\Lambda_{fs}F_{t}^{s}+\\Lambda_{fr}R_{t}+\\Lambda_{ff}F_{t}^{f}+e_{t}^{f}$$\n", "And\n", "$$\\begin{bmatrix}F_{t}^{s}\\\\\n", "R_{t}\\\\\n", "F_{t}^{f}\n", "\\end{bmatrix}=\\Phi(L)\\begin{bmatrix}F_{t-1}^{s}\\\\\n", "R_{t-1}\\\\\n", "F_{t-1}^{f}\n", "\\end{bmatrix}+\\begin{bmatrix}\\eta_{t}^{s}\\\\\n", "\\eta_{t}^{r}\\\\\n", "\\eta_{t}^{f}\n", "\\end{bmatrix}$$\n", "\n", "In the paper (p.405) they decribe the following procedure:\n", "- get $F_{t}$ from the $\\mathcal{X}_{t}$ whole dataset.\n", "- get $F_{t}^{s}$ from the $\\mathcal{X}_{t}^{s}$ sub-dataset.\n", "- regress $F_{t}=\\beta_{s}F_{t}^{s}+\\beta_{r}R_{t}+u_{t}$\n", "- $F_{t}^{r}=F_{t}-\\hat{\\beta}_{r}R_{t}$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def facrot(F,Ffast,Fslow):\n", " \n", " # computes the rotation of the factors as descrobed in p.405 of the paper\n", " # Inputs: F: Unrestricted PC estimates (from all the dataset)\n", " # Ffast: Factors assumed to be fast moving (e.g. policy instrument)\n", " # Fslow: Proxy of the slow moving factors\n", " # Outputs: Fr: rotation of factors\n", " \n", " F, Fslow, Ffast = np.array(F),np.array(Fslow),np.array(Ffast)\n", " Fslow = np.hstack([Fslow, Ffast])\n", " betas = LA.inv(Fslow.T@Fslow)@Fslow.T@F\n", " Fr = F - np.dot(Ffast,betas[num_factors:,:])\n", " Fr = pd.DataFrame(Fr)\n", " \n", " return Fr" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "#xir=df.loc[:,df.columns[xindex]]\n", "F0, Lf0 = extract_svd(X,K)\n", "xslow = df.loc[:,df.columns[slowindex]]\n", "Fslow0, Lfslow0 = extract_svd(xslow,K)\n", "Fr0 = facrot(F0,Y,Fslow0)\n", "u0 = X -F0@Lf0.T" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "X = pd.concat([Fr0, Y],axis=1)\n", "XLAG = pd.DataFrame()\n", "num_lags = 13 \n", "for i in range(1,num_lags+1):\n", " XLAG = pd.concat([XLAG,X.shift(i).add_suffix(\"-\"+str(i))],axis=1)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "#change names to frames that we modify \n", "X2 = X.iloc[num_lags:,:]\n", "XLAG2 = XLAG.iloc[num_lags:,:]\n", "num_vars = X2.shape[1]\n", "num_obs = XLAG2.shape[0]\n", "\n", "#Building arrays for using OLS\n", "X3 = np.array(X2)\n", "XLAG3 = np.array(XLAG2)\n", "\n", "#VAR - standard OLS\n", "Bhat = LA.inv(XLAG3.T@XLAG3)@XLAG3.T@X3" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(52, 4)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Bhat.shape" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "#Estimated errors\n", "EPS = (X3 - XLAG3@Bhat)\n", "num_obs = T\n", "num_vars = 4\n", "#estimated covariance matrix\n", "Omegahat = EPS.T@EPS/(num_obs - num_lags*num_vars - 1)\n", "# Putting problem in canonical form (VAR(8) into VAR(1))\n", "# c_x(t) = c_Bhat*c_x(t-1) + c_G*eta(t)\n", "# c_Bhat = [ Bhat' ; eye((n_lags-1)*n_vars) zeros((n_lags-1)*n_vars,n_vars) ] ;\n", "\n", "c_Bhat = np.vstack((Bhat.T,np.hstack((np.identity((num_lags-1)*num_vars),np.zeros([(num_lags-1)*num_vars,num_vars]))))) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Identification\n", "$$\n", "\\begin{bmatrix}\\eta_{t}^{s}\\\\\n", "\\eta_{t}^{r}\\\\\n", "\\eta_{t}^{f}\n", "\\end{bmatrix}=\\begin{bmatrix}A_{ss} & 0 & 0\\\\\n", "A_{rs} & 1 & 0\\\\\n", "A_{fs} & A_{fr} & A_{ff}\n", "\\end{bmatrix}\\begin{bmatrix}\\epsilon_{t}^{s}\\\\\n", "\\epsilon_{t}^{r}\\\\\n", "\\epsilon_{t}^{f}\n", "\\end{bmatrix}$$" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.20335119, 0. , 0. , 0. ],\n", " [-0.0699285 , 0.12389894, 0. , 0. ],\n", " [ 0.10439795, -0.0108517 , 0.05556132, 0. ],\n", " [-0.02396523, 0.01069045, 0.05442887, 0.13593807]])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A0 = LA.cholesky(Omegahat)\n", "A0" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "A0 = LA.cholesky(Omegahat)\n", "d = np.zeros(A0.shape)\n", "np.fill_diagonal(d,np.diag(A0))\n", "A0 = np.dot(np.linalg.inv(d),A0)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "#IRFs\n", "'''IRFs are stored in a 3-dimensional array. Dimension 1 is time. Dimension\n", " 2 is variable, and 3 is shock. So IRF(:,2,1) gives the impulse response\n", " of the second variable to the first shock.''' \n", " \n", "IRF = np.zeros([num_impulses,num_vars,num_vars])\n", "Temp = np.identity(c_Bhat.shape[0])\n", "\n", "psi = []\n", "for t in range(num_impulses):\n", " psi_t = Temp[:num_vars,:num_vars] \n", " IRF[t,:,:] = psi_t@A0 # store the IRF\n", " Temp = c_Bhat@Temp # computes the exponent of the matrix\n", " \n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "# \n", "shock = np.hstack([np.zeros([1,K+M-1]), np.ones([1,1])*0.25/stdffr])\n", "shock = shock.T\n", "IRF = IRF@shock \n", "irf = pd.DataFrame({i:IRF[i].flatten() for i in range(num_impulses)}).T #save IRFs into dataframe" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## recover Impulse response from variables of the dataset\n", "Now you have the factors therefore you can estimate the loadings with OLS $$\\mathcal{X}_{t}=\\hat{\\beta}F_{t}^{r}+\\hat{\\beta}R_{t}$$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "xir = df.loc[:,df.columns[xindex]]\n", "bx0 = LA.inv(X.T@X)@X.T@xir\n", "irf_x = irf@bx0" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot the IRFs\n", "\n", "plt.figure(figsize=(16,10))\n", "\n", "plt.subplot(221)\n", "plt.plot(np.exp(np.cumsum(irf_x[15]))-1,label='mp shock on IP')\n", "plt.legend()\n", "plt.xlabel('period')\n", "plt.title('mp shock')\n", "plt.grid()\n", "\n", "plt.subplot(222)\n", "plt.plot(np.exp(np.cumsum(irf_x[107]))-1,label='mp shock on CPI')\n", "plt.legend()\n", "plt.xlabel('period')\n", "plt.title('mp shock')\n", "plt.grid()\n", "\n", "plt.subplot(223)\n", "plt.plot(irf[3],label='mp shock')\n", "plt.legend()\n", "plt.xlabel('period')\n", "plt.title('mp shock')\n", "plt.grid()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# PART II" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bootstrapping the IRF\n", "The issue can be understood as follows. When we estimate the VAR $$X_{t}=B(1)X_{t-1}+B(2)X_{t-2}+...+v_{t}$$ then invert to obtain the IRF:$$X_{t}\t=C(L)^{-1}v_{t}$$ or\n", "$$X_{t}\t=v_{t}+C(1)v_{t-1}+...$$ or on the strucrural shocks : $$X_{t}\t=A(0)\\epsilon_{t}+C(1)A(0)\\epsilon_{t-1}+...$$\n", "we are :\n", "- estimtating $B(L)$ with OLS, therefore subject to small sample bias (on top of the issues due to autocorelation not handled well), same for the covarianche of the innovations (reduced form residuals)\n", "- obtain non the IRF from the non linear transformation of the $B(L)$ and of the covariance\n", ".This can result in substantially biased IRF." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Kilian bootstrapping\n", "Denote by * a bootstrapped quantity.\n", "1. Step 1a:\n", "Estimate the VAR(p) and generate 1000 bootstrap replications of $\\hat{B^*}$ from $$X^*_{t}=\\hat{B}(1)X^*_{t-1}+\\hat{B}(2)X^*_{t-2}+...+v^*_{t}$$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- We are going to create a set of procedures to make the code more readable" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def extract_fac(x,Y,K,slowindex):\n", " # Routine to extract the factors\n", " # 1. Extract factors from whole dataset F\n", " # 2. Extract factors from slow moving dataset Fslow\n", " # 3. Regress factors F on Flsow and Y and subtract effect of Y from F to obtain Fr\n", " \n", " x = pd.DataFrame(x)\n", " xslow = x.loc[:,x.columns[slowindex]]\n", " F,Lf = extract_svd(x,K)\n", " Fslow , Lfslow = extract_svd(xslow,K)\n", " Fr = facrot(F,Y,Fslow)\n", " \n", " return Fr" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "def shuffle(x,new_index):\n", " # Reshufle index of a variable (here a DataFrame)\n", " \n", " T = x.shape[0]\n", " x_s = np.zeros(x.shape)\n", " for ii in range(0,T):\n", " x_s[ii,:] = x.iloc[new_index[ii],:]\n", " return x_s " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### def simulate\n", "this routine simulate a dataset $X^*_{t}$ by using the estimated VAR(with $\\hat{B}$) using randomly selested initial conditions from $X_t$ observations and reshufling the innovations of the var $$X^*_{t}=\\hat{B}(1)X^*_{t-1}+\\hat{B}(2)X^*_{t-2}+...+v^*_{t}$$. It does this in canonical form $$ X^*_{c,t} = \\hat{B}_c X^*_{c,t-1} + \\epsilon^*_{t}$$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "def simulate(X,e,num_vars,num_lags,num_obs,A0,bhat,i2):\n", " \n", " T_var = num_obs - num_lags\n", " X_sim = np.zeros([num_vars,num_lags])\n", " \n", " for lag in range(num_lags):\n", " X_sim[:,num_lags-lag-1] = X.iloc[lag,:]\n", " X_sim = np.reshape(X_sim,(num_lags*num_vars,1),order='F')\n", " X_sim = np.hstack((X_sim,np.zeros([num_lags*num_vars,num_obs-1]))) \n", " D = np.vstack((A0,np.zeros([(num_lags-1)*num_vars,num_vars])))\n", " c_b = np.vstack((bhat.T,np.hstack((np.identity((num_lags-1)*num_vars),np.zeros([(num_lags-1)*num_vars,num_vars]))))) \n", " \n", " for t in range(T_var-1):\n", " X_sim[:,t+num_lags+1] = c_b@X_sim[:,t+num_lags] + D@e.T[:,np.int(i2[t])]\n", " \n", " X_sim = X_sim[:num_vars,:].T\n", " return X_sim" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "def lags(X,num_lags):\n", " # routine to lag a series or a dataset\n", " lfy = pd.DataFrame()\n", " fy = pd.DataFrame(X)\n", " for i in range(1,num_lags+1):\n", " lfy = pd.concat([lfy,fy.shift(i).add_suffix(\"-\"+str(i))],axis=1)\n", " fyr = np.array(fy.iloc[num_lags:,:])\n", " lfyr = np.array(lfy.iloc[num_lags:,:])\n", " return fyr,lfyr" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "def identific(Omegahat):\n", " #routine to perform the cholesky identification\n", " smatr = LA.cholesky(Omegahat)\n", " d = np.zeros(smatr.shape)\n", " np.fill_diagonal(d,np.diag(smatr))\n", " smatr = LA.inv(d)@smatr\n", " return smatr\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### def impulses\n", "$$\\hat{X}_{t+s}=\\sum_{i=0}^{s-1}C_{i}A(0)e_{t+s-i}$$\n", "define $$\\Psi_{i}=\\left[\\left(C\\right)^{i}A(0)\\right]$$\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "def impulses(num_impulses,num_vars,shock,bhat,A0):\n", " IRF = np.zeros([num_impulses,num_vars,num_vars])\n", " c_br = np.vstack((bhat.T,np.hstack((np.identity((num_lags-1)*num_vars),np.zeros([(num_lags-1)*num_vars,num_vars]))))) \n", " Temp = np.identity(c_br.shape[0])\n", " psi = []\n", " for t in range(num_impulses):\n", " psi_t = Temp[:num_vars,:num_vars] \n", " IRF[t,:,:] = psi_t@A0 # store the IRF\n", " Temp = c_br@Temp # computes the exponent of the matrix\n", " IRFr = IRF@shock \n", " irfr = pd.DataFrame({i:IRFr[i].flatten() for i in range(num_impulses)}).T #save IRFs into dataframe\n", " return irfr" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "'''LOOP to COMPUTE the Confidence Intervals using bootsrapping'''\n", "# Containers of the IRF\n", "imp = np.zeros([num_impulses*(M+K),nrep1*nrep2])\n", "impx = np.zeros([num_impulses*xir.shape[1],nrep1*nrep2])\n", "\n", "#main loop\n", "repetition=0\n", "for frep in range(0,nrep1):\n", " # this loop appears to be less important it was designed to bootstrap the estimates coming from the factors extraction\n", " T_data = Y.shape[0]\n", " \n", " # create the new index to reorder the osbervations randomly\n", " i = (T_data-1)*np.random.rand(T_data,1)\n", " i = np.round(i)\n", " \n", " # reorder the residuals of the X_t = LAMBDA*F_t + u_t\n", " u_star = shuffle(u0,i) # u_star_t is reordererd u_t\n", " \n", " # build a new dataset X_star_t = LAMBDA*F_t + u_star_t\n", " x_star = F0@Lf0.T+ u_star\n", " \n", " # get the factors from the new dataset\n", " Fr_star = extract_fac(x_star,Y,K,slowindex)\n", " \n", " # build the VAR data\n", " fy = np.hstack([Fr_star, Y])\n", " \n", " # keep the OLS coef of the (original) variables to the VAR variables(xir is a subsample we are interestd in)\n", " # X_t = beta*Y_t + e_t \n", " \n", " bx = LA.inv(fy.T@fy)@fy.T@xir\n", " ex = xir - fy@bx\n", " \n", " # Estimate the VAR with the new VAR data \n", " fy2,lfy2 = lags(fy,num_lags)\n", " bhat = LA.inv(lfy2.T@lfy2)@lfy2.T@fy2\n", " eps = fy2-lfy2@bhat\n", " \n", " # keep the number of observations in the VAR\n", " T_var = fy2.shape[0]\n", " k_var = fy2.shape[1]\n", " p = np.int((lfy2.shape[1]-1)/k_var)\n", " \n", " btilda = bhat\n", " bxtilda = bx\n", " \n", " for rep in range(1,nrep2):\n", " # this loop computes the IRF\n", " \n", " repetition = repetition+1\n", " # new index for the bootsrap\n", " i2 = (T_var-1)*np.random.rand(T_var,1)\n", " i2 = np.round(i2)\n", " \n", " Xr = pd.DataFrame(fy)\n", " # randomly select intial values for the lags\n", " i3 = (T_data-1)*np.random.rand(T_data,1)\n", " i3 = np.round(i3)\n", " Xr = shuffle(Xr,i3)\n", " Xr = pd.DataFrame(Xr)\n", " \n", " # SIMULATE THE NEW TIME SERIES Y = B*Y(-1) + u(reshufled)\n", " X_sim = simulate(Xr,eps,num_vars,num_lags,num_obs,np.eye(num_vars),btilda,i2)\n", " \n", " # Compute the Xir_star_t = beta*Y_star_t + e_t \n", " ex2 = shuffle(ex,i3) \n", " xr2 = X_sim@bxtilda + ex2\n", " bxr = LA.inv(X_sim.T@X_sim)@X_sim.T@xr2\n", " \n", " # Estimate the VAR\n", " fyr,lfyr = lags(X_sim,num_lags)\n", " br = LA.inv(lfyr.T@lfyr)@lfyr.T@fyr\n", " er = fyr - lfyr@br\n", " Omegahatr = er.T@er/(er.shape[0]-p*k_var-1)\n", " \n", " # indentify the SVAR\n", " A0r = identific(Omegahatr)\n", " # compute the IRF\n", " irfr = impulses(num_impulses,num_vars,shock,br,A0r)\n", " impr = np.array(irfr)\n", " impxr = np.array(impr@bxr)\n", " \n", " # STORE THE IRFS \n", " imp[:,repetition-1] = np.reshape(impr,(num_impulses*(1+num_factors),1)).flatten()\n", " impx[:,repetition-1] = np.reshape(impxr,((num_impulses*len(xindex)),1)).flatten()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(511, 1)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "i3.shape" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "# KEEP THE 5% - 95% IRF sorted \n", "imp = imp.reshape(num_impulses,M+K,nrep1*nrep2)\n", "impx = impx.reshape(num_impulses,len(xindex),nrep1*nrep2)\n", "imp = np.sort(imp,axis=2)\n", "impx = np.sort(impx,axis=2)\n", "nrep = nrep1*nrep2\n", "impci = imp[:,:,[np.int(0.05*nrep),np.int(0.95*nrep)]]\n", "impxci = impx[:,:,[np.int(0.05*nrep),np.int(0.95*nrep)]]" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7QAAAE0CAYAAAAc6H9fAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzs3Xd4VFXixvHvyUx6SEghISRA6L2HIjUoKBZE3VWxrKggFiwsuq7lZ1kU18IqrrIqIizYEBW7SA8dBATpvYbeAiQh/fz+SGRDUyCT3Ex4P88zz8zcuffOO7MryZt77rnGWouIiIiIiIiIt/FxOoCIiIiIiIjIhVChFREREREREa+kQisiIiIiIiJeSYVWREREREREvJIKrYiIiIiIiHglFVoRERERERHxSiq0IiIiIiIi4pVUaEXKEWPMVmNMN2PMncaYPGNMmjHmqDFmmTHmGqfziYiIXAyMMbcaYxYX/hzebYyZaIzpaIx53hiTU7g81RgzzxhzSeE2dxpj5jidXcTbqNCKlF/zrbUhQEXgA2C8MSbC4UwiIiLlmjFmEDAMeAmIAaoB/wF6Fa7yWeHP50rAHGCCMcY4kVWkPFChFSnnrLX5wCggEKjpcBwREZFyyxgTBgwGBlhrJ1hr0621Odba76y1fyu6rrU2BxgDVAYiHYgrUi6o0IqUc8YYN9APSAM2OBxHRESkPLsECAC++qMVjTH+wJ1AirX2QAnnEim33E4HEJES084YkwrkAhuB6621RxzOJCIiUp5FAgestbm/s85NhfNaZAMrgetKJZlIOaVCK1J+LbDWdnQ6hIiIyEXkIBBljHH/Tqkdb629vTRDiZRnGnIsIiIiIuIZ84FMdNRVpNToCK2IiIiIiAdYa48YY54FhhtjcoHJQA7QDegKZDiZT6Q80hFaEREREREPsda+DgwC/g/YD+wAHgS+djKXSHllrLVOZxARERERERE5bzpCKyIiIiIiIl5JhVZERERERES8kgqtiIiIiIiIeCUVWhEREREREfFKKrQiIiIiIiLilbzyOrRRUVE2ISGh2PtJT08nODi4+IEc4s35ld0Z3pwdvDu/sjvnXPIvWbLkgLW2UilFKpf0s7mAN+dXdmd4c3bw7vzK7hxP/mz2ykKbkJDA4sWLi72f5ORkkpKSih/IId6cX9md4c3ZwbvzK7tzziW/MWZb6aQpv/SzuYA351d2Z3hzdvDu/MruHE/+bNaQYxEREREREfFKKrQiIiIiIiLilVRoRURERERExCup0IqIiIiIiIhXUqEVERERERERr6RCKyIiIiIiIl5JhVZERERERES8kgqtiIh4pdz8XKcjiIiIiMPcntiJMWYUcA2wz1rb+AyvG+BN4CogA7jTWvtL4Wt9gP8rXPVFa+0YT2QSEZHy68PVHzJ562Te6/4eQb5BTscRkT+Qb/PZeWwn6w6vY93hdaw9tJZDmYeICYqhSnAVYkNiiQ0uuFUJqUKoXygFvz6KiPw+jxRa4L/A28DYs7x+JVCn8NYWeAdoa4yJAJ4DEgELLDHGfGutPeyhXCIiUo5YaxmxfARvL3ub7tW74+vj63QkETlFZm4mG1M3svbQWtYdKiiw6w+vJz0nHQAf40P10OpEB0az4fAGZqXMIisv66R9BLoDCwpuSCwNIxrSMqYlzSo1o4JfBSc+koiUYR4ptNbaWcaYhN9ZpRcw1lprgQXGmIrGmFggCZhirT0EYIyZAvQAPvVELhERKT+stQz7ZRijVo6iZ82eDO4wGLePp/4uKyIXIicvh/Wp61l1YBWrDq5i5YGVbErdRJ7NAyDYN5i64XXpWbMn9SLqUT+iPrUq1iLQHXhiH9ZaDmcdZnfabnan72ZX2i52pxc83pm2k1ErR/H+ivcxGOqG16VFdAtaxrSkRXQLKgdXduqji0gZUVq/CcQBO4o8TylcdrblpzHG9Af6A8TExJCcnFzsUGlpaR7Zj1O8Ob+yO8Obs4N351f24sm3+Xxx+AtmH5tNx5COdMvtxpxZc85p27KQX6Qsy83PZXbKbOYdm8exTcfwc/nh7/I/cV/0cWZuJqsPrmbVwVWsOrCKdYfXkZOfA0CYfxiNIxvTJb4LDSMbUi+iHnEhcfiY35+yxRhDREAEEQERNIpqdNrrGTkZrDiwgl/2/cLSvUv5dtO3jFs3DoDY4FhaRLfA94gv+9fvJ8Q3hGDf4P/d+4UQ4htCkG+QRnSIlFOlVWjPdBKE/Z3lpy+0dgQwAiAxMdEmJSUVO1RycjKe2I9TvDm/sjvDm7ODd+dX9guXl5/Hc/OeY/ax2dzZ6E4GtRp0XufWOZ1fxNMycjKYvG0y32/+nkB3INfXvp5O8Z3Ou7Cl56QzYcMEPl7zMTvTdgIwbs64c9o22DeYhpENub3B7TSMakjjyMbEhcSVyHmvQb5BtI1tS9vYtkBBAV9/eD1L9y3ll72/8POenzlw/ADfzP/md/cT6A6kWaVmdIrrRKf4TiSEJug8XZFyoLQKbQpQtcjzeGBX4fKkU5Ynl1ImEREp43LycnhyzpNM2jqJB5o/wH1N79MvoHJRstaybP8yvtrwFT9t/YnjucepVqEaGbkZJO9IJiowil61enF9neupHlr9d/e1J30PH6/5mC/Wf0FaThoto1vyt8S/cXTDUVq1aUVWXhbZedlk5WWd9thlXNSPrE9CaMIfHnktKW4fNw0jG9IwsiG3NbgNay2TZkyiZbuWpOWkkZ6dXnCfU+Q+O42DmQf5effPvLb4NV5b/BrxIfF0iu9E5/jOJMYkEuAOcOTziEjxlFah/RZ40BgzjoJJoY5Ya3cbYyYBLxljwgvXuxx4spQyiYhIGZaVl8WjyY8yM2UmjyU+Rp9GfZyOJFLq9mXs49tN3/LNxm/YenQrge5AeiT04Lra19EiugV5No/ZKbOZsGEC/131Xz5Y+QGJMYncUOcGulfvflJJW31wNWNWjWHy1snkk0/36t3p07APTSo1ASB5SzLVQqs59VEvmDGGAJ8AooOiiSb6D9ffmbaTOSlzmL1zNl9t+IpP135KgCuANrFt6BTXiQ5VOhBfIV5/PBPxEp66bM+nFBxpjTLGpFAwc7EvgLX2XeBHCi7Zs5GCy/bcVfjaIWPMC8Ciwl0N/m2CKBERuXhl5GTw8PSH+XnPzzzT7hluqneT05FEPGLH0R3sSt/1h+sdPH6Q7zd/z9xdc8m3+bSMbknfJn25vPrlJ12qym3cdK3Wla7Vup4ovxM2TOCpOU/xz4X/5OqaV9MsuhkTNkxg0Z5FBPsGc0uDW7itwW3EhZxx2pJyLy4kjpvr38zN9W8mKy+LxXsWM3vnbGalzGJWyiwAqgRXoU1sG9pULrjFBMc4nFpEzsZTsxzf8gevW2DAWV4bBYzyRA4REfF+R7OPMmDqAJYfWM6QjkPoWaun05FELlhefh4rDqxgxo4ZJO9IZvORzee8bXRQNH0b96VX7V5/OIz4t/X7NenH3Y3vZvGexUzYOIEJGyYwbt04KgdX5rHEx7ihzg269E0R/i5/OsR1oENcB55o8wRbj2xlwe4F/LznZ2bsmMHXG78GICE0oaDcxrahdeXWRAREOJxcRH6j6x2IiEiZcTT7KP0m9WND6gaGdhlK9+rdnY4kct4ycjKYv2s+ySnJzEqZxaHMQ7iNm1aVW3FTvZuoG14Xc8Z5Mf/H3+VPw8iGuHxc5/3+Psan4OhibBuebPMkGw5voFl0M83yew4SwhJICEugd/3e5Nt81h9ez8LdC/l5z898v/l7xq8fD0Cd8Dq0rdyWdrHtSKycSLBvsMPJRS5eKrQiIlImZORkMGDqADakbuDNrm/SOb6z05FEzllOXg7fbvqW8fvG8+i4R8nOz6aCXwU6xXWia9WudIjr4MiR0TD/MBIrJ5b6+5YHPsaH+hH1qR9Rnz6N+pCTn8Pqg6v5effPLNyzkPHrxvPRmo9wGzeNoxqfmIm5WaVm+Ln8nI4vctFQoRUREcdl52UzcMZAlh9YztAuQ1VmxatsOLyBp+c8zZpDa4hyR3Fz/ZtJik+iRUwLHRUtR3x9fGlWqRnNKjXjnqb3kJWXxbJ9y1iwewELdy/k/RXv897y9wh0B9IyuiVtY9vSvkr7giPymmBKpMSo0IqIiKNy83N5fNbjzN89nxc7vKhhxuI18vLzGLt6LG8tfYsKfhUYljQMn80+dG3d1eloUgr8Xf4nXR/3aPZRFu9ZzMLdC1m4eyGvL3md15e8TnRgNB3jO9IxriPtYtvpHGYRD1OhFRERx+TbfJ6d+yzTtk/jiTZP0Kt2L6cjiZyTHcd28H9z/o9f9v3CZdUu45l2zxAZGEnylmSno4lDQv1CubTapVxa7VKg4JJL83bNY3bKbKZsncKEDRNwGzfNo5vTKb4THeM6UqdiHYdTi3g/FVoREXGEtZZ/Lvwn323+jgebP8htDW5zOtJFwxjTA3gTcAEjrbUvn/L6IKAfkAvsB+621m4r9aBlkLWWz9d/ztDFQ3EbNy91fIlral6jIaVymuigaK6rfR3X1b6O3Pxcft3/K3N2zmF2ymzeWPIGbyx5g5igGKqZaiTPSyY3P5c8m0defh65Nve0+8iASOqG1z1xiw6K1v/vRFChFRERh7y19C3GrRvHXY3uon/T/k7HuWgYY1zAcKA7kAIsMsZ8a61dXWS1pUCitTbDGHM/8Cpwc+mnLVv2pu/lufnPMXfnXNrFtuOFDi9QObiy07HEC7h93LSKaUWrmFY80vIR9qbvZe6uucxOmc2inYvYlrINl48Ll3Hh9nH/797Hhdu48TE+LN23lB+3/Hhin2H+YScV3LrhdalVsRaB7kAHP6lI6VOhFRGRUjdq5SjeX/E+N9a9kb+2+quOMpSuNsBGa+1mAGPMOKAXcKLQWmtnFFl/AXB7qSYsY6y1TNwykSELh5Cdl81TbZ/i5no342N8nI4mXiomOIYb6tzADXVuIDk5maSkpHPa7mj2UTYc3sD6w+tP3CZsmMDx3OMAuI2bppWa0iGuA+2rtKdBRIMLuvSTiDdRoRURkVI1ft143ljyBlfVuIqn2z6tMlv64oAdRZ6nAG1/Z/2+wMQSTVSGrTqwiuHLhjN752yaVWrGkI5DqB5a3elYcpEK9Qs9caT3N/k2n53HdrI+dT0r9q9g/u75vLX0Ld5a+hZh/mG0i21H+yrtaV+lvUYUSLmkQisiIqXmu03f8eKCF0mKT+LFji/qyIEzzvQXBHvGFY25HUgEupzl9f5Af4CYmBiSk5OLHS4tLc0j+ymu7VnbmXhkIiuPryTIJ4jrwq+ja2BXtvyyhS1sOet2ZSX/hVB2Z3gquwsXzWlO85DmHAs8xrrMdaw9vpYFOxYwaeskACr7VqZ+QH1q+Negil8VKrkr4TLF+3dY370zvDk7eDa/Cq2IiJSK6dun88zcZ2hduTVDk4bq+pzOSQGqFnkeD+w6dSVjTDfgaaCLtTbrTDuy1o4ARgAkJibacx02+XvOZ/hlSVh1YBXv/PoOM/fMJMw/jEdaPsIt9W8h2Df4nLZ3On9xKLszSip7T3oCBUPmN6ZuZN6ueczbNY/5e+eTfCwZKLj0UK2KtU47Fzc8INzx/KVB2Z3jyfwqtCIiUuLm7ZzHYzMfo1FkI/596b/xd/k7HelitgioY4ypAewEegO3Fl3BGNMCeA/oYa3dV/oRS9+JIptyYUVWpKwyxlAnvA51wuvQp1EfsvOy2ZS66aTzcGelzOLrjV+f2KZSYCXqhtelTngdalesTZ3wOtQMq0mAO8DBTyJyZiq0IiJSohbvWcwjMx6hZlhN/tPtPyoIDrPW5hpjHgQmUXDZnlHW2lXGmMHAYmvtt8BrQAjweeE5ztuttdc6FroErTq4ineW/a/IPtziYW6pfwshfiFORxMpEX4uPxpENqBBZIOTlh84foD1h9efNOnUojWLyM7PBsDH+FCtQrUTBfe3+3yb78THEDlBhVZERErMiv0reHD6g8SGxPJe9/cI8w9zOpIA1tofgR9PWfZskcfdSj2UA77Z+A3PzH2GUP9QFVm56EUFRhEVGEX7Ku1PLMvNz2X7se1sPLyRDakb2HB4AxtSNzBt+zRs4an3ASaAppOa0iSqCU0qNaFJVBOig6Kd+hhyEVKhFRGRErHu0Drum3of4f7hvN/9fSIDI52OJHLCVxu+4rl5z9Euth2vJ72uIityBm4fNzXDalIzrCaXc/mJ5cdzj7M5dTPrD69n8vLJHMo5xJhVY8i1uQDEBMWcVHAbRDTQf2NSYlRoRUTE4zYf2Uz/Kf0JdAcy8oqRxATHOB1J5ITfyuwlVS7hza5v6rxAkfMU6A6kUVQjGkU1InxnOElJSWTmZrL20FpWHFjBiv0rWHFgBVO3Tz2xTbh/OHEhccRViCM+JJ64CnHEhRQ8jg2OxdeliQLlwqjQioiIR+04toN7Jt2DwTDy8pHEhcQ5HUnkhC/Xf8nz85+nQ5UODOs6TGVWxEMC3AE0j25O8+jmJ5YdyjzEygMrWX94PTvTdrLz2E5WH1zNtG3TThzNhYLzc2OCYmgY2ZAW0S1oHt2chhENVXLlnKjQioiIx+xJ38M9k+8hKz+LUVeMIiEswelIIid8sf4L/jH/H3SI68CbXd/UbNsiJSwiIILO8Z3pHN/5pOV5+Xnsy9hHSloKO9N2knIshe3HtrNi/wqmbZ8GFFxSqFFkI1pEtzhRcjUPg5yJCq2IiHjEgeMHuGfyPaRmpfLB5R9QN7yu05FETvh8/ecMnj+YjnEdGdZ1mMqsiINcPi5iQ2KJDYmlNa1Pem1/xn6W7V/G0n1LWbZvGWNWjeGDlR8AUDOsJg0iGxATFEN0UPSJ++igaKICo3D7qNpcjPS/uoiIFNuRrCP0n9KfvRl7ebfbuzSKauR0JJETxq8bzwsLXqBTXCeGdR2Gn8vP6UgichaVgirRvXp3ulfvDhRMQLXywEqW7ftfyd2XsY+c/JyTtjMYIgMjTxTcyIBIKvpXJDwgvODmH05EQAQVAyoS7h9OoDvQiY9X7uTbfNJy0jiSdYSjWUfJzMukVUyrUs2gQisiIsWSnpPOfVPuY+uRrQy/bDgtY1o6HUnkhHFrxzFk4RA6x3fmjaQ3VGZFvEygO5DWlVvTuvL/juTm23xSs1LZl7GPfRn72JO+58TjfRn72Jm2k5UHVpKamXrSubpF+bv88bW++H/mj4/xwRiDweBjfAqeF3ns5/IjwBWAv9ufAFcAAe4A/F3++Lv8CXAHEOAKwM/lh6+PL74+vrh93AWPXSc/d/u48TE+uIzr5Hufk5/7GJ8//F52ZO9gzcE1Jy377VJK5ysvP4/MvEyO5x4/6ZaZm3niPiM3g2PZxziSXVBcj2Qd4Uj2EY5lHzvpWsShfqHMvWXuBeW4UCq0IiJywbLysnh4+sOsObSGN5Le4JIqlzgdSeSET9d+yksLXyIpPol/Jf1LZVaknPAxPkQERBAREEH9iPpnXc9ay7GcY6RmpnIo8xCpWakczjzM4azDpGamsmHbBqpUqUI++Vhrybf55Nt8LP97nG/zycrLIisvi8zcTA7lHCIzN5PMvMyC5blZZOZlnnbEuFR8Xzpv81txD/ULJcwvjFD/UOJD4gn1DyXMP4wwv7CCe/8wKvpXLJ1QRajQiojIBcnJz+GxmY+xaM8iXur0El2rdXU6ksgJ49eNLyizVZP4VxeVWZGLkTGGUL9QQv1CqRZa7bTXk9OSSbokySPvZa0lNz+XnPycE7fc/Fxy8k5+nmfzyLf5J9/nn/z8XI60rly5kiaNm5y23GDOO7uP8SHQHUigO5AAd8CJ+yB3EP4uf1w+rvPeZ2lSoRURkfOWb/N5du6zJO9I5um2T3NNzWucjiRywsQtE3lxwYt0ie/C611e16U/RKTEGWMKhhiX0r83rs0ukqollcp7lXV/PED7HBhjehhj1hljNhpjnjjD628YY5YV3tYbY1KLvJZX5LVvPZFHRERKjrWWl39+me83f89DLR6id/3eTkcSOWHeznk8NecpWkS3YGiXoSqzIiLlXLGP0BpjXMBwoDuQAiwyxnxrrV392zrW2r8WWf8hoEWRXRy31jZHRES8wvBlw/l07af0adiHe5rc43QckROW71/OwOSB1AqrxVuXvUWAO8DpSCIiUsI8cYS2DbDRWrvZWpsNjAN6/c76twCfeuB9RUSklI1ZNYb3lr/HDXVu4NHERzHm/M/VESkJm1I38cC0B4gMiOTd7u8S6hfqdCQRESkFnjiHNg7YUeR5CtD2TCsaY6oDNYDpRRYHGGMWA7nAy9bar8+ybX+gP0BMTAzJycnFDp6WluaR/TjFm/MruzO8OTt4d/7ykH1+2nw+OfgJzYOa0yWrCzNnznQ62jnx5u9ezs3utN3cO+Ve3MbNiO4jiAqMcjqSiIiUEk8U2jP9ef5sU3P1Br6w1uYVWVbNWrvLGFMTmG6MWWGt3XTaDq0dAYwASExMtElJScWMDcnJyXhiP07x5vzK7gxvzg7end/bs2cnZDNu1jg6VOnAvy/9t1fNGOvN3738sUOZh+g/pT8ZORmM7jGaqqFVS/X9M3Py2H4og60H0tl7LIucI3l0zrf4+Gj0gohIafBEoU0Biv70iAd2nWXd3sCAogustbsK7zcbY5IpOL/2tEIrIiLOWHN8DSNmj6BZpWa8nvS6V5VZKd/Sc9J5YOoD7E7fzXvd36NeRL1z3jblcAbf/bqb6Wv3YowhPMiXioF+VAwuvA/yJTzIl7BAP8KDfcnNs2w9mM62gxlsO5jO1oMZbD+YwZ6jmaft+z8rppFUrxKX1o+mU50oKgRoYioRkZLiiUK7CKhjjKkB7KSgtN566krGmHpAODC/yLJwIMNam2WMiQI6AK96IJOIiHjA4j2LGbl/JLUq1uLty94myDfI6UgiAGTnZfPIjEdYe2gtb3Z9k1Yxrf5wm4NpWfy4YjffLNvF4m2HAWgSF0agn4utBzI4nJFKakYO2Xn5v7ufShX8SYgMokPtKBIig6gWGURCZDARwX6MnTiX3SaCyav28MWSFNw+htYJEVxaP5qu9aOpVSlY556LiHhQsQuttTbXGPMgMAlwAaOstauMMYOBxdba3y7FcwswzlpbdDhyA+A9Y0w+BRNUvVx0dmQREXFO8o5kHpv5GOGucE2yI2VKXn4eT8x+goW7FzKk4xC6VO1y1nXTsnKZvGoP3yzbxZyNB8jLt9SJDuFvV9SjZ9MqVIs8+Y801lqO5+SRmpHD4YxsjmTkcDgjB5cPVI8MplpEEMH+Z//1qUOcL0lJLcnNy2fJtsNMX7ePGWv3MeTHNQz5cQ3VIoK4pmksd1ySQOUwzcIsIlJcnjhCi7X2R+DHU5Y9e8rz58+w3TygiScyiIiI53y36TuemfsM9SPqc3vg7ZpkR8qUlxa+xJRtU3gs8TGurXXtaa/n5OWTvG4/Xy/dydQ1e8nKzSeuYiD9O9fk2mZVqF+5wlmPkhpjCPJzE+TnpkrFwAvO6Hb50LZmJG1rRvLklQ1IOZzBjHX7mbZmL+/O3MT7szfTs2kV+nWqScMq+mORiMiF8kihFRGR8uOj1R/xyqJXaFu5LW9e+iaL5i5yOpLICdO2TWP8+vHc1egu+jTqc9Jrq3cd5ctfUvh66U4OpmcTGezHza2r0qt5FVpWC3d0qG98eBB/aVedv7Srzo5DGXwwZwvjF+9gwtKddKgdSb9ONUmqW0nDkUVEzpMKrYiIAAVDLf/z639499d3uazaZbzS+RX8Xf5OxxI5IS07jZd+fom64XV5qOVDQMF5sd8s28UXS1JYvfsovi5DtwYx/LlVPJ3rVsLX5eNw6tNVjQji+Wsb8ddudfnk5+38d94W7hq9iDrRIfTrVINezeMI8HU5HVNExCuo0IqICPk2n38u/Cfj1o3j+trX8+wlz+L20Y8IKVveWvoW+zP281qn15m+5iBfLElhxtp95OZbmsaHMbhXI3o2rUJ4sHfMxB0W5Mv9SbXo27EG3y/fxfuzt/D3L1fw2qR1/KVdAr2aVyEhKtjpmCIiZZp+WxERucjl5OXw9NynmbhlInc2upNBrQZp2KOUOSv2r+DTtZ9ydcKfeXD0AXYdSaFSBX/6dqzBn1rFUzemgtMRL5if24cbWsZzfYs45m06yPuzN/PG1PW8MXU99WIqcHmjGK5oVJlGVUL136aIyClUaEVELmLHc48zKHkQc3bOYWDLgfRt0tfpSCKnycnP4R/z/0FkQBTzFrcmIyePkXckklSvEu4yOKT4Qhlj6FA7ig61o0g5nMHkVXuZtGoPw2ds5K3pG4mrGHii3CZWDy9Xn11E5EKp0IqIXKSOZB3hwWkP8uv+X3nukuf4c90/Ox1J5Iw+Xv0x6w6vI+b4vew6DJ/ck0ir6hFOxypR8eFB3N2xBnd3rMHBtCymrdnHpFV7+HjhdkbP3UpEsB+X1Y+mT/sEGseFOR1XRMQxKrQiIheh1MxU+k3ux6YjmxjaZSiXJ1zudCSRM9qZtpPhy4ZTkeZs2pbAO7e1KPdl9lSRIf7c1LoqN7WuSnpWLjPX72fSqj38tHIP3y/fzft3JNKxji6tJSIXJ41VERG5yBzJOkL/Kf3ZcmQLb1/6tsqslFnWWl5c8CI5eZCyoQf/uLYxPRpXdjqWo4L93VzVJJY3e7dg+mNJVIsI4u4xi5i6eq/T0UREHKFCKyJyETmafZR7p9zLxtSNDOs6jA5xHZyOJHJWk7ZOYs7OOaTv6ca9HVpxxyUJTkcqUypV8Gdc/3bUr1yB+z5awvfLdzkdSUSk1KnQiohcJI5lH+O+Kfex7vA63kh6g07xnZyOJHJWR7OP8vy8l8g7HsdV1f7M41fUczpSmRQe7MfH/drSolpFHv50KZ8v3uF0JBGRUqVzaEVELgLpOencP/V+1hxcw7+S/kWXql2cjiTyu/4+/WXSclKp5x7Aaze2wMen8HI1m2bA9BcgfT9gwJiT7+F/j/1DIKIWRNYuvBU+Dgh15kOVkAoBvoy5uw33friEv32xnOM5eTqaLSIXDRVaEZFyLiMngwemPsDKAysZ2mUol1a71OlIIr/ry1WzmbP3OypkXcbYPjfg5/aBo7th0lMNuLyzAAAgAElEQVSwagKE14Bq7QEL1hZu9dvjIveZRyBlEaz8suD5b0JiihTcOtDoeqhYtdQ/pycF+bl5/45EHvxkKc9+s4qM7Dzu61LL6VgiIiVOhVZEpBzLyMnggWkP8Ov+X3ml8yt0q97N6Ugiv2tPejYvbXwNY8L59MZnqeBrYME7MH0I5GVD0lPQ4RHwDTj3neZkwuEtcHBjkdsmWDcR0sfCtH9As97QcVBByfVSAb4u3rm9JYPG/8rLE9eSkZXLX7vXxRjjdDQRkRKjQisiUk4dzz3OQ9MfYum+pfyz4z+5IuEKpyNJGWGM6QG8CbiAkdbal0953R8YC7QCDgI3W2u3lnSuw+nZvLpxMrbiHp5q+RoJ6Rvhs0GwdwXUugyueu3CCqdvAEQ3KLidKnU7zHsbfhkDyz4pOFrb6VGIaVT8D+QAX5cPw25uTqCvD/+evpGM7DyevrqBSq2IlFsqtCIi5VBmbiYPT3+YRXsWMaTjEK6qeZXTkaSMMMa4gOFAdyAFWGSM+dZau7rIan2Bw9ba2saY3sArwM0lne2fU+aQHTqNNuHtuWXLD/DLWKhQBW4aCw2uLTw31sMqVoOrXoXOj8H84bBoZMEQ5XpXQafHIL6V59+zhLl8DC/f0JQgPzcj52zhaGYO9yfVJiEySMVWRModFVoRkXImKy+LgckDWbh7IS90eIGetXo6HUnKljbARmvtZgBjzDigF1C00PYCni98/AXwtjHGWGstJSgqdgmBqfDyuimQkQrtH4Iufwf/CiX5tgVCoqH7P6DjQFg4Ahb8B9ZdCjWTCoptQseSKdQlxMfH8FzPhgT7uxg+YxPjF6cQVzGQTnWi6Fgnig61oggP9nM6pohIsanQioiUIxk5GTw842EW7l7IP9r/g161ezkdScqeOKDotV1SgLZnW8dam2uMOQJEAgeKrmSM6Q/0B4iJiSE5OblYwW7atJI/79mOX1BdFrV6lnS/BJi/pFj7vDBtcSU2ocqun6i64xv8xlzD0Qp12B3bjX3RnchzB591y7S0tGJ/D57U2h9e7RzIygN5rDyQzTdLdzBu0Q4MkBDqQ6MoF40iXdQO9yErI71MZT8fZe17Px/enB28O7+yO8eT+VVoRUTKiaPZRxkwdQDLDyxnSMchXFvrWqcjSdl0psOMpx55PZd1sNaOAEYAJCYm2qSkpOIla1KVtZOrUvHmwbT28SnevjziKsh5BZZ+ROjiUYSuf4d6m0dDg57Q/Fao0QV8XCdtkZycTLG/hxJwU+F9bl4+v6YcYfaG/czZcICJW1P5fnMOgb4uOlbx5c2+HQny875fD8vq934uvDk7eHd+ZXeOJ/N7379YIiJymkOZh7hvyn1sSN3A0C5D6V69u9ORpOxKAYpeoyYe2HWWdVKMMW4gDDhU4skia7Enthv1y0SZLeQbCG3ugdb9YNdSWPYxrPi84BYaD81vgWa3eM3syG6XD62qh9OqejgDu9XlWGYOCzYfYtKqPXyxJIUew2Yz9MZmtKkR4XRUEZFzUoZ+YoiIyIXYm76Xu366i81HNvPWpW+pzMofWQTUMcbUMMb4Ab2Bb09Z51ugT+HjPwPTS/r82TLPGIhrCVf/Cx5dD38eDdH1Yfa/4K2WMOpKWPoxJj/P6aTnpUKAL90bxjD0xmY80abgUkg3j5jP4O9Wczzbuz6LiFycVGhFRLxYyrEU+vzUh70Ze3m327t0jOvodCQp46y1ucCDwCRgDTDeWrvKGDPYGPPbOPUPgEhjzEZgEPCEM2nLKN8AaHwD3P4l/HUVXPYcpO+Dbx6g6fLnIaPkD2aXhPoRLn4a2Ik72lVn1NwtXPXv2Sze6p2fRUQuHiq0IiJeanPqZvpM7MOx7GOMvHwkiZUTnY4kXsJa+6O1tq61tpa1dkjhsmettd8WPs601t5ora1trW3z24zIcgahVaDTIHhwMfQaTtiR1fB+V9i3xulkFyTIz80/ejXmk3vakpOXz43vzWfID6vJzNHRWhEpm1RoRUS80JqDa7jzpzvJs3mM7jGaxlGNnY4kcnEzBlrczrLmL0HOcRjZDdb+4HSqC9a+VhQ/DezMrW2q8f7sgqO1v2w/7HQsEZHTeKTQGmN6GGPWGWM2GmNOG5ZkjLnTGLPfGLOs8NavyGt9jDEbCm99Tt1WREROtmzfMvpO6ou/258xV46hbnhdpyOJSKGjYfWgfzJE1YVxt8LMV8FLTz8O8Xcz5PomfNi3DZnZefz5nXkM+WE1+45mOh1NROSEYhdaY4wLGA5cCTQEbjHGNDzDqp9Za5sX3kYWbhsBPEfB9e/aAM8ZY8KLm0lEpLxasHsB/af0JzwgnLE9xlI9tLrTkUTkVKFV4K6J0LQ3zBgCn/eB7HSnU12wTnUqMemvnbkpsSrvz95C+5enM+CTX1iw+SAX+1xhIuI8TxyhbQNstNZuttZmA+OAXue47RXAFGvtIWvtYWAK0MMDmUREyp2ZO2YyYOoA4kLiGHPlGGJDYp2OJCJn4xsA178Ll78Ia76DDy6Hw9ucTnXBKgT48vKfmpL8WBJ3tk9gzoYD9B6xgCuGzeLD+VtJy8p1OqKIXKQ8UWjjgB1FnqcULjvVn4wxy40xXxhjfrv+3bluKyJyUftp608MnDGQOuF1GH3FaKICo5yOJCJ/xBho/xDc+jmk7iiYLGrrHKdTFUtCVDD/d01DFjx5Ga/+qSl+bh+e+WYVbYdM5ZmvV7J+7zGnI4rIRcbtgX2YMyw7dfzJd8Cn1tosY8x9wBjg0nPctuBNjOkP9AeIiYkhOTn5ggP/Ji0tzSP7cYo351d2Z3hzdvDu/MXJviBtAZ8c/IQa/jXoE9SHZQuWeTbcH/Dm7x28P7+UA3W6wT3T4dPeMLYXXPkqtO7rdKpiCfRzcVPrqtyYGM+yHal8uGAbny3ewYcLttG2RgR3XJLA5Y1i8HVp/lERKVmeKLQpQNUiz+OBXUVXsNYeLPL0feCVItsmnbJt8pnexFo7AhgBkJiYaJOSks602nlJTk7GE/txijfnV3ZneHN28O78F5r907Wf8vHCj7kk9hKGdR1GkG+Q58P9AW/+3sH780s5EVUb7pkGX/aDHwbBwU1w+Qvg43I6WbEYY2hRLZwW1cL5v6sbMn7xDj5asI0Bn/xC5dAAbm9Xjd5tqhEV4u90VBEppzzxZ7NFQB1jTA1jjB/QG/i26ArGmKInel1LwYXcoeCi7pcbY8ILJ4O6vHCZiMhFb9TKUby08CWSqibx1mVvOVJmRcSDAsLglnHQ9j5YMBw+ux2y0pxO5TERwX7c16UWM//WlffvSKR2dAhDJ6+n/T+nM2j8MpanpDodUUTKoWIfobXW5hpjHqSgiLqAUdbaVcaYwcDiwou0P2yMuRbIBQ4BdxZue8gY8wIFpRhgsLX2UHEziYh4M2stw5cN573l73FlwpUM6TQEXx9fp2OJiCf4uODKVyCiFvz0dxh9Jdz6WcHMyOWEy8fQvWEM3RvGsHHfMcbO38aXS1KY8MtOmletyJ3tE7iqSSx+bg1HFpHi88SQY6y1PwI/nrLs2SKPnwSePMu2o4BRnsghIuLtrLW8tvg1Plz9IdfXvp7nLnkOl5cPSRSRM2jbH8IT4Iu74P1LC0ptbDOnU3lc7egKDO7VmMeuqMeXS1IYO38bAz9bxos/rOH2dtW4q0MNwgL1BzsRuXD605iISBmRb/MZvGAwH67+kNsa3Mbz7Z9XmRUpz+peDndPAuOCUT1g7Y9/vI2XCg3w5a4ONZg2qAv/vas1TeJCGTZ1A51fncHwGRtJ12V/ROQCqdCKiJQBOfk5PD3nab5Y/wX9mvTj763/jo/RP9Ei5V7lxgWTRVWqB+NuhfnDwZ7xgg/lgo+PIaleNKPvasMPD3ekdUI4r01aR+dXZzBy9mYyc/KcjigiXka/LYmIOOxY9jEGTB3A95u/56EWD/FIy0cw5kxXNRORcqlCZbjzR2hwDUx6Cn54FPLK/xHLRlXCGNmnNV890J6GVUJ58Yc1dH51BmPnbyUrV8VWRM6NCq2IiIN2pe3ijol3sGjPIga3H0z/pv2djiQiTvALghvHQodHYPEH8MlNkLbP6VSlokW1cD7s25Zx/duREBnMs9+s4tKhM/ls0XZy8vKdjiciZZwKrYiIQ1YeWMmtP9zK3vS9vNP9Ha6vc73TkUTEST4+0H0w9Pw3bJkFbyfC4lGQf3GUunY1I/ns3naMvbsNURX8+fuXK+j++ky+WbaT/PzyOwxbRIpHhVZExAHTtk3jrp/uIsAdwIdXfUi72HZORxKRsqJVH7h/HlRuCt//FUZdDntWOJ2qVBhj6Fy3El8/0J6RdyQS4OvikXHL6Pn2HGau348tx+cXi8iFUaEVESlF1lrGrBrDX5P/St3wunx01UfUqljL6VgiUtZUqgt9voPr34NDW+C9LjDpachKczpZqTDG0K1hDD8+3IlhNzfnaGYOfUb9zK3vL2TZjlSn44lIGaJCKyJSSnLzc3lhwQsMXTyUbtW78cEVHxAVGOV0LBEpq4yBZr3hwUXQ8i8w/20Y3gbWfO90slLj42O4rkUc0wYl8XzPhqzfe4zrhs/l/o+WsGn/xVHuReT3qdCKiJSC4/nHeXDag3y+/nP6Nu7L0C5DCXAHOB1LRLxBUAT0fBPungwBFeGz2+CT3pC63elkpcbP7cOdHWow8/GuDOxWh1nr93P5G7N4csJy9hzJdDqeiDhIhVZEpITtTtvNsD3DWLB7Ac9f8jwDWw3UNWZF5PxVawv3zoTuL8CWmTC8LSz92OlUpSrE383AbnWZ+XhX/tKuOl8sSaHLazMYvy6bA2lZTscTEQfoNyoRkRK07eg2/jLxLxzKPcR/uv2HP9X9k9ORRMSbuXyhw8Mw4GeIawXfPgRb5zidqtRFhfjz/LWNmP5oElc3iWXilhw6vjKdF79fzb6jOmIrcjFRoRURKSGbUjdx5093kp2XzSOVH6F9lfZORxKR8qJiVej9CUTUhM/vhCM7nU7kiKoRQbx+c3Ne6hjIVU1iGT1vK51encHz365i95HjTscTkVKgQisiUgLWHVrH3ZPuBmDUFaOI94t3OJGIlDsBodD7Y8g5DuP/ArkX75Db2BAfXr+pOdMf7cJ1zeP4aME2uryazNNfrSDlcIbT8USkBKnQioh42KoDq7h70t24fdyMvmI0tcNrOx1JRMqrSvXg+ndh5xL48W9Op3Fc9chgXvlzU5L/lsSNifF8vjiFpNeS+fsXy9l2MN3peCJSAlRoRUQ8aNm+ZfSb3I8KfhX4b4//khCW4HQkESnvGvSETo/CL2NgyX+dTlMmxIcHMeT6Jsx8PInb21Xn62U7ufRfM3n2m5WkZmQ7HU9EPEiFVkTEQxbtWUT/Kf2JCIhg9BWjqVqhqtORRORi0fVpqHVZwVHalMVOpykzYsMCef7aRsx+vCu3ta3GRwu2kTQ0mQ8XbCMv3zodT0Q8QIVWRMQD5u2axwNTH6BycGVG9xhNbEis05FE5GLi44I/jYQKsfDZXyBtn9OJypTo0AAG92rMj490okHlUJ75eiXXvDWHhZsPOh1NRIpJhVZEpJhmpczioWkPUTW0KqOvGE10ULTTkUTkYhQUUTBJ1PHDBTMf5+U4najMqV85lE/uact/bmvJ0eM53DxiAQ9+8gu7UjUjsoi3UqEVESmGadum8ciMR6hVsRajLh9FZGCk05FE5GJWuQlc+xZsmwuTn3E6TZlkjOGqJrFMHdSFRy6rw5TVe7n0X8n8e9oGMnPynI4nIudJhVZE5AJ9t+k7Hp35KA0jGzLyipFUDKjodCQREWh6I7R7ABa+A79+5nSaMivQz8Vfu9dl2qNduLR+NK9PWU+312fy08rdWKvza0W8hQqtiMgFGLtqLE/NeYrEmERGdB9BqF+o05FERP6n+2Co3hG+ewR2L3c6TZkWHx7Ef25rxSf3tCXYz819H/3CHaN+ZtP+NKejicg5UKEVETkP1lr+/cu/eW3xa3Sr1o3h3YYT7BvsdCyRc2KMiTDGTDHGbCi8Dz/DOs2NMfONMauMMcuNMTc7kVWKyeULN46GwHD47DY4sNHpRGVe+1pR/PBwR569piHLtqfSY9gsXp64lvSsXKejicjvUKEVETlHefl5DF4wmPdXvM+f6vyJoV2G4u/ydzqWyPl4Aphmra0DTCt8fqoM4A5rbSOgBzDMGKPx9N4oJBp6fwRZafBeZ/h1nNOJyjy3y4e7O9Zg+mNJXNssjndnbqLb6zP5fvkuDUMWKaNUaEVEzkF2XjZ/m/U3vlj/Bf2a9OO5S57D5eNyOpbI+eoFjCl8PAa47tQVrLXrrbUbCh/vAvYBlUotoXhWXCu4fy5UaQ5f3Qtf3V9QcOV3Vargz79uasaX919CeJAfD36ylNtGLmTD3mNORxORU7g9sRNjTA/gTcAFjLTWvnzK64OAfkAusB+421q7rfC1PGBF4arbrbXXeiKTiIinpOek88iMR1i4eyGPJT5Gn0Z9nI4kcqFirLW7Aay1u40xv3uNKWNMG8AP2HSW1/sD/QFiYmJITk4udsC0tDSP7McpZTZ/wqMkUJXqv37K8fUzWdXocdJDEk5apcxmPwclmf2xppYZ4X58uf4gPYbNolt1N9fV9iPQbTyyf2/+3sG78yu7czyZv9iF1hjjAoYD3YEUYJEx5ltr7eoiqy0FEq21GcaY+4FXgd/OyTlurW1e3BwiIiXhcOZh7p96P2sPrWVIxyFcW0t/c5OyzRgzFah8hpeePs/9xAIfAn2stflnWsdaOwIYAZCYmGiTkpLOL+wZJCcn44n9OKVs578MttxO0Jf9aL30cejxEiT2BVNQzMp29t9X0tkvBQamZfHapHV8tngHSw+6+L9rGtKzaSzGFK/YevP3Dt6dX9md48n8nhhy3AbYaK3dbK3NBsZRMKTpBGvtDGttRuHTBUC8B95XRKRE7U7bzR0T72Bj6kaGdR2mMitewVrbzVrb+Ay3b4C9hUX1t8K670z7MMaEAj8A/2etXVB66aXE1ehUMAS5Rmf44VEYfwccT3U6lVeIDPHn5T815asHOhATGsDDny7ljlE/s+VAutPRRC5qnii0ccCOIs9TCpedTV9gYpHnAcaYxcaYBcaY087lERFxwubUzfxl4l84cPwA73V/j6SqSU5HEvGEb4Hfxsz3Ab45dQVjjB/wFTDWWvt5KWaT0hIcBbeOh+4vwLof4b1OkLLY6VReo3nVinw9oAP/uLYRS7encsWwWbw5dQNZuXlORxO5KHniHNozjbM44zRwxpjbgUSgS5HF1ay1u4wxNYHpxpgV1trTztXReTqn8+b8yu4Mb84OpZd/ZcZKxhwYg6/xZUDMAI6tOUbymuK9rzd/996cHbw/v4e9DIw3xvQFtgM3AhhjEoH7rLX9gJuAzkCkMebOwu3utNYucyCvlBQfH+jwMFRvD1/cBaOuoEqtu4Ekp5N5BZePoU/7BHo0rswL36/mjanr+WbZTl64rjEdakc5HU/kouKJQpsCVC3yPB7YdepKxphuFJy/08Vam/Xb8sIZFLHWbjbGJAMtOMPkEzpP53TenF/ZneHN2aHk81tr+WDlB4zYNoL6EfV5s+ubxIbEemTf3vzde3N28P78nmStPQhcdobliymYvBFr7UfAR6UcTZwSnwj3zoav76fuuhEwvSJ0ferEebXy+2JCA3j71pbclLifZ75ZyW0jF9KreRWevroB0RUCnI4nclHwxJDjRUAdY0yNwmFKvSkY0nSCMaYF8B5wrbV2X5Hl4cYY/8LHUUAHoOhkUiIipeJ47nEen/U4b/7yJj0SejDmyjEeK7MiImVaYEW46UN2V+4Gs16FHwZBvobPno/OdSsxaWBnHr6sDhNX7OGyf83kwwXbyMvXtWtFSlqxC621Nhd4EJgErAHGW2tXGWMGG2N+m0HlNSAE+NwYs8wY81vhbQAsNsb8CswAXj5ldmQRkRK3O203fSb2YdLWSQxsOZBXOr9CoDvQ6VgiIqXH5WZdvQeh419h8Sj44m7Izfrj7eSEAF8Xg7rXZeLATjSJC+OZr1dywzvzWLXriNPRRMo1j1yH1lr7I/DjKcueLfK421m2mwc08UQGEZELsXjPYh6d+SjZedm8fdnbdI7v7HQkERFnGAPdnoegSJj8f5CZCjd/DP4hTifzKrUqhfBxv7Z8s2wXL/6wmp5vzeGuDjUY1L0uwf4e+dVbRIrwxJBjERGvNH7deO6ZfA+hfqF8cvUnKrMiIgDtH4Lr3oEts2FMT0g/6HQir2OM4boWcUwblETvNtX4YM4Wur0+k0mr9jgdTaTcUaEVkYtOTl4Og+cP5oUFL3BJlUv4+OqPqRFWw+lYIiJlR/NboffHsG81jO4BqTv+eBs5TViQLy9d34Qv729PWKAv9364hH5jFrMz9bjT0UTKDRVaEbmo7ErbRb/J/fh8/ef0bdyXty59i1C/UKdjiYiUPfWuhNsnwLE9MOoK2L/O6UReq1X1cL57qCNPXlmfuRsP0P31mbw/azO5eflORxPxeiq0InJRsNby1YavuOHbG1h7aC2vdHqFga0G4vJxOR1NRKTsSugAd/0IeTkwqgekLHE6kdfydflwb5daTBnUmUtqRjLkxzX0fHsuG1M1o7RIcajQiki5d+D4AR6a/hDPznuWBhENmNBrAlfVvMrpWCIi3qFyE+g7CfwrwH+vhllDNQNyMcSHBzGyTyLv3t6Kw+nZvLggk77/XcSirYecjibilVRoRaRc+2nrT1z3zXUs2L2Av7f+Ox9c8QFxIXFOxxIR8S4RNaHvFKjTDaa/AO+0h00znE7ltYwx9GhcmamPduH62r4s3ZHKje/O50/vzGPyqj3k6/q1IudMhVZEyqXUzFQen/k4f5v5N6pVqMb4nuO5veHt+Bj9sycickEqxMDNH8FtX0J+Hnx4HXx+Fxzd5XQyrxXi76ZXbT/m/v1SBvdqxN6jmfT/cAnd35jJ+EU7yMrVcGSRP6Lf7ESk3JmVMovrv72eKdun8FCLhxh75VhqhtV0OpaISPlQpxs8sACSnoS1P8DbrWHe2wXn2coFCfRzccclCSQ/lsS/b2mBv9vF418up/OrMxgxaxPHMvXdipyNCq2IlBtp2Wk8P+95BkwbQHhAOJ9e/Sn9m/bH7aML2YuIeJRvACQ9AQMWQPX2MPlpeK8LbJvndDKv5nb5cG2zKvzwcEfG3t2G2tEhvPTjWtq/PJ3XJq3lUHq20xFFyhz9lici5cK8nfN4fv7z7M3YS78m/bi/2f34ufycjiUiUr5F1IRbxxccqf3pCRh9JTS7BboPhpBop9N5LWMMnetWonPdSixPSeW9mZv5T/ImRs/dyl8uqc49nWoSFeLvdEyRMkGFVkS82rHsYwxdPJQJGyZQI6wGY68cS7NKzZyOJSJy8TAGGlwDtbrCrNcKhh+v+R46Pwbt7ge3ildxNI2vyPDbWrJx3zHenr6R92dtZsy8rdzWtjr3dq5JdGiA0xFFHKUhxyLitWalzOK6b67j641f07dxXz7v+bnKrIiIU/yCodvzBefXJnSAqc/B8LYF5dZq1t7iqh1dgWG9WzB1UBeublKF/87bSsdXZ/D8t6vYfeS40/FEHKNCKyJe50jWEZ6e8zQDpg0g1C+UT676hIGtBuLv0lEAERHH/T979x0eZZX2cfx7ZjLpvYdU0kkISSBAQg29SBMRUZoKWMCy69p9dcFdBV0rKFaQakOQjkgLPRTpJbTQkxBqSAgh7Xn/eCIoBikJGRLuz+Vc056ZuWcImN+cc+7jHgoP/QD9Zuijsz/0hYldIWuHuSurEYI97Hm/dyzL/pVMz3hfpqQepuW7Kbz283aOnc03d3lCVDkJtEKIamXpkaX0mNWDeenzeKzeY/zQ5Qei3aPNXZYQQoirhbaBJ1ZD5/fgxA74ojnMeRbyTpq7shohwM2WUffVI+WFZO5P8OPHjUdJ/l8KL0/fxpHTEmzF3UPW0AohqoWzBWeZcHICvx3+jQiXCMa2GUsdtzrmLksIIcTfMVpAoyEQ0wtS3oENX8GOGdDiBWj8BFhI876K8nOx5a17Y3iqdSifpxzguw1HmfbbMe6N92VYq1Bqu9uZu0QhbisZoRVC3PGWHVlGj1k92Jy/maFxQ/nunu8kzAohRHVi4wKdRsGTayEgERa9Dp8lQcYWc1dWY/g42TCie11WvtiKgUlBzNmaQZv3U3juhy0cOJln7vKEuG0k0Aoh7lh5hXm8vvp1nln2DB42Hrzo8yJPxj6JyWgyd2lCCCFuhUc49J0GfadD0UX4ui2sHStNoyqRl6M1b3SNYuVLrRjcPJgFO7Jo+8FynvluM/tO5Jq7PCEqnQRaIcQdaUPWBu6bfR+zD8xmSMwQvrvnO3wtfc1dlhBCiMoQ1haeWAVh7WHhK/Btb7hwytxV1SieDta82rkOK19qxeMtQli8+wTtP1rBsKmb2JmRY+7yhKg0EmiFEHeUguIC3t3wLo8ufBST0cTEjhN5pv4zMiorhBA1ja0r9JmqN41KXw6fNYWDK8xdVY3jbm/Fy50iWfVSa4Ylh7J870nuGb2Kh75KZWnaCUpLZXRcVG8SaIUQd4ydp3bywNwHmLxrMn0i+vBjlx+J84wzd1lCCCFuF6X0plFDloCVA0zsBkv+AyXF5q6sxnG1s+T5DhGsfrk1r3SKJP3kBR6dsJF2Hy7nu/VHKCgqMXeJQtwSCbRCCLMrKi3isy2f0Xd+X/KK8vii7Re8lvgatiZbc5cmhBCiKnjHwOPLIb4vrHwPJnSGc0fMXVWN5GRj4vGWIax8qRUfPRCHtcnIKzO203TUUj5ctJdTeZfMXaIQN0UCrRDCrNLOpDFg/gDGbh1Lx9odmdFtBk18m5i7LCGEEFXN0g66fwr3jYMTu+DzZrBrlrmrqrFMRgM94n2Z+3QzvhuSSJy/MyverewAACAASURBVB8v2UeTUUt5efo29mdLAylRPcg+tEIIs8jIy2DM5jHMS5+Hk5UT77d8n/ZB7c1dlhBCCHOL6QW+DWD6IPhxADR4GDq8rQdeUemUUiSFuJEU4sb+7DzGrTrIjE3H+H7DUZIjPBjSPJgmIW4opcxdqhDlkkArhKhSOZdy+Hr710zdPRWF4pG6jzAoZhCOlo7mLk0IIcSdwrU2PPILLHsLVn8Mh1bDfV9DLemrcDuFetozsmcMz7cPZ+q6I0xae4i+X68j0tuBwc2D6Rrrg5WF0dxlCvEnlTLlWCnVUSm1Rym1Xyn1cjn3Wymlfii7f51SKugP971SdvsepVSHyqhHCHHnuVRyiQk7JtBpRicm7pxI59qdmddzHv9s8E8Js0IIIf7KwhLajYCBs6Hwgr5n7aqPoLTU3JXVeG72VjzTJoxVL7Xm3V710DR4ftpWmr2zjE+W7uPshUJzlyjEZRUeoVVKGYFPgXbAMWCDUmq2pmm7/nDYIOCspmmhSqk+wDvAA0qpKKAPEA3UAhYrpcI1TZM2a0LUEKVaKfPS5zFm8xgyL2TSzLcZ/6j/DyJcI8xdmhBCiOqgdgt4cjXM/Qcs/jccWAI9Pgcn2Zv8drM2Gemd4M/9DfxYtf8UX688yHu/7uWTZfvp1cCPR5vWNneJQlTKlONGwH5N09IBlFLfA92BPwba7sDwsss/AZ8ofSJ+d+B7TdMuAQeVUvvLnm9tJdT1txYeXMSkE1PI2J1BvGc84S7hGA0yhUKIyrQmYw0fbPyAPWf3EOUWxX+a/ofGPo3NXZYQQojqxtYV7p8IW6bC/BfhsybQbTREdTd3ZXcFpRTNwzxoHubB3hO5jF91kB83HmNK6hFiPYwYap2keZi7rLMVZlEZgdYXOPqH68eAq39jvXyMpmnFSqkcwK3s9tSrHlslX7ct3byO9LztjFy/CQBbC1tiPWKJ94wn3iueeu71ZMsQIW5RZl4m7254l8VHFuNr78s7zd+hY+2OGJQ0VhdCCHGLlIL4fhCQBNMH6w2j4vtDx1HmruyuEu7lwKj76vF8hwimpB5m/Ir9DBi/nhAPOx5uEkTP+n7YWUmbHlF1KuOnrbyvYrQbPOZGHqs/gVKPAY8BeHl5kZKSchMl/lWfk8d4J/MAU1QC45xaEuCdyeFT6aRmpqKhYcCAr6UvwVbBhFmHEWYVhq3xzgq4eXl5Ff4czEVqN4/bXXuRVsSy88v4JecXALo6d6WVYytMR0ysOLKiws8vn715VOfaofrXX5mUUq7AD0AQcAjorWna2Wsc6wjsBn7WNO2pqqpRiOtyC4FBv0LKSFj5ARxejUPQUCDZ3JXdVdztrfhH23DqGo6T5xLON6sP8vqsnbz7yx7uT/BnYJNAAt2kM7W4/Soj0B4D/P9w3Q/IuMYxx5RSFoATcOYGHwuApmlfAl8CJCQkaMnJyRWrumVL9k+2pF/6RCLPXeCx7Od4oMWzPNrMmz05O9icvZkt2VtYd3Idy3OXY1AGolyjaOzTmMY+jYn3jMfawrpiNVRQSkoKFf4czERqN4/bWfua42t4b/17HD5/mLYBbXmx4Yv42PtU6mvIZ28e1bl2qP71V7KXgSWapo0qa+L4MvDSNY79D7C8yioT4mYYTdDmDQhpDTMep/6mF8H6MCS/CpZ31gBETWdhUPSI96VHvC+bj5xlwppDTFp7iG/WHKR1hCcPNw2iWahMRxa3T2UE2g1AmFKqNnAcvcnTQ1cdMxsYiL42thewVNM0TSk1G/hWKfUBelOoMGB9JdR0fUpxLKAnofEtaPDzEyxw+C/3pvyL2Vv8GdEtmqfjmwFQVFLEtlPbWJe5jtTMVCbunMi4HeOwNFgS7xlPY5/GJPokEuUWJWtwxV0p60IW7254l0WHFxHoGMjnbT+nqW9Tc5clhChfd64MY00EUign0CqlGgBewC9AQhXVJsTNC2oGT64mc9Jj1FozBnbPgS4fQUgrc1d2V4oPcCE+wIVXO9dh6rojfLvuMP3H6dOR+ycG0rOBH47WJnOXKWqYCgfasjWxTwELASMwXtO0nUqpN4GNmqbNBsYBk8uaPp1BD72UHfcjegOpYmBYlXc4jumFsvfE6/t+pLj8l2eMrzJ40kXaRXkxvFs0vs42NPBqQAOvBgyNG8qFogv8duI3UjNTWZe5jtGbRzN682g8bTwZFj+M7iHdJdiKu0JRSRETd03ky21fomkaz8Q/w8DogVgaLc1dmhDi2rw0TcsE0DQtUynlefUBSikD8D7QH2jzd09W2cuBoPpPEa/O9Vfr2n0HcMKrBRF7PsV2cg+yvFqzP/QRik13/rZw1flzh2vXX98EMU0sWJ8JS45cZPicXbw9fxdJPha0DrAg0NH8vy9X58++OtcOlVt/pazY1jRtPjD/qtve+MPlAuD+azz2LeCtyqjjltVuAY8uwHLq/XxW8DrzGr/DC5uMtH1/Oc+2DWNQs9qYjHozGzuTHS38WtDCrwUApy+eZl3mOqamTeXfa/7N5F2Tea7BczTzbSZTK0SNlF+Uz8JDCxm/YzyHzh+iTUAbXmz4IrXsa5m7NCEEoJRaDHiXc9drN/gUQ4H5mqYdvd7/xyp9ORDVf4p4da6/utcen/wUFA2GFf/De/VHeOdu0xtGxfTSG0rdoarz5w7Xr78d+j8+24/lMCX1MLO2Hmf5sQLqBzjTLzGQzjE+WJvME26r82dfnWuHyq1fWo7+zisaBi1COQfQZfszrO50gmZh7oxakEbXMavYfKTcnhm42bjRObgzUzpN4f2W73Op5BJDlwxlyKIh7D69u4rfhBC3h6ZpbMnewhur3yD5x2TeWPMGRmVkbJuxfNTqIwmzQtxBNE1rq2la3XJOs4ATSikfgLLz7HKeIgl4Sil1CHgPGKCUkjayonowWUOb1+HxFeASCDMGw9RecO6IuSu768X4OfFOr3qse6Utr3eJ4lx+Ec/9uJWkkUsYuWA3R07nm7tEUU1JoP0jJ194dAEENsH112f4KiiFr/o3IOdiET0/W8Pw2TvJu1Rc7kOVUrQPas+s7rN4qeFLpJ1J44G5D/DqylfJzMus4jciROU4ffE0E3ZMoMesHvRf0J9fDv1Cx6COTO40mZ+7/0xzv+bmLlEIcXN+72lB2fmsqw/QNK2vpmkBmqYFAc8DkzRNe7nqShSiEpQNVNBxFBxeC58mwtqxUFq1K9vEXznZmhjUrDZL/tWSqYMb07i2G1+vPEjL95YxaMIGVu47iaaVu+mJEOWSTaKuZu0EfafDrGGw9D+0SzhO4rNv8/7idCauPcTCnVm82b0u7aK8yn24yWiiX1Q/uoV24+vtXzN111QWHlpIv6h+DI4ZjIOlQ9W+HyFuUnFpMWsy1jBj3wyWH11OsVZMrEcsI5qMoENQB+xM0oJfiGpsFPCjUmoQcISy5UBKqQTgCU3TBpuzOCEqlcEIiU9C5D0w9zlY+AqkzYWeX4KTn7mru+sppWga6k7TUHeycgr4dt1hvl1/hP7j1hPqaV+2p60vtpYSV8Tfk5+Q8lhYwr1f6CO2qz7E4Xwmw3uNp3tcLV6ZsZ0hkzbSqa43I7pF4+lY/tY9jpaOPNfgOfpE9GHM5jGM3zGeGftm0K9OP3pH9MbF2qWK35QQf6+otIg5B+bw5bYvOZ53HFdrV/rW6UvPsJ4EOwebuzwhRCXQNO005TR60jRtI/CXMKtp2gRgwm0vTIjbyTkA+k6DLd/CghfhsyZ6J+S6Pc1dmSjj7WTNc+0jGNY6lHnbMvlm9SH+b+YO3v0ljQca+jMgKQh/V9mOSZRPAu21GAzQdjg4+sL8F2BSd+If+oE5TzfjyxXpfLxkH6v2n+KljpE81CgAg6H8ZgO17GsxsvlI+kf1Z/Tm0Xyy5RO+2v4VXYK70D+qPyHOIVX6toS4WnFp8eUgeyzvGNFu0fwr4V8k+yVjMkprfSGEEDWAUhDfFwISYcYQ+OkR2L8YOr0DVjJ77k5hZWGkZ30/7o33ZdORs3yz+hDjVx9i3KqDtK3jxcNNg0gKdpPGq+JPJNBeT6MhYO8F0wfDuPaY+k1nWKtQOsf48NrP2/m/mTv4efNxRvWMIczr2v8gRrlF8Xnbzzlw7gCTd01mbvpcpu+bTtNaTRkQNYCkWknyl1NUqeLSYuYfnM/nWz/naO5Rotyi+KTRJ7TwayE/i0IIIWomtxB4dCGkjIKV78PhNXDfOPBrYO7KxB8opWgQ6EqDQFcycy4yJfUw3647wq+7ThDmac/9CX70iPfF06H8mZLi7iJNoW5EVDcYMAsuZMO4dpC5jdrudkwd3Jj37o/lwMk8uoxZxeytGdd9qhDnEIY3Gc6vvX7lqbin2HN2D48vfpyes3syfe90CooLquANibtZSWkJcw7MocesHry26jXsTfaMbjWa7+/5npb+LSXMCiGEqNmMJr0T8sPzoLRY/91uxf+kYdQdysfJhhc6RLL2lTa826seDtYWvD0/jaSRSxk0YQMLtmdSWFxq7jKFGUmgvVGBSfDor2AwwTedIT0FpRS9Gvix6J8tifVz5pnvNvO/hWmUll6/M5urtSuPxz7OwvsW8lazt7AwWDB87XDa/9SesVvGcq7gXBW8KXE3KSopYuOFjfSY1YNXV72KtdGaj1p9xA9dfqBVQCsJskIIIe4uQU3hiVUQ1R2W/hcmdoVzR81dlbgGa5OR3gn+zBjalCX/asljLYLZkZHDk1M30fjtxQyfvZMdx3OkQ/JdSALtzfCMhEG/grM/TOkF26YB4OFgxZTBjenT0J9Plx3gscm/XXN7n6tZGi3pFtKNH7v8yPgO44n1jOWzrZ/Rfnp73tvwHtn55W0RKMSNKSktYV3mOoavGU7yj8lMPDURk9HEh8kf8mPXH2kT0EaCrBBCiLuXjTP0Gg89PofMrfB5U9j+E0gouqOFeNjzUsdI1rzchgmPNKRpqDvfrj9ClzGr6PTxSr5emU72eZn1eLeQNbQ3y8kXHlkA3/fVN+vOy4ImT2NpYWBkzxgivR34z7zd9By7mq8HNCTA7cY6simlaOjdkIbeDTlw7gBfb/+aKbun8G3at/QI7cEjdR/B38H/Nr85URNomsa2U9tYcHABCw8t5NTFU9ha2NI6oDV+eX482fFJDEq+yxJCCCEAvWFU3IMQ0BimD4Hpg2DXTLjnA7D3NHd14m8YDYrkCE+SIzzJyS9i9rYMfvrtGP+dt5u35+8mMdiNbrG16FTXBydbaXRZU0mgvRU2ztBvOvz8OPz6f3A+E9r/F2Uw8HDT2oR6OjDs2010+3QVY/vWp0mI+009fYhzCCObj2Ro3FC+2fENM/fPZMa+GXSq3YnBMYOlM7L4C03T2Ht2LwsOLuCXQ79wPO84lgZLWvi1oFPtTrTwa4G1hTUpKSkSZoUQQojyuAbrDaPWjoFlI+FQI+j0P4jppYdecUdzsjXRPzGQ/omB7M/OY/bWDGZvOc7LM7bz+qwdtAz3oGtsLdpFecnetjWM/GneKpM19PoGFvpA6qeQd0LfqNtgpFmYO7OGNWXwpI0MGLeef3eLpn9i4E2/hL+DP28kvcETsU8wcedEpu2dxtz0ubQJaMOQmCG34U2J6uZswVnmps9lxr4Z7D+3H6MyklQriaFxQ2nt3xp7S3tzlyiEEEJUH0YLaPZPiOgMs4bps/F2zoAuH4KDt7mrEzco1NOe59qF88+2YWw/nsPsLRnM3ZbJ4t3Z2JiMtI3yoltsLdQN9L0Rdz4JtBVhMEDHkfp0lCUjwNIWuo4GpQhyt2PG0Cb84/stvD5zB2mZ5xneLRqT8eZHxzxtPXmh4QsMjhnM1N1T+TbtW5YcWUKYVRiGYwaa+TaTUbe7SElpCamZqczYN4OlR5dSXFpMPfd6vJ74Ou0C2+Fi7WLuEoUQQojqzSNCH61NHas3jPq0EXR6F+o9IKO11YhSinp+ztTzc+bVznVYf+gMs7dmsGB7JnO2ZmBjAR1PbqFDtDctwz2wsTSau2RxCyTQVpRS0Pw5KLwAK98DOw9o8wYAjtYmvhqQwLsL0/hieTr7s/P4tG993O2tbumlXKxdeCr+KR6Ofphpe6cxfst4hi0ZRrBTMAOiBtAlpAtWxlt7bnHnO553nJn7ZzJz/0yyLmThbOVMn4g+9AzrSZhLmLnLE0IIIWoWgxGaPA3hnfTR2p8fhx0zoOtH4FjL3NWJm2QwKBKD3UgMdmNEt2hW7TvF+EWbWbYnm583H8fGZCQ5woOOdb1pHemJg7Wsua0uJNBWltb/B/mn9E26bd0haSigL1Z/pVMdIr0deGn6djp9vJKPHoijaejNrav9I3tLe71J1El/LgZcZNKuSQxfO5zRm0fzYOSDPBDxgIzS1RA5l3JYfXw1M/fPJDUzFYAmtZrwfMLztPJvhaXR0swVCiGEEDWceyg8Mh/WfQFL3oRPE6HDWxDfT0ZrqymT0UCrSE9UlhVNm7dg/cEz/LIji4U7s1iwIwtLo4GmoW50rOtNuyhvXO3k9607mQTayqKU3g0v/wwsfAVsXSG2z+W77433I9Lbkae/20y/cet4omUIz7ULv6UpyL+zUBZ0DelKl+AurM9az4SdE/h0y6eM2z6ObiHd6B/VnyCnoEp4c6Kq5FzKYeOJjWzM2siGrA3sPbsXDY1adrV4MvZJeoT2wMfex9xlCiGEEHcXg1EfrAjvALOfhtlPQdpc6DZGOiFXcyajgaah7jQNdWdEt2g2Hz3LLzv0YLts+nZembGdRrVd6RDtTftob3ydbcxdsriKBNrKZDDCfV/D1F4wcyjYuOj/8JWp4+PI7Kea8p+5u/gs5QBrDpxmTJ/4G97a51qUUjT2aUxjn8YcOHeASbsm8fP+n5m2dxqt/FvxaMyjxHrEVvTdidvgWgHW2mhNnGccT8U/RUPvhsR6xMo6aSGEEMLc3EJg4FxY9zksHg5jE/X+KXW6mLsyUQkMBkWDQFcaBLryauc67Mw4z8Kd+sjtiDm7GDFnFzG+TnSI9qJDtDehnvYoGaU3Owm0lc3CCh6YChO7wI8DYcBMCEi8fLetpQUje9ajWagHL8/Yxj2jV/JWzxi6xVbOWowQ5xBGNBnB0/FP813ad3yf9j1Ljy4lwSuBR+s+SjPfZvIXz4wKigvYlL2J1IxUUjNTSTuTdjnAxnrGMixuGI18GlHXrS4mo6zdEEIIIe44BoM+WhvSGmYMgR/6Qlw/vVGotaO5qxOVRClFXV8n6vo68a/2EaSfzGPhzhMs3JnFe7/u5b1f9xLsbkf7aG86RHsR6+eMwSC/Y5uDBNrbwdoR+k6H8R3g297wyALwiv7TIffU8yHW34lnv9/CM99tZuXek4zoHl1p+2K527jzdPzTDKo7iOn7pjNx50SGLhlKuEs4j9Z9lA5BHbAwyB//7VaqlZJ2Jo3UzFTWZqxl04lNFJYWYmGwIM4jjqFxQ2nk3Yi67nVlPawQQghRnXhGwuAlsPwdWPUBHFoB934BgU3MXZm4DYI97Hky2Z4nk0PIyilg0a4sft11gq9XpvP58gN4OFjRKsKDVhGeNAtzl6ZSVUgSze1i7wH9f9ZD7eSeMOhXcPnzXrR+Lrb88FgiHy/ZxyfL9vPbkbOM7hNPXV+nSivD1mRL/6j+9Inow/yD8xm/Yzwvr3yZMZvHMCBqAPeG3YuNhawFqEzZ+dmsPr6aNRlrWJe5jrOXzgIQ6hzKA5EPkOiTSIJXAramik01F0IIIYSZWVhCm9chrD38/Bh80xmaPgutXtVn7YkaydvJmv5JQfRPCiInv4ile06weHc2C3Zk8ePGY1gYFA2DXGkd6UmrSA9CPGRq8u0kgfZ2cgmEfjPgm04wuQc8+qsedP/AwmjgX+0jaBLizj9+2EzPsWt4pXMkDzcJqtQffJPRRPfQ7nQN6cryo8sZt2McI9eP5POtn/Ng5IMk1UoiwjVCwu0tKC4tZvup7aw8tpKVx1eSdiYNAA8bD5r5NiOpVhKJPol42Hpc55mEEEIIUS0FNIYnVsPCV2H1R7B/CfT8EryizF2ZuM2cbE3cG+/HvfF+FJeU8tvhsyzdk01K2knemr+bt+bvxt/VhlYRnrSK9CSxtpvsd1vJJNDebl5R8NCPMKk7TOkJD88rd31FUogbC55twYs/bWXEnF1sPHyWd+6rh71V5f4RGZSBVgGtSPZPZlP2JsZtH8fYrWMZu3UsRmUk2DmYaLdootyiiHaLJsI1Qva2LceZgjOsPr6alcdWsjpjNecLz2NURuI84/hH/X/QzLcZ4S7h8m2cEEIIcbewsoduoyGis94F+cuW+raOicPAKL9y3w0sjAYaB7vRONiNVzrV4djZfFL2nGRZWjY/bjzKpLWHsbQw0Li2Ky3DPWgZ7iGNpSqB/O2qCgGNofck+P5BfaS270/6tj5XcbWz5KsBCXyxIp13f0kjLfM8X/RvQKinQ6WXpJSigVcDGng1IDs/mx2ndrDr9C52nt7JimMrmLl/JqBvDRTqEkqUWxQJXgm09G+Jo+Xd1fBA0zSO5x1n5+md7Dy9k6WZSznywxE0NNys3Wjl34rmfs1JqpV01302QgghhLhKREcYmgpznoVFb8DOn6HbJ+Bd19yViSrm52JLv8RA+iUGUlBUQmr6aVbsPcWKfSf577zd/Hfebmo5WdMyQg+3TULdcZS1tzdNAm1VCW+vh9ppD8PEbvr6Wvu/TkFVSvFEyxBi/Zx5+rtNdPtkNe/2qkeXepXTBbk8nraetA5oTeuA1oAe4LIuZF0OuDtP72TJkSXM2DcDC4MFiT6JtA1oS6uAVrha/zWYV2eapnEi/4T+vk/tvPwZnLt0DgCTwYSfyY+hcUNp7tecOq51ZDsdIYQQQvyZnTs8MEUPs/Nf0Edrmz0HLZ6XtbV3KWuTkeQIT5Ij9H2Lj53NZ8XeUyzfm83crZl8t/4oRoOifoAzzUI9SApxI9bfCSsLmZ58PRUKtEopV+AHIAg4BPTWNO3sVcfEAZ8BjkAJ8JamaT+U3TcBaAnklB3+sKZpWypS0x0t8h548Dv4vi9M6AwDZoOjT7mHJoW4Mffp5gz7dhNPfbuZ3w6f5ZVOdbC0uP3hSSmFj70PPvY+tAlsA+jderef2s7iw4tZdHgRw9cO583UN0nwSqBtYFvaBLTB07Z6bSxeWFLIwZyD7Du3j/1n97Pv3D52nd7FqYunADAqI6HOobQOaE20WzTR7tGEOYexZuUakmOTzVu8EEIIIe5sSkHdnhCcDL+8Aivehd2z9dFa/4bmrk6YmZ+LLQ81DuChxgEUlZSy+cg5lu/NZsXeU3y0ZC8fLgZrk4EGgS4kBbuRFOJGjK9zlWSB6qaiI7QvA0s0TRullHq57PpLVx2TDwzQNG2fUqoW8JtSaqGmaefK7n9B07SfKlhH9RHaFvpNh28f0JtFDZwNzgHlHurtZM33jyUycn4a41cfZNuxHD59qD7eTtZVXLS+9jbWI5ZYj1iea/Ace87uYdHhRSw+vJi3173N2+veJs4jjuZ+zXGwdMCojJgMJiwMFhiVEQuDxZWTsiC9IB3/c/44WDpgb7LHxsLmtq0fKCopIuNCxuXQuu/sPvaf28/h84cp0UoAfWp1kFMQTWo1ubx+ONI1EmuLqv+shRBCCFGD2LpCzy8gphfM+QeMaweJT+rray3tzF2duAOYjAYa1XalUW1XXugA5/ILWXfwDKnpp1l74DTv/boXABuTkYQgF5JC3LA6V0LTklJMRgm4FQ203YHksssTgRSuCrSapu39w+UMpVQ24AGc424V1Az6z4Sp98H4slDrFlLuoSajgTe6RhEf4MxL07fRZcxKRj8YT5MQ9you+gqlFJGukUS6RvJ0/NOkn0vXw+2RxYzZPOaGn+fDWR9evmyhLHCwdCj/ZHLA3tIeB0sHHC0dsTfZX77P3tKevMI8svOz9dPF7MuXT+af5ET+Cc4UnPnT6/rZ+xHqEkqbgDaEuYQR5hxGoGMgJqOsWRBCCCHEbRLWDoalwuIRkDoW0uZB148BaQgk/szZ1pIO0d50iPYG4MyFQtaln2ZtWcB995c9AHyw6VcSglxpHOxKYrAbMb5Od2XArWig9dI0LRNA07RMpdTfzjlVSjUCLIEDf7j5LaXUG8AS4GVN0y5VsKbqwb8hDJyrN4n6phMMmAWeda55eNfYWkR6O/DElN/o9/U6XuwYSYSmVWHB1xbsHMzjzo/zeOzj5BXmcankEsWlxZRoJRSXFusnrfjK5dJi1m1aR+3I2pwvPE9eUR65hbnkFuZyvvA8uYW5l0NqXmEeuUW5XCy+eMP1uFq74mnriYeNB1FuUXjZeuFt502ocyghziGy/6sQNUSRfDMthKhurBzgnvf0qcizn4bJPYjwbgMNIsHB29zViTuUq50lnWJ86BSjL1U8mXuJb+auJNfGm9T0KwHX1tJIQpAricGuNK7tRj2/uyPgXjfQKqUWA+X9DXvtZl5IKeUDTAYGappWWnbzK0AWesj9En10981rPP4x4DEALy8vUlJSbubly5WXl1cpz1MRttHDid36Buqr9myrN4I8h+C/Pf75WI3xO4yMWpBGXVeNC0XLsLesft/s+Zf4Y33YGmus8eSq70Esyk5/yJ0lWgkXSy+We7I2WONkdMLZwhkHowMm9YeR1sKy0zk4ffw0pzld4drvhJ+bW1Wda4fqXb/UfusuFmtkXiglI6+UjDyN43n65aJS+KjV9b+gMnf9QgjxF4FN9H1rl7+D1+qP4eM4aDgImv1TbyglxN/wcLCikY8Fycl65+xTeZdYXzZF+eqAWz/AhYZBrjSs7UK8v0uN3AP3uoFW07S217pPKXVCKeVTNjrrA2Rf4zhHYB7wf5qmpf7huTPLLl5SSn0DPP83dXyJHnpJSEjQkpOTr1f6daWkpFAZz1NhiU1hUncSdg6HfjPAL+FvD+/YRmPCmkP8d+4u3iqxjQAAIABJREFURm7SGP1gHA0CXaqm1kpyx3z2t0BqN5/qXL/Ufn0FRSXsPZHL7szz7D2Rx77sPPafyCUjp+DyMZZGA7Xd7WgUZk+Ypz3NW4RhNPz9l3rV+bMXQtRgJmto+2/WF4WTWLBCn4a88Rto/Bg0eabcLR6FKI+7vRWdY3zoXDaCe/oPAXfdwTN8tGQvmgYmo6KurxONglz1kBvkipNt9V9yV9Epx7OBgcCosvNZVx+glLIEfgYmaZo27ar7fg/DCugB7KhgPdWTWwg8Ml/fzmdSd3joB32d7TUopXikaW04lc74PfDAF2t5sWMEg5sFY7jOL3ZCCHEnOJl7id2Z59mVeV4/zzhP+qkLlJTqSymsTQZCPe1pVNuVMC8HQj31ABvgaovFXTB9Sghx9yiw8YFOn0Hzf8HyUbDqI1j/td44KmkY2Dibu0RRzbjZW/1pinLOxSJ+O3yG9QfPsuHQGcavPsgXK9IBiPR2ICHIhfoBLsQHuBDkZnvbGrXeLhUNtKOAH5VSg4AjwP0ASqkE4AlN0wYDvYEWgJtS6uGyx/2+Pc9UpZQH+mr4LcATFayn+nIOgEcW6IF26v3Qd9rfhlqA2k5G5j7dlJd+2sbb89NYl36G9+6PxcXOsoqKFkKIv1dQVML+7Dz2ZOXqo69Z+gjsydwr7RJ8nW2o4+NAp7re1PFxpI6PIwGutvIFnRDi7uIeCvd9rQfblFH6Nj/rvoAmT0HjJ8Da0dwVimrKycZE60gvWkd6Afr/m7ccPceGg2dYf+gMMzdnMCX1CADOtibi/Z2JD3AhPsCZWH9nHK3v7FHcCgVaTdNOA23KuX0jMLjs8hRgyjUe37oir1/jOPrAw3NhQheY2lvf3icw6W8f4mRj4rN+9Zm09jBvzdvNPaNXMuaheBoEyjQVIUTVKS4p5dDpfPaeyGVPVu7lAHvo9AXKBl2xNBoI8bSnRZgHUbUcqePjQJSPI8628iWcEEJc5lkHek+ErO16sF32lj4ducnT0OgxvbGUEBVgbTKSGOxGYrAbACWlGvuz89h85Cybj5xj89GzpOw9iabp2ymHetgT56+H23p+TkR4O2Blceesxa3oCK2obPaeMHAOTLgHpvaC/j+Df6O/fYhSioFNgqgf4MKwbzfR+4tUXuwQwZDmMgVZCFH5TuVdYk/ZSGtaVi5pWfqa18Jivd+fQUGQmx3hXg50KevQHu7lQJCbTBcWQogb5h0DfaZCxmZYNhKWvAlrxkiwFZXOaFBEeDsQ4e1An0YBAJwvKGLb0Rw95B49x+LdJ5j22zFA/4I60seBGF8n6vk5EePrTJiXvdk6KkugvRM5eF0JtZN7woCZ120UBRDj58TcZ5rx8vRtjFyQRmr6ad7vHYerTEEWQtyCi4X6dOHVx4tYPW8XaVm57M7M5VTelenCHg5WRHo7MDApkEhvRyK89fWu1qY755tbIYSo1mrFQ98f4fhvkPKOBFtRJRytTTQLc6dZmN51W9M0jp29yLZjOWw7fo7tx3KYvTWDqev0qcpWFgaiajlSz9eJN7pGX7dhY2WSQHuncvQpC7Wdr4Ra3/rXf5i1iU8fqs/k1MP8d+5uOn28gnd7xdIy3KMKihZCVEcXLhWzP1vvKrwvO5d9J/TzY2cv8vt211YWhwn3cqBVhAeRPo5Eln2T625vZd7ixU1RSrkCPwBBwCGgt6ZpZ8s5LgD4GvAHNKCzpmmHqqxQIcRf+TYoP9gmPaUHW1ljK24jpRT+rrb4u9pyTz292VRpqcbhM/lsO6YH3G3Hc1h38EyVhlmQQHtnc/KFgXPLQm0PGDAbasVd92FKKQYk6VOQ//nDFgaOX8+ApEBe6VSnRu49JYS4cdnnC9h2LIftx3PYcTyHtKxcjp+7ePl+S6OBYA874vxduL+BP+Fe9pw5tJvenZJlunDN8DKwRNO0UUqpl8uuv1TOcZOAtzRNW6SUsgdKyzlGCGEOfwy2y9+Fpf+BtZ9IsBVVzmBQ1Ha3o7a7Hd3jfAF9JLeqSaC90zn7l4Xae/RQO3COvqbiBtT1dWLO083438I9jFt1kFX7TvHBA3HE+Uv7dyHuBtm5Bew4nsO2YzmXz7PLugv/3uShfqALfRr6E+blQJiXPYHlbIuTcmqPhNmaozuQXHZ5IpDCVYFWKRUFWGiatghA07S8KqxPCHGjfBvoWz0e3wTL37kSbJs+C40eB0tbc1co7kLm2PJHAm114BJ4ZU3txG56J2Sv6Bt6qLXJyOtdomgT6cnz07Zy32drGNYqlKdbh5pt4bYQonL9PuVnV8b5y3u77so4T9b5AkAPryEe9jQNdSfG14kYPyeifByxs5L/BdyFvDRNywQo2wfes5xjwoFzSqkZQG1gMfCypmklVVinEOJG+da/EmyXvQ2Lh0PqZ9DiBag/ECykl4qo2eS3merCtfZVoXbeTT28Sag7C/7RghGzdzJ6yT5S9mTzQe84Qj3tb1PBQojb4WJhCWlZemjdXRZc07JyyS/Us4bRoAj1sCcx2JW6vk7U83MmqpYj9hJe7xpKqcWAdzl3vXaDT2EBNAfi0feY/wF4GBhXzms9BjwG4OXlRUpKys0XfJW8vLxKeR5zqc71S+3mUam1+z2Fk31rah+cgvP857m49F0OB/bhhFcymuH2LDuTz948qnPtULn1y2841YlbyJU1tRO7Ylfn/27q4U42Jj54II52UV68+vN27hm9klc6RTIgKUi29xHiDpRfWMyujPNsP35lzev+7LzL+7o6WFlQp5YjvRP8ifJxJKqWo3QYFmia1vZa9ymlTiilfMpGZ32A7HIOOwZs1jQtvewxM4FEygm0mqZ9CXwJkJCQoCUnJ1e4/pSUFCrjecylOtcvtZtH5deeDNqTcGApNkveJHLPaCJP/wKtXoM63cBQuTP05LM3j+pcO1Ru/RJoqxv3UD3UTuxK3JZXoG4oBDW9qafoFONDg0AXXpq+jeFzdrF4dzb/ah9OnL+zWea9CyEgJ7+IPSdyLwfX7cdzOHAy73KXYXd7K2J8HekY7U1ULSeiazni52Ijf2fFzZoNDARGlZ3PKueYDYCLUspD07STQGtgY9WVKISoMKUgtA2EtIbdc2DZWzBtIHjXgzZvQGhb/RghagAJtNWRRzgMXkThl50wTb4Xen4J0T1u6ik8Ha0Z/3BDvlt/lJHzd3Pv2DXU83NiQFIQXer5yAiPELdJfqG+Rc6erFz2nshlz4k89mblXl7vCuDpYEWMrxP3xPhQ19eJGF8nvBytJLyKyjAK+FEpNQh9OvH9AEqpBOAJTdMGa5pWopR6Hlii9B+634CvzFaxEOLWKQVR3SDyHtg+TV9jO7WXvrdt4jD990ejydxVClEhEmirK+cANsePpNmRT2Daw5D3LjR+7KaeQinFQ40D6BZXi583H2fSmkM8P20rb83bRZ9GAfRtHICfi3TIE+JWaJpG1vkCth/LYUfGeVZuL+DfG5Zx5Ez+5VFXSwsDYZ72NAlxI9zbgXAve+rWcsLT0dq8xYsaS9O000Cbcm7fCAz+w/VFQL0qLE0IcTsZjBDbB6J7wpapsPZTmDEYFr0OjYZAg0fA1tXcVQpxSyTQVmPFJkcYMAt+GgQLXoDcDGjz75ueQmJvZUH/xED6NQ5gbfppJq05zBfLD/DF8gO0qePFwKQgmoa6yeiQENegaRrHz11kx/Hzl6cL78zI4VReIQAGBV62ivrBTvSM9yPC255wLwcCytkiRwghhLhtLCwh4RG9+/GBJXqwXfImLP+fHngTh+ozAYWoRiTQVncmG+g9CeY/D6s+hPOZ0P2TW5o+opSiSYg7TULcOX7uIt+uO8x364+yaNcJQjzseKRpbXo18JPpyOKuVlqqceRMPjszzrMjQ1/vujPjPGcu6OHVaFCEedqTHOFJjK8TdX0dqePjyPo1q0hOrm/m6oUQQgj0xlBh7fTTiV2QOha2fAu/fQOh7SBpKAS3knW2olqQQFsTGC2gy4fg6AvL/gsXsvWQa+Vwy0/p62zDCx0iebp1GPO3ZzJxzSH+b+YOPl6yj0HNatO3cQAO1rLmQtRsxSWlpJ+6wI7jOew4fp6dGTnsyjhP7qViACwMijAvB9rW+T28OlHHx1G+9BFCCFF9eEXpgyFth8PG8bD+K5h8L3jUgcaPQ73eYGln7iqFuCYJtDWFUtDyBXDwhjnP6vvV9v0J7D0r9LTWJiM96/txb7wvqelnGJuyn1EL0hi7bD8DmwTxcJMg3OytKulNCGEemqZxMu8Se7PySMs6/4eGTbkUFJUCYG0yEOntSPf4WtStpYfXMC97rCwkvAohhKgB7Nyh5YvQ9FnYMR1SP4O5/4DFw6F+f2g4BFwCzV2lEH8hgbamqd9fD7HTHoav20L/n/X9aytIKUVSiBtJIW5sO3aOscsOMGbpfr5amc6DjQIY0jyYWs42Fa9fiNvsXH4hB05e0ANrVtnpRO7lKcMA7vaWhHs58FCjQOr6OlLX14lgdztZ7yqEEKLms7CCuIcg9kE4ug7WfQ5rx+rrbSM666O2Qc1lOrK4Y0igrYnCO+h71X57P3zVGu7/Rt+HrJLU83Pm8/4N2J+dy2cp6Uxae5gpqYfpEefL4y1DCPW0r7TXEuJWFJeUcuRMPuknL5B+Ko8D2fp5+skLnP5DcLW1NBLu5UC7Ol5EeDsQ6e1AuLcD7jLrQAghxN1OKQhI1E85x2HjONj4DaTNBc8oPdjG9DZ3lUJIoK2x/BrA4MXwfV+Ycp++LqLJM5X6bVqopwPv947ln+3C+GpFOt9vOMq0344R5mlP8zAPWoS707i2GzaWMiVTVL7C4lKOnc3n8Jl8jpzO5/DpfI6cucDBUxc4ciafohLt8rFudpYEe9jRLsqLYA87gt31LsN+LjYYDPINsxBCCPG3nHyhzRvQ4gV9OvK6z/Ulbov+TYh7C4jyAs865q5S3KUk0NZkrsEwaBHMGgqL3oDMrdBtTKUv7PdzsWVE97o81TqMmZuPs2LfSaasO8z41QextDDQKMiVFuHuNA/zINLbQbb/ETestFTfDmdfdi77TuSxZsclvtyXyuHT+WTmXKT0SmbFxmQk0M2WUE972kd7E+xuR4inPSHu9jjZSgMzIYQQosJMNhDfD+L6wpFUWP8FvrvmwNjZ4NcQ6g/Q97q1ktl6oupIoK3prOzh/on6lj5L3oSTe6HPFHAJqvSX8nCwYkiLYIa0COZiYQnrD51h5d6TrNh3krfnpwFpeDhY0TzMHY/iYmLyLklDKQH8ObjuPZHH3hO57M/OY392HvmFJZePczBBiHcJCUEuBLr6EuhmR6CbLQFutnjYW8mXJUIIIURVUAoCkyAwibW/zqKp/VHYNAlmPw2/vALR9+p73folyFpbcdtJoL0bKAXNnwPvGJg+CL5MhvsnQHDybXtJG0sjLcM9aBnuAUBWTgEr9p1k5b5TLEvL5mx+EV9uX0yMrxMtwjxoGeFBvL+zNN2pwUpKNTJzLnLkdD6HTudz+MwFDp/SpwwfOnWBi0VXgqungxXhXg70TvAn3MuBcC97Qj3t2bJ+DcnJTc34LoQQQgjxR0WWTtCkOyQNg2MbYNNEfVry5sn61j/1+0O9PmDnZu5SRQ0lgfZuEtYOhizT19VOvhfa/Uf/x6cKvjnzdrKmd4I/vRP8KSnVmDhnKXn2AazYe5LPlh/gk2X7cbCyoGmoOy3C9fW3fi62t70uUblKSzUyci5y8NQFDp26QPqpCxw+nc/h0xc4euYihSWll4+1NBrwc7UhyM2OxGBXwjz14Brm6SBThIUQQojqRinwb6SfOoyEnTP0UduFr8Kif0NEJ326ckgbMEoEEZVHfpruNm4hMHgRzHwSfn1NX1fb9WOwrLrwaDQogp2MJCeH8UybMHIuFrFm/ylW7DvJ8j0n+WVnFgDB7nbEB7gQ5+9EnL8LkT4OmGQE16xKSzXOFxRx5kIhJ3Mvcej0BQ6eyufgqTwOloXXS8VXQuvv61rDPB1oW8fr8hThQDdbfJxsMEpDJiGEEKLmsXaEBg/rpxM7YfMU2PYD7J4N9t4Q20cPt+5h5q5U1AASaO9GVg5w/yRY9T4sfQtOpkG30VAr3izlONmY6BTjQ6cYHzRN48DJPFL2nCQ1/TTL92YzfdMxvWwLA3V9nYjzd7588nOxkXWTFVRUUkp27iWyci6SlXOJzJyLnL5QyNkLhZy5UMjZfP38XH4RZ/ML/9SICcBkVAS42lLb3Z6W4R7UdrcnyN2WYHd7vBxlXasQQghxV/OKho4joe0I2LdQD7drxsDqj8CvkR5so+/VQ7AQt6BCgVYp5Qr8AAQBh4DemqadLee4EmB72dUjmqZ1K7u9NvA94ApsAvprmlZ49ePFbWAw6K3Xvevpo7VfJkPdXtD6/8C1ttnKUkoR6ulAqKcDg5sHo2kax85eZMvRc5dPU1IPM27VQQDc7S3xc7HF1c4SF1tLXGxNuNhZll034WKrX3ayNeFobcLKwlDjApamaeRcLCK3oJiLRSUUFJVwsbCEguJS/fz324pK2H6gkCXndpB1voCsnAKyzhdwKu8SWjkh9ffPzsXWkghvhz9dd7Ez4WZnRZCbHbWcrWXtsxBCCCH+noUl1Omqn3JPwLbvYfNUmPMMLHgJorpD3IMQ1EL/PVWIG1TREdqXgSWapo1SSr1cdv2lco67qGlaXDm3vwN8qGna90qpz4FBwGcVrEncjPAO8MxmWD0a1n4Ku2ZBw8F62L0DFu8rpfB3tcXf1ZausbUAfURxT1Yum4+eY9vRc2SdLyA7t4A9WbmcuVD4p+ZCVzMZFQ7WJhysLfST1e+X9XNrkxErCwOWFgasLp+Ml69bWhjYebKY0rQTFJdolJRqlGhl56UaxaVXLuv1g0KVnV+5XvYfBqUwGPRzpdSV25T+3g0KNOBcfiGn8go5nVfI6QuXOHPh9+v65eKrh03/htOxDHycrPFytCa6liPeTtZ4O1rr52WXnWxMNS74CyGEEOIO4eAFTZ+FJs/A8d/0Udsd0/WQ6+gH9XpD7IPgEW7uSkU1UNFA2x1ILrs8EUih/ED7F0r/bbk18NAfHj8cCbRVz9oJ2ryuB9mUkbD+C9gyVf+HJnFola6vvREmoz71uK6vEyQG/uX+gqKSP02T1c8LOV9QTG5BMbkFReRdunL5yJl8cguKOV9QxKWi0j81Lrqm3zbehnd2fXaWRtzsrXCzt8TX2YZYPydc7Sxxs7fC0doCG0sjNiYj1mUn/bLh8u3r166mfZtWZqldCCGEEOJPlNK39vFL0Kcl75kPW7+H1R/Dqg+gVn092Na9744YaBF3pooGWi9N0zIBNE3LVEp5XuM4a6XURqAYGKVp2kzADTinaVpx2THHAN9rvZBS6jHgMQAvLy9SUlIqWDrk5eVVyvOYy22p37EntgkNCU6fjPvS/3Bp1SccCnqILO82aAZjpb1MVX72DmUnFGBTdvoLA6DviVuqaRSXQnEpFJVCcalGUdnlolKNvAsXsbezwaiujKYaAKMB/XLZddBHV38//31ab3mXNaC07BwNStGnEv/+eDuTwsFSYWX8fdS0qOxUphjIu3L193tzr3qXhRcvyM+8mUjt5lPd6xdCiLuCyUYPrnXv06ck7/gJtn4HC17QOyWHd9CbSYW1Bwsrc1cr7iDXDbRKqcWAdzl3vXYTrxOgaVqGUioYWKqU2g6cL+e4a86b1DTtS+BLgISEBC05OfkmXr58KSkpVMbzmMvtrb8/HF6L1aI3iNj7KRFnFkPb4XrL9UqYilqdP3up3Xyqc/1Su/lU9/qFEOKu4+Clby2ZNAyydujBdvs0SJsLVk4Q0VFfixvS5o6bSSiq3nUDraZpba91n1LqhFLKp2x01gfIvsZzZJSdpyulUoB4YDrgrJSyKBul9QMybuE9iNslMAkG/ar/47F4BHz/IAQ1hw5vgU+suasTQgghhBA1nXdd8H5L75Kcvgx2zoQ98/RtgCxsIKwt1Ommj9zaOJu7WmEGFW0hNhsYWHZ5IDDr6gOUUi5KKauyy+5AU2CXpmkasAzo9XePF2amlP4N2NC10Pk9fS+xL1rCzKFwXr5/EEIIIYQQVcBoAWHtoMen8Px+GDBb3/Ln6AaYMQT+FwpT7oPfJkDeSXNXK6pQRQPtKKCdUmof0K7sOkqpBKXU12XH1AE2KqW2ogfYUZqm7Sq77yXgOaXUfvQ1teMqWI+4XYwmaDRE74jc5Gl92seYBrBsJBReMHd1QgghhBDibmG0gOCWcM978NxuGLQIEp+E0/thzrPwXhiMaw8rP4DsNP6yP6GoUSrUFErTtNNAm3Ju3wgMLru8Boi5xuPTgUYVqUFUMRtnaP8faDgIFg+H5aNg00R9/9rYB6ESG0cJIYQQQgjxtwwG8G+kn9q9qc8m3D0H9i6AJSP0k0sQRHSG8I4Q2EQfqBE1RkW7HIu7lUsQ3D8BGj+pd56bNQzWfQ7t/wu1W1ZK4yghhBBCCCFumFJla27rQqtXIOc47P1FP20YB6lj9aZSYW0hvBMWRdbmrlhUAgm0omICGsPgxfpm2ItHwKTu4Bamt1Wv9wA4+5u7QiH+v717D66zrvM4/v7mnt6vSUvvN+hFIGrLrdjGgi4KU3AGXFidxR0RmdUZd8YLsKyuusMqOqv84Y6zeCszK2oFtKi4UtoGFGuhanqxQC+0hWKaUNpiQ9Pcznf/+D3JOU1P0oQk5zlPz+c185vn/pxvfic5v3zP7/c8j4iIiBSisdPCqMJlHw2XyO3bFHpud/8Gdj7Ccorg5WUw/+pQptaEHl9JFCW0MnhmcOGNsPA62LE2PBB743+EMvtdYSjy4tVQPjruSEVERESkEJWNhEXXhZJKwV//xMH1DzC7fQ9s+k/YdC+MmATzrwrJ7bxVMHJS3FFLPyihlaFTWgHv+MdQjh2A7WvDc8PW/TP86tPhbskX3wxza2MOVEREREQKVlERTF/KgTnNzK6thTePwL6NsGc97H0yPBIIg/PeHu6sPG8VTFsabkYleUfvigyP8bNh5edgxWfh0NaQ2O58JPTgjprC3PGXwaLJUL0k7khFREREpJCNnAQXfTCUVAoa/gx7N4QE9+mvw1P3QfkYmLMiJLfzrwr/60peUEIrw8sMZiwL5ZqvhGsWtv2I6bt/Ad/+OVRfGHptL7wJRlfHHa2IiIiIFLKiIpj2zlBWfg5OHoX9T4ce3H0b4YVfhv0mzA3J7byrYPaVUDEm3rgLmBJayZ2S8nAt7eLVbH7iMZaPaww9t0/cA+s/Hz4ULroZFl4LZSPijlZERERECt2ICbDkhlDcw7Nu920MPbj1D8Fz34WikpAAz7w8PBZoxqXhUZeSE0poJRbtZWPgktVwycfgyJ5wI6nta+HR26BsFCy+Pgz7mHWlrlcQERERkfiZwaQFoVz6cehohVeehX0b4MAzsPlb8Mz9gIXL6mZeDrMuh5lXwJipcUd/zlKmIPGbtACu+jy8+x54+fchud21Dup/GO42t+g6WLQ6XLegB2GLiIiISD4oKYc57woFoO0kvLoVDm4O/9PWPwTPfSdsGz87JLYzLw09uJMu0COChogSWskfRUXhGoTZV8L7vw57noBdj8GOh+GPa6BiXHg00OLV4U7JJeUxBywikixmNgH4CTAbOAB80N2PZdnva8C1QBGwHviUu3vuIhURSaCyEaEDZs6KsNzZDoe3RwnuZtjzG9j2UNhWMRamLwvJ7YxLwl2Uy0fFF3uCKaGV/FRaGYYdL74e2k+FaxV2rYPnfwH1/xvuNHfB+0LP7awrwvUNIiJyNncBG9z9q2Z2V7R8Z+YOZnYFsBy4KFr1O2AlUJfDOEVEkq+4NH2DqSs+Ga7BPfoSvLIlKs+GZ+DiYEVQ/bZ0cjv1Yph0vi696wfVkOS/0gpY+P5QOlrhpadCcvvir6LnhBGGJk9eCJPPD0M4uqZjzgvXO4iICMD1QG00/yAhSb2zxz4OVABlgAGlQGNuwhMROYeZwcR5odT8Q1jXcjwMU37l2ZDkbvtxuNEUQElFSHKnXpwuVYs0SrEHJbSSLCXlcP57Q+m8Hw7+PgzleO3FUHY+AqfeSO9fNjpKbs8PHx4T5sHE+eFW6xrWISKFp9rdGwDcvcHMqnru4O6bzWwT0EBIaL/l7s/nOE4RkcJQOQ7mXx0KQKoz3Em5YVu67PgpbP1e2F5UClWLuIAqGLEHplwYkt4C/r9WCa0kV3EpzF0ZShd3aG6CIy+mk9wjL8JLdeERQZlGTQnJ7cS56UR33AwYOwMqx6tnV0QSycyeBKZk2XRPP4+fDywCpker1pvZCnd/Osu+twO3A1RXV1NXV/eWYs7U3Nw8JOeJS5LjV+zxSHLskOz48zv2Kih/D8x+D8xKUXGqkdEnXmL0ib2Man6JiSf+AI8/CYBjtFROpXnUHJpHzY3KHNrKx8f8M/RuKOteCa2cW8xgdHUoXRfkd2l7M1y38PpeeH1fev6Fx+HkkdP3LamEsdNgzDQYOz09HTuNkc2H4I1XQ9JbWqnEV0Tyirtf3ds2M2s0s6lR7+xUoCnLbh8A/uDuzdExvwYuA85IaN39AeABgKVLl3ptbe2g46+rq2MozhOXJMev2OOR5Ngh2fEnOvZNm6h9x/lweAd2eDsjDm9nRMN2qvY/k95pZFV4fFD1EqhaDNWLwyV6pZXxBR4ZyrpXQiuFo2xkGJYx5cIzt7Uch6P74I0oWf3bq9H8oXBDqhOHCZeVwTKArdFxxWUhsa0YF6aVXdPxMHJS+CAZVQ2jqkIZOVmPHhKROD0G3Ap8NZquy7LPy8DHzOwrhCHHK4H7cxahiIicnVnofBk7DS64Jr2+5Tg07oTDO6Bhe5h/9jvQ2RodVxQuvatanJHoLgmPFSoqjuVHGSwltCIQEtGuu9Bl09kOJxrgjVf5y5aNLJl7HrQcg1PHw7TleJj/26vnwVr3AAANv0lEQVTQuAtajkJbc/ZzjZgYJbqZyW41jJ6Ssa5aw54lP7hjqc5wQ7ZUJ3gneCqaz5h2re8u3mN7Kr1fZwek2sPfVaq9x3JHmHoK8HCe3qbFpfDOj8RaPQn0VWCtmX2UkLjeBGBmS4E73P024GFgFbCD8E3e/7n7L2KKV0REBqJyXPoxmF06O+DYfmj8CzTtCtPGneHpIVGHDcXl4Z4zky+AqoXRzVYXhUQ3z++0nN/RieSL4lIYNxPGzeS1/a2wtPbsx7S3hOt5m5uguRHebDp9ubkp3M2uuRE6Tp15fFFplNxOhtKR4YZYJRXpaWnF6ctlo9K9w5Xjw6OMunqPS8qGvEqkD6kUdLaFb0M726GzjYqWxjDMPRUldZmJYGZymHlcR2u03BbNt0fb2jKSwLbTE8LuJLG9+7VDyZhPdWSs7wjL3hmmqdTpy55iJWQZbJoHykYroR0gd38duCrL+q3AbdF8J/DxHIcmIiLDpbgEJi0IZckN6fVtb8JrL0DT89H0hXC35Z0PZxxbHo6bfEF0k9X5UZkH5aNz/7NkoYRWZLiUVsL4WaH0xR1aT0RJblRONKaT3jebQnJ86nhIajpOnTntbOv7NaJkd2lHCeweD0UloRSXpOeLSsNQk6KSEHvZqDBMu3xUSBy650eG5dJKunvKMnvkunvWuuaz6dnz7Kf3zvXsrUu1Q6qTaYd2w5bd0Sn66L3ueu1svYeprmnX+Tsy5qNp5nx3IhhNU+091nXNZySh3nlGSJcBbOn7bRowKw7D3otLo/czc740NELFpVEpg9Ix6X2Ky8J7nvk7YNH7X1R02rr9B19mztx54ffDisNwpa75oqKwbMXRuqIexdLHdJXMGLtjKD192YoAi97nXqZWNMQVKiIiUkDKRmYfodh6Ao7sDgnua1F55TnY+SjdPboAo6dmJLhRmbQgDGnO4ShDJbQicTODijGhTFrw1s6RSoUhzi1HoyHQx+Dk0fRw6JZj0HKUU4f2MWrE2O4Ekc52aDsZJXGd6WStoxXaTkBrc9bkLC4LAPYO0cmsOJ1YdSdXGYl9d3JVmk4Cy0ZE82WnJ5Bd60rK0vOZpaSMF3bvZeGiJemkr7fksLi8x7mipLSk/PRzdiWeOXCwro45K2pz8loiIiISs/LR2RPd9paMG6zuhSPRdNfPw/+aEDo97n4lp+EqoRU5FxQVpZPi8bN73W3nQO8o5x4lt82htDaH4SltJ8KHGpalR470fHePWo9zZpO1ty6jF6+ohGd+v5nly5dz2reDZ5zTz+w57E4ae/Qc5tDhE3UsrKnN6WuKiIiIDJnSyvRdk3s6eTQkt28eyfn/WEpoRaR3ZuFa3dKKcNfmmLWXjYGRE+MOQ0REREQyjZgAIy6J5aV1AZKIiIiIiIgkkhJaERERERERSaRBJbRmNsHM1pvZnmg6Pss+7zaz+oxyysxuiLatMbP9GdtqBhOPiIiIiIiIFI7B9tDeBWxw9wXAhmj5NO6+yd1r3L2G8KD2k8ATGbt8tmu7u9cPMh4REREREREpEINNaK8HHozmHwRu6GNfgBuBX7v7yUG+roiIiIiIiBS4wd7luNrdGwDcvcHMqs6y/83AN3qsu9fMvkDUw+vurdkONLPbgdsBqqurqaurG1TgAM3NzUNynrgkOX7FHo8kxw7Jjl+xxyfp8YuIiEjvzprQmtmTwJQsm+4ZyAuZ2VTgQuA3GavvBg4DZcADwJ3Al7Md7+4PRPuwdOlSH9CzNHtRN9BncuaZJMev2OOR5Ngh2fEr9vgkPX4RERHp3VkTWne/urdtZtZoZlOj3tmpQFMfp/og8DN3b884d0M022pmPwA+08+4RUREREREpMAN9hrax4Bbo/lbgXV97HsL8KPMFVESjJkZ4frbnYOMR0RERERERAqEuftbP9hsIrAWmAm8DNzk7kfNbClwh7vfFu03G3gGmOHuqYzjNwKTAQPqo2Oa+/G6rwEH33LgaZOAI0NwnrgkOX7FHo8kxw7Jjl+xx6c/8c9y98m5COZcpba5W5LjV+zxSHLskOz4FXt8hqxtHlRCm3RmttXdl8Ydx1uV5PgVezySHDskO37FHp+kx19okv5+JTl+xR6PJMcOyY5fscdnKOMf7JBjERERERERkVgooRUREREREZFEKvSE9oG4AxikJMev2OOR5Ngh2fEr9vgkPf5Ck/T3K8nxK/Z4JDl2SHb8ij0+QxZ/QV9DKyIiIiIiIslV6D20IiIiIiIiklAFm9Ca2TVm9qKZ7TWzu+KOZyDM7ICZ7TCzejPbGnc8Z2Nm3zezJjPbmbFugpmtN7M90XR8nDH2ppfYv2hmr0b1X29m748zxt6Y2Qwz22Rmz5vZX8zsU9H6vK/7PmJPSt1XmNmzZrYtiv9L0fo5ZrYlqvufmFlZ3LH21Efsa8xsf0bd18Qda2/MrNjM/mxmv4yW877eJVDbnDtqm+Ohtjk+apvjNZxtc0EmtGZWDPw38D5gMXCLmS2ON6oBe7e71yTkdt1rgGt6rLsL2ODuC4AN0XI+WsOZsQN8M6r/Gnd/PMcx9VcH8Gl3XwRcBnwi+j1PQt33Fjsko+5bgVXufjFQA1xjZpcB9xHiXwAcAz4aY4y96S12gM9m1H19fCGe1aeA5zOWk1DvBU9tc86tQW1zHNQ2x0dtc7yGrW0uyIQWuATY6+4vuXsb8GPg+phjOme5+9PA0R6rrwcejOYfBG7IaVD91EvsieDuDe7+p2j+BOFDZBoJqPs+Yk8ED5qjxdKoOLAKeDhan69131vsiWBm04Frge9Gy0YC6l0Atc05pbY5Hmqb46O2OT7D3TYXakI7DXglY/kQCfqDJPwCP2FmfzSz2+MO5i2qdvcGCB+QQFXM8QzUJ81sezTsKe+GBfVkZrOBtwNbSFjd94gdElL30dCaeqAJWA/sA467e0e0S95+7vSM3d276v7eqO6/aWblMYbYl/uBzwGpaHkiCal3UducBxLVPmSRiPahi9rm3FPbHJthbZsLNaG1LOsS8y0HsNzd30EYlvUJM1sRd0AF5tvAPMKQjwbgv+INp29mNgp4BPgXd/9b3PEMRJbYE1P37t7p7jXAdELP06Jsu+U2qv7pGbuZvQ24G1gILAMmAHfGGGJWZnYd0OTuf8xcnWXXvKx3Sfx7pbY5XolpH0Btc1zUNudeLtrmQk1oDwEzMpanA3+NKZYBc/e/RtMm4GeEP8ikaTSzqQDRtCnmePrN3RujD5UU8B3yuP7NrJTQ6PzQ3R+NViei7rPFnqS67+Lux4E6wvVG48ysJNqU9587GbFfEw01c3dvBX5Aftb9cmC1mR0gDFddRfhWOFH1XsDUNscvEe1DNklqH9Q2x09tc04Ne9tcqAntc8CC6O5aZcDNwGMxx9QvZjbSzEZ3zQPvBXb2fVReegy4NZq/FVgXYywD0tXgRD5AntZ/dH3C94Dn3f0bGZvyvu57iz1BdT/ZzMZF85XA1YRrjTYBN0a75WvdZ4v9hYx/tIxwnUve1b273+3u0919NuFzfaO7f4gE1LsAapvzQd63D71JUPugtjkmapvjkYu22dzzsld92Fm4pfj9QDHwfXe/N+aQ+sXM5hK++QUoAR7K99jN7EdALTAJaAT+Hfg5sBaYCbwM3OTueXeDh15iryUMq3HgAPDxrute8omZXQn8FthB+pqFfyVc75LXdd9H7LeQjLq/iHCDg2LCF4dr3f3L0d/vjwnDgv4MfDj6VjVv9BH7RmAyYZhQPXBHxg0q8o6Z1QKfcffrklDvEqhtzh21zfFQ2xwftc3xG662uWATWhEREREREUm2Qh1yLCIiIiIiIgmnhFZEREREREQSSQmtiIiIiIiIJJISWhEREREREUkkJbQiIiIiIiKSSEpoRfKQmXWaWb2Z7TSzn5rZiAEe/10zWzyA/T9iZt8aeKQiIiKFQW2zSH5SQiuSn1rcvcbd3wa0AXf090AzK3b329x91/CFJyIiUnDUNovkISW0Ivnvt8B8ADP7sJk9G31D/D9mVhytbzazL5vZFuByM6szs6XRtlvMbEf0jfJ9XSc1s38ys91m9hSwPGP9TdG+28zs6Zz+pCIiIsmgtlkkTyihFcljZlYCvA/YYWaLgL8Hlrt7DdAJfCjadSSw090vdfffZRx/HnAfsAqoAZaZ2Q1mNhX4EqGxfA+QOQTqC8DfufvFwOph/QFFREQSRm2zSH4piTsAEcmq0szqo/nfAt8DbgfeCTxnZgCVQFO0TyfwSJbzLAPq3P01ADP7IbAi2pa5/ifA+dH6Z4A1ZrYWeHQofygREZEEU9sskoeU0Irkp5bom95uFlrKB9397iz7n3L3zizrrY/X8Kwr3e8ws0uBa4F6M6tx99f7G7iIiMg5Sm2zSB7SkGOR5NgA3GhmVQBmNsHMZp3lmC3ASjObFF3TcwvwVLS+1swmmlkpcFPXAWY2z923uPsXgCPAjOH4YURERM4BaptFYqYeWpGEcPddZvZvwBNmVgS0A58ADvZxTIOZ3Q1sInwj/Li7rwMwsy8Cm4EG4E9AcXTY181sQbT/BmDb8PxEIiIiyaa2WSR+5p51ZIOIiIiIiIhIXtOQYxEREREREUkkJbQiIiIiIiKSSEpoRUREREREJJGU0IqIiIiIiEgiKaEVERERERGRRFJCKyIiIiIiIomkhFZEREREREQSSQmtiIiIiIiIJNL/A16PC8p8+88IAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# PLOT THE IRS WITH CI\n", "\n", "plt.figure(figsize=(16,10))\n", "plt.subplot(221)\n", "plt.plot(np.exp(np.cumsum(irf_x[15]))-1)\n", "plt.plot(np.exp(np.cumsum(impxci[:,0,0]))-1)\n", "plt.plot(np.exp(np.cumsum(impxci[:,0,1]))-1)\n", "plt.xlabel('Periods')\n", "plt.title('IP')\n", "plt.grid()\n", "plt.subplot(222)\n", "plt.plot(np.exp(np.cumsum(irf_x[107]))-1)\n", "plt.plot(np.exp(np.cumsum(impxci[:,1,0]))-1)\n", "plt.plot(np.exp(np.cumsum(impxci[:,1,1]))-1)\n", "plt.xlabel('Periods')\n", "plt.title('CPI')\n", "plt.grid()\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.18" } }, "nbformat": 4, "nbformat_minor": 2 }