{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "オリジナルの作成:2015/06/27\n", "\n", "ここで紹介したSageワークシートは、以下のURLからダウンロードできます。\n", "\n", "- http://www15191ue.sakura.ne.jp:8000/home/pub/52/\n", "\n", "また、Sageのサーバを公開しているサイト( http://www15191ue.sakura.ne.jp:8000/ )にユーザIDを作成することで、ダウンロードしたワークシートをアップロードし、実行したり、変更していろいろ動きを試すことができます。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 0M-ソフトウェアラジオその1(AM波)\n", "## ソフトウェアラジオ(Software Design Radio)AMラジオ編\n", "トランジスタ技術別冊トラ技Jr 2015/3.4号に紹介されている「第1回パソコンでAMラジオ放送を聴く」をMacで試してみました。\n", "\n", "### ブレッドボードで作ったAMラジオ\n", "ソフトウェアラジオ(Software Design Radio)AMラジオ編は、サポートページでより詳しく説明されています。\n", "\n", "- [第1回 パソコンでAMラジオ放送を聴く(補足資料)](http://www.mybook-pub-site.sakura.ne.jp/TG_Jr/Appendix_2015_2_10.pdf)\n", "\n", "私の作成した「ブレッドボードで作ったAMラジオ」は、以下の様な物です。\n", "\n", "\n", "\n", "\n", "### Mac用ソフトウェアラジオ・アプリケーション\n", "第1回パソコンでAMラジオ放送を聴く」で紹介されているソフトウェアラジオのPC用アプリケーションは、 SDRadio.exe ver.0.99というWindows用のアプリです。\n", "\n", "私は、Mac OSXを使っているので、Mac用のソフトウェアラジオ・アプリケーションを探しました。 今回「ブレッドボードで作ったAMラジオ」の再生用に使ったのは、 \n", "[Dream 1.11](http://dl2sdr.homepage.t-online.de/)\n", "です。\n", "\n", "Dreamを起動し、入力をマイクとし、DemodulationをAMにし、15kHzあたりのピークをクリックすると赤い線がそこに移動します。 次にFilter Bandwidthを5kHz程度にするとラジオの放送が聞こえてきます。\n", "\n", "\n", "\n", "私の住む高岡市で最も電波の強い放送局は北日本放送(738kHz)です。 Dreamで受信した北日本放送は、以下の様な音でした。音声は小さいですがアナウンサーの声が聞き取れます。\n", "\n", "「ブレッドボードで作ったAMラジオ」で受信した放送の一部\n", "- [KNB_radio.wav](data/KNB_radio.wav)\n", "\n", "### 「ブレッドボードで作ったAMラジオ」の構成\n", "「ブレッドボードで作ったAMラジオ」の構成を回路をトラ技Jの図1から引用します。\n", "\n", "\n", "\n", "ブレッドボードで処理しているのは、同調・講習は増幅、局部発振、ミキサの3つの機能だけです。 どうしてこんな単純なもので、ソフトウェアラジオが聞こえるのか不思議ですね。\n", "\n", "### 「ブレッドボードで作ったAMラジオ」の回路\n", "「ブレッドボードで作ったAMラジオ」の回路をトラ技Jの図7から引用します。\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 「ブレッドボードで作ったAMラジオ」の仕組み\n", "第1回 パソコンでAMラジオ放送を聴く(補足資料)の4.1に周波数変換の原理について説明があります。\n", "\n", "ミキサの原理は、放送波を$v_{rin} = sin(2 \\pi f_r t)$、局部発振の出力を$v_{LO} = sin(2 \\pi f_{LO}t)$とすると、\n", "ミキサーからでる信号は、以下の様になります。\n", "\n", "$$\n", "\\begin{eqnarray}\n", "v_{mix} & = & sin(2 \\pi f_r t) \\times sin(2 \\pi f_{LO} t) \\\\\n", "& = & \\frac{1}{2} \\left \\{ -cos(2\\pi(f_r + f_{LO})t) + cos(2\\pi(f_r - f_{LO})t) \\right \\}\n", "\\end{eqnarray}\n", "$$ \n", " \n", "つまり、$f_r - f_{LO}$の周波数を持つ低い波と$f_r + f_{LO}$の周波数を持つ高い波の2つの信号に分けることができます。\n", "ローパスフィルターを使って高い波を取り除くと、$f_r - f_{LO}$の低い周波数帯で放送波を扱うことができます。\n", "これが、ミキサによる周波数変換のマジックです。\n", "\n", "ミキサの原理を第1回 パソコンでAMラジオ放送を聴く(補足資料)から図A.14を引用します。\n", "\n", "\n", "\n", "AM波では、バンド幅を15kHzとしているので、北日本放送(738kHz)に対する局部発振周波数は、753kHzになります。 「ブレッドボードで作ったAMラジオ」の発振モジュール(秋月のLTC1799)の周波数をみてみると753kHzになっています。\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sageを使ってAM変調試す\n", "実際にAM放送の信号が局部発振波(ここではsin波)を使ったミキサによって音声(ここでは2kHzのsin波)が取り出される様子を Sageを使って見てみましょう。\n", "\n", "### 搬送波\n", "周波数が100kHz(北日本放送ではこれが738kHzです)で振幅1のsin波をVc(t)を定義し、Tend(0.002秒)まで出力してみます。" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t= var('t')\n", "Tend = 0.002\n", "fc = 100000 # 100kHz\n", "Vcm = 1.0\n", "Vc(t) = Vcm*sin(2*pi*fc*t)\n", "plot(Vc(t), [t, 0, Tend], figsize=4)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### 音声として2kHzのcos波\n", "次に音声の代わりに2kHzのcos波をVs(t)と定義し、プロットします。" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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apewXzyi32QAFkJEjlWk/IYCMDPp7GUWHDrS6JyPD9ceqraUev3SXawSmDvyj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\nU6cwdepUSCmBGhoaAACenp4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NTY38v7QCmmtTq9Uq3n333SvvceQ7/Nxzz4l+/foJHx8f\n0aVLFzFixAjx4Ycf2lc3IThlA2OMmYn+7p8YY4w5hQM/Y4yZDAd+xhgzGQ78jDFmMhz4GWPMZDjw\nM8aYyXDgZ4wxk+HAzxhjJsOBnzHGTIYDP2OMmQwHfsYYM5n/A52+vmYqPSKdAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fs = 2000 # 2kHz\n", "Vsm = 0.25\n", "Vs(t) = Vsm*cos(2*pi*fs*t)+0.75\n", "plot(Vs(t), [t, 0, Tend], figsize=4, ymin=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### AM変調\n", "WikipediaによるとAM変調は、以下の様に定義されています。\n", "\n", "$$\n", "V_{am}=(V_s+V_{cm})sin 2\\pi f_c t\n", "$$\n", "定義にそってAM変調された波をVam(t)を定義し、プロットします。 AM変調では、上下のエンベロープ(信号の端の形)に音声信号が現れます。" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Vam(t) = (Vs(t) + Vcm)*sin(2*pi*fc*t)\n", "plot(Vam(t), [t, 0, Tend], figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 局部発振とのミキサ\n", "搬送波+15kHzの局部発振のsin波とVam(t)と掛け合わせると、以下の様に15kHzの波で音声波が 見えてきます。\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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8zfPPW5FiVT8zgE2HKKtpRLcJakcsShiRMMrK9AgCR+HII+XIDUMLw79qlfXm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\n9msN0eA2/EOHDkV5eTn27duX9fNXhQd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2/s2ECRNwZcVMYSqVwttvv42TKgLN7927F/37\n98eGDRswe/ZsX8NfVlaGOnXqYOvWrb+FbACA776zDisxPQaDIZls3px9QLpBX0iGf/v27dhk7zwA\nUFxcjOrVq2Pv3r0YOHAgVq9ejffffx/16tXzlWEb/jPOOAP7ubpfgwcPxuCwQ3cNBoPBwAXJ8Hth\nG/2VK1di9uzZqB/yyvfr8RsMBoMhHrh8/Pv27cOAAQOwePFivPXWW/j1119/GxHUr18fVc3Mo8Fg\nMGgHV49/zZo1aOHacZVOp5FKpTB79mx09Qgyb3r8BoPBoBZuVw+VdDqNbdu2obCwECkzk2swGAyx\nE7vhNxgMBoNatIjOaTAYDIb4MIbfYDAY8gxj+A0GgyHPMIbfYDAY8gxj+A0GgyHPMIbfYDAY8gxj\n+A0GgyHPMIbfYDAY8gxj+A0GgyHPMIbfYDAY8gxj+A0GgyHP+H//35PvPN+z+AAAAABJRU5ErkJg\ngg==\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "band = 15000 # 15kHz\n", "Vcros(t) = Vam(t)*sin(2*pi*(fc+band)*t)\n", "plot(Vcros(t), [t, 0, Tend], figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### AM波の復調\n", "AM変調の復調には、ミキサされた信号を絶対値absを使って片方向に揃えます。 これで、音声の2kHzの形がぼんやり見えてきます。" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(abs(Vcros(t)), [t, 0, Tend], figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ローパスフィルターを掛ける\n", "scipyを使ってローパスフィルター(butter_lowpass_filter関数)を定義します。" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib/sagemath/local/lib/python2.7/site-packages/traitlets/traitlets.py:770: DeprecationWarning: A parent of InlineBackend._config_changed has adopted the new @observe(change) API\n", " clsname, change_or_name), DeprecationWarning)\n" ] } ], "source": [ "# scipyを使う準備\n", "import numpy as np\n", "from scipy.signal import butter, lfilter, freqz\n", "import matplotlib.pyplot as plt\n", "import seaborn\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# ローパスフィルターを定義\n", "def butter_lowpass(cutoff, fs, order=5):\n", " nyq = 0.5 * fs\n", " normal_cutoff = cutoff / nyq\n", " b, a = butter(order, normal_cutoff, btype='low', analog=False)\n", " return b, a\n", "\n", "def butter_lowpass_filter(data, cutoff, fs, order=5):\n", " b, a = butter_lowpass(cutoff, fs, order=order)\n", " y = lfilter(b, a, data)\n", " return y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### サンプリングとフィルタリング\n", "サンプリングレートは、96kHzとし、ローパスフィルターのカットオフ周波数を4kHzとしました。" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# フィルターの仕様を決定\n", "order = 6\n", "fs = 96000.0 # サンプリングレート( 96kHz)\n", "cutoff = 4000.0 # カットオフ周波数( 4kHz)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# scipyを使ってローパスフィルターを掛けるため、96kHzでサンプリング\n", "T = Tend\n", "n = int(T*fs)\n", "t = np.linspace(0, T, n, endpoint=False)\n", "# データを作成\n", "data = [abs(Vcros(t_i)).n() for t_i in t]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ローパスフィルタを掛けた結果yとサンプリングデータdataをプロットします。 緑のフィルター後の波形に2kHzの波が取り出されています。" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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fuDBE27ZQXi6/3+719+0rjz/8MMQxx8T4zcgIVa/2ds9nYWFdPmfOrH2cSF7/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\nl1FcEq3xCIx7AFmFhuwoAqvxafQIMjMhL4/q9Ss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iWQl6RaCXEwxCICPCyl1yH/ec3Ue6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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# dataにローパスフィルターを掛けて、オリジナルデータとフィルター後のデータを表示\n", "y = butter_lowpass_filter(data, cutoff, fs, order)\n", "\n", "plt.figure()\n", "plt.plot(t, data, 'b-', label='data')\n", "plt.plot(t, y, 'g-', linewidth=2, label='filtered data')\n", "plt.xlabel('Time [sec]')\n", "plt.grid()\n", "plt.legend()\n", "plt.savefig('data/LPF.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## スイッチによる方形波\n", "局発のスイッチによる方形波をpiecewise使って以下の様に定義します。これから求まるフーリェ級数から、 奇数倍の周波数のsin波の足し合わせになっていることがわかります。" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "verbose 0 (3757: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 100 points.\n", "verbose 0 (3757: plot.py, generate_plot_points) Last error message: 'point 0.990150753769 is not in the domain'\n" ] }, { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 方形波が周波数が奇数倍のsin波を足し合わせたもの\n", "# フーリェ級数の係数を求めます。\n", "g = piecewise([[(-1/2,0), lambda x: 1], [(0, 1/2),lambda x:0]])\n", "plot(g, figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$v_{LO}$は、以下の様になります。\n", "\n", "$$\n", "v_{LO} = \\frac{1}{2} + \\frac{2 \\,\n", "\\sin\\left(2 \\, \\pi x\\right)}{\\pi} + \\frac{2 \\, \\sin\\left(6 \\, \\pi x\\right)}{3 \\, \\pi} + ...\n", "$$ \n", "\n", "次数を変えて、フーリェ級数で表される方形波をみてみましょう。nを31にすると定義の波に近くなりますが、\n", "値が急に変わる不連続点では急な盛り上がりがでます。これはギブスの現象と呼ばれるものです。" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-2/5*sin(10*pi*x)/pi - 2/3*sin(6*pi*x)/pi - 2*sin(2*pi*x)/pi + 1/2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# フーリェ級数\n", "show(g.fourier_series_partial_sum(7,1/2))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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EN2F0h9EATOg8gasXXs3AFUNp5PTjxqXbYZbKsEuG8ei6R4mrH0dD/4b0iOqO\n4a9NtAyKYafyB9uOh+Bn9CMhLEFTYpKd6diCIETnj5/RDx+DD4XOQo/9jS6Y7CNdlerXq85zzz1H\n165d6dGjB9999x1ffvklo0eP9uhn1CQ2pxAKJdxHYQEcPH1Qa5IXGRRJo8BGfJn4LY7gw3Ss1ws2\nb6aeIYArm13JvK3zaOjfkH5x/WDtWqJSMrm7+VCO5xxnUtdJWkFRVL0o5t84n/YR7flsyCL875wI\nH3zA6Gv9iPhtGS0zJ7Fk6BJ0v/4KGzbQ5cEX+W7EdzzX9znm3zRfW/MVsVewYtgK5lw9hzn3rtBS\n8sZ3Gs/4mBfhtyeZN/wJEZgLDeWhOz/g+hbXc0vCLUzrNU07zpSeUzDpTTQKbMRd/r1h6VIMegND\n2wzlnS3vkFOYwy1tboE//iA+tAXkNWLZnqUcyT5Ct6hu2rmxOW0cD/PF4q8SZhIPfn+jv0f9sZLK\nKRFTcPiQHgAHA8UDLb5BSaGwNXUjQZmXYUIPGzcyoOUAdqbuZPX+1YzpMEYUmS1ezNQGA8i15+Jn\n9OPB7kVtSV+79jX6xPRhYpeJjJjwJlgsGJcs4tHej6Lfcj9vX/053ZtcJiYWXn45H477hqevfJqf\nRv1Es/rNAPFc+nb4tzx5+ZOsG72OsPsegY8/xnD8BItu+Zww891ctn8VPYOPwrJlREx6lHkD5tE+\noj2fDv5U+65XNbuKPjF9OJR5iKda3InPvgOwdSu3XnIrhc5C3tr8FoNbD8Zw6DAcOUK8zxWk+/7F\nb+bf6NqkK0a9Eb1OT/MGzTmQdZi0MD8iVGEu+Bp9NaXRI1R3Sk9dn7w2e/Zs9cMPP1Tnzp2rZlQ6\naLV6uKcsbTi4QVVVVa33lEF95f7Oaod3O6j3rrpX2++6z64T05ie1qk7F64Sk5q2b1fXHVinRr0W\npX60/SOx47Bhqtqhg+pwOtTE1MSiSW7lceSIGO78/PPqG2+I/x41O8QIrG7dqj6mbd48VdXpVHXH\nDrVvX9cEraS94oAvvljpW5MzktXUnFQxnctgUNWTJ9UjWUfUNm+3Ue///n6xU9u2qjpunNrwniEq\nT6ByD+r6jetVnU6nTn9uuso9qO+99aDKM6hf/TJfVVVVbf5/zdXpP02Xk9dqiOs+u069demtqqqq\n6rsfTFQNM1E//f1tlWdQc2w5qqqq6up9q7WJYl0enqGqnTqp6qhRqs1hU/t92k+9/KPLVWuhtWgq\n2YYNakpyX4BOAAAgAElEQVRminoy92TlH37bbaoaHa2ePm5VAwNd88gXLjy7MW3Z2WLg8ujR6urV\n4q3r1hUdWy0oqPCteYV56s4TO1XFbhcj2aZMUVVVVR/58RE14e0EdX/Gfu36fvmDn7RzMP2n6dox\nbl58s3rDohvU/42rp17xZJSqqqr65l9vqn6z/aq2/ipwwVgKksop7j4CCCvQkx6s58DpA5qlAHBr\nG9H5znDoetrd2g8CA2HNGvo178fRqUcZ12mcGF6yciWMHIlBb6B9RHsM+koK+6KjRd727Nnc1fM/\nAgJg5/9eErnFr79exS5liDmz7dphvW00f/1s5bGHHejumSiGA02eXOlb4xvGExEUUdTZb8UKoutF\ns/u+3bw14C1Rcv3ffzBgAF0ChsJx4D24ps816HQ6Xnn6FXgP3lwm2r42KRCeU3+jv0f9sZLKsSt2\njHpx7hvlKDj1sDU7iYjACM1deHXc1fgZxHU+pNUIkZG2Zg0+OiPrRq/jt3G/CQ180SLRD/7KK2ka\n0pTwwPDKP/z55yE9nfpzHuWee+Dr/0tBmfwQDBtWtqNuRQQHw6uvwsKF/PLQN/TsCVdnfiX6aLzw\ngiiaq4AAUwAdIjugMxrFZy5dCk4nL1/zMnvu20OLhi1EkWa3btzS70qwhgIw9JKh2jHiG8Rz4PQB\n0uoZiMgXj++L1n0kqZzi7iOAqCyVLX6nyC3MpVVoUdvh8Z3Gc1nKYrqf+AR9gGu04TfflDzY55+L\nwrf//a/qC3j2WWjZksCb+rIx+jZu/PNJciY/Bb17V/0YPj6wcCG6QwfZ5tOTW9+8UnTc+/RTUXBX\nFcLCRFFS6dmF338v0hKvvZYRlw6HrUvYlXIYp9Op/Yt6NQr/28WDp4mrEM/H4CNy4iU1gt1px2QQ\nSSHhmeJB9ufRjeKB6MLX6MvbHbbAwp8Y3LuNqLZPTxeV8m4KCkSP6pEjS3YRrYyWLYUS8/bbPP/v\nQH6y9iLLGSwKLs+GsWM52fsWZu0bzjK/kehG3iHaa9xxR9WP8b//iY4Ev/1WtM1mEwWg11xDfDMT\n9Vb8xv9039K1SVdtlxYNW3Do9CGOBjiIyBE9tn2NviiqoqXrVhcpFGoJxbOPcDppcdLBz+pBAFo2\nbKntZ9AbOLl+BD3bizYCDBok+gYfdVVOqqoYCzVwoNDQq0pQkGgBef31tPY5xBP+c3m88OzbkPyR\n04Fezt+p36oROqNBHNM9MrOq3H236KC3c2fRtq++EsV29erRtasO/r2djAOxJd7WvEFztqYnolcg\n4rQQBJ7WsiSV41AcRZZCpvgbbD+xnTZhbUrsl7X/UvxP9Bedonv2FMpA8RkXK1aIMX3jx5/dAiZN\nggUL8D2dxqnWPelu/4OTztCzOoSKjhF8wYqI+2hy+j+47z6haJ1NXLR7dzFM6LNiRXBr1oi237ff\njk4HXWMvIX9nydmjLRq2wK7Y2eubQ1y6K03dIBRFT13HUijUEtzuI1+jL5w+TUsxEgCDzlDCfWSx\niD5cXd3KxcCB4oH+3nvi959+ElWbEyee/SIiImDhQow7tlJv5kO8/4HuTG2NSqCqojhU16kTEYk/\nCS3p6qvPfh2DBwuXlrsf8r59oqJ17FhA9EHz9y812hC07Jb4LD0+p0TBkI/Bh0JFCoWawq7YMemF\npdDYUhQcbR3WusR+iYlioI7BgLAAx44VzRHz88WMgjlzhFup+HCeqjJ+PPz9N1F/LiPNFK21S6oq\n334LG/70pcFHr6HbsUO4k6pq6brR6WDCBCFMjh0T2z76SEygu+QSQHSy37Gj5Nvc1zBAy6MiQcLH\nIKYLeirYfFEKBZvNxrhx42jfvj0mk4khQ4aU2Sc1NZU77riDhIQEDAYDU89mTNJ5wO0+8jP6gcXC\npa6hVVH1ojSXEhQ9CLWGsCEh4iZ4+23RofGhh0TjuzP2066cBx4QhsZ991V9Bu7y5aLN0iuvVN3i\nLxejUYyG++wz0Rb1sceEwBo6VHu5Q4ey/fO6NhaSsk2un5jtiLQUahqH4tCEQj1LDv6KiGX1atqr\nxH6JidCxY7ENEyeKWNjLL4tmWbt3V6lJXWU0bCgunbfeOmNndg2bTXRBve460TeyWtx7r4hR3Hef\niCWsXFmiG3DnziJUdrrYpM3YkCLrt2NyLiiKdv+7nxHV5aIUCk6nk4CAACZPnsw1xYdeF8Nms9Go\nUSOeeuopOpa4+i5MSriPLBauPQADGl/B2zeU7Ae8c6cwDIpP6GTmTHHxtWsnppLNm3d2pm45BAYK\nObN2LXz55Zn3T08X3YgHDRIhgWpzzz2icZl7bsM775TQ1tq3F6N/i3P7pbdzVbOrmHK0qZgdQVmh\nIMdxehe7syjQTEYGb2f15tY2t2qpwwCFheKZ36FDsTe2aAFPPCF6bE2dKpQb1wCa6jBtmuiuMGGC\nMEDOxDPPiLkMZ5NfUSEhIaLT5HffielSV15ZIi7hKrMqYS2YDCbmXD2Hu+v3o2mmCjk5mqXgKeXm\ngile69u3L+3bt8fPz48PP/wQHx8f7rnnHp5++umzPlZAQADvvPMOAH/88QdZWVll9omNjWWuy/1Q\nG4raSriP0tPxdcL3Q1YIX2sx/v1XmN0lNPHQUDEE/JtvxMVXQmKcOzfdJJKB7r9fuH1d4wrKoKpC\nKXI6Yf788vc5a4xGEVx2D++97LISL7drBx9/LOLp7mL3sIAwfh7zMyy5oUJLQRaveReH4tACzWRk\nMN7/GsYPK+m/SUoSf7cSQgGEZdCli/Ap3XijR9bj4yM8q336iG7tTzxR8b5//ikMleee0zw81Wfw\nYDHLJClJ3EzFqulbtRLdIXbsKOllffzyx6GwG7AeTp3SYgqech95RyhYreV3vCtOQoL4xsVYuHAh\nU6dOZfPmzWzcuJGxY8fSp08f+vXrx4ABA/j9998rPFyzZs3YVVo1vIgo7T5Cp4MGDcrst2uXaHBa\nhoiIc4sjnIH33hPxi1tuEbN1goLK7vPssyIuuHy5aDbpMfz8YPjwcl9q1048WPbuLWfYe8OGWuDd\nx+BDlq2s0iDxDsVTUjl1SvwtSpGYKH6W6o8prvlBgzy+pt69Rf3aU0+Ja2XgwLL7HDokrvHeveHR\nRz28gK5diwUBizAYxDlwn48SuM9bRga+kZ51H3lHKLjbpFbGtm1lGiS5W2cDxMfH8/bbb7N+/Xr6\n9etX7d5HtR23+8ikNwmhEBrqisIV4XCIsbBnm5BRHUJDhffmiiuEEbJ8uYgBu9fz7LNCs3r++aIS\ng5rA3R9x165yhEJoqOZEljGFmsXudAWa7XYxTCm0bObPzp0iMacmDbZZs8S9M2SI8Oi4cha09Qwa\nJNbz1VdnmADnYdq2LRtsBorO26lT+EQJb8GF7T5yt0k90z6lOFPr7LqMzWHD1+Ar2oFYLGXcRiDm\n5RQWFj0Qa4qOHUXyz8CBwqwePlwYMStWiKlqc+accc6Ox2nYUATCd+0Skz3LvFhBTEHiXTT3kTt6\nWo5QKBNkrgEMBlFLds89YmDahx8KRScpSbj8L71U/CzntvMqbduK4T2KUsol7LYUTp3C1xAFXOju\no3Nsk3qm1tl13X3krmbWLIVSuMe/ltGMa4CuXUVw8KWXYNUqMeWqZ08RhPZ0x9yq0q5d2WAzIM7d\nqVOgqlIo1DCa+8gllMtzH/33nyhFqWmMRvjgA7j5ZhH7+vxzaNxYBJUnThTxh5qmbVuRhXvoUKlQ\nYGCgCJadOuXx7KMLJtB8JqT7qEDLMuD06XJvpl27ROgg/AzV/t6ifn1R6X+2ed/eol070X2gDA0b\nitxCq1UKhRpGS0l1C4VSyk1mJqSmilqT84E7bOGF0MU54Q5o//dfKaGg04nr+NSpizf76Eycrfto\nz5492Gw2Tp06RW5uLomuaE2HYikNiYmJqKpKbm4u6enpJCYm4uPjQ5vzdUVWgkNxFAmFzEwxs7gU\nu3bVvOvoQqZdO1FXlJ1dyj9d3B9r8PFsh0lJpWgpqeki+6u0UNizR/z0WHZPLScqSly7//1XTgA8\nNFQEmmtF9tE54OnW2QMGDCAlJUX7vVOnTuh0OpzFkpHd2wC2b9/O4sWLiY2N5eDBgx5diycokd+d\nmSnU8lL8+69IE5UI2rYVP/fuLZWxWswfKy2FmsWuuHofuS2FUhl0u3cLJfhcCpUvRnQ6cR3v3l3O\niy5Lwe0+uugshQ0bNpTZ9vXXX5/z8Q4dOnTGfdzxitpAifzucoSCzSaCuhegkXPeaO3qnJCUVEoo\nuLXTjAwpFGoYrffRqVOioLKUo37PHmjeXLQpkQjatq0gb6eU+0hWNNcxSuR3lyMUDhwQGQrlzb6u\nqwQFifTYMiUzxXK8ZUVzzaGoCoqqFMUUykmW2L1bKjaladtWCMsyFdelhcLF5j6SVI6mYTkckJNT\nxux2P/haty7nzXWYhIRyhEJIiLDLMzPxiZIVzTWFu7WzlpJaTvHlnj1w2201vbILm7ZtRafwQ4dE\ntw8Nl1Aw6ES9kmydXcfQsjbcLTtKWQp794pnXaNG52FxFzDlCgW9XrgusrKk+6gGcc+tMOqN4joO\nCSnxel6eaAAng8wlcZ+PMnGFkBDIykKn02HSm7ArnpkLclEKhX379nH11VcTGRmJv78/8fHxzJgx\nA4ejSJLu3r2boUOHEhcXh16v58033zyPKz4zWqA5M1NsKEcoJCR4oEnXRUZCgijqc5RWolw3lBQK\nNYdmKbiVm1JCYe9e8VO6j0rSpIkoS9i/v9QLrmsYhPXlqWFRF6X7yGQyMWbMGDp37kz9+vVJTEzk\nrrvuQlVVZs+eDYDVaiU+Pp5hw4YxZcqU87ziM+NQXYHmCoRCUpJ0HZVHQoLoqHDokBi8pRESItxH\nhjicqhOnUoUWmZJq4dZkNUuhVGNGtyYshUJJ3NlY+/aVeiEkRPSZs9s9ailcMELBk11S4+LiiIuL\n035v2rQpd9xxR4mK6K5du9LV1YRq+vTp1f8CXkaLKZQjFFRVaFnlNfKq67gD70lJpYRC/fqapQB4\n7IaSVIxbkzUZyrcUkpKEVixDOmWpUCgAZGVd+JaC1W4lyVJ5l9SEsAQCTDXTJTU5OZk1a9YwdOjQ\ncl+vDWjuI3fPmGJCIT1dyAqZeVSWJk1EFlJSkmhfoFHMfQSey/GWVMyZ3Ef798v6hIpo1UqMMy9B\nMaFg1BsvbEshyZJEl/cr75K6bcI2Ojf2bpfU3r17s337dgoLC5kwYQKzqjmp6XyiBZozM4U9WeyG\nkplHFaPTVZKBdOxYkaXgIS1LUjFl3EelhEJy8vnrk3Wh06oVHD8ueopp7emLWwp6k8eyj7wiFBLC\nEtg2ofIuqQlh3u+S+uWXX5KTk0NiYiKPPPIIr7zyCo888shZH+dCQKtTyMwU9nWxlol794pfS6Sr\nSTQSEoraJ2iEhMDu3dpoSNnqwvtoloLOINKqiwkFVRWWwu23n6/VXdi4Laj9+4smstUq91GAKaCM\nFVAVPN0lNSpKtJRNSEjA4XAwYcIEHn74YY+31KgJSlgK5WQexcWBr28Fb67jtGoFa9aU2uhyH7mr\nxN0PrOHDh2M0GhkxYgQjyvTcllQHLSW1oFBIgWJC4eRJISekYlM+7njY3r0VCIWLMdB8JqrbJdXp\ndOJwOFBVtdYKhQBTQLlCQWYeVU6LFqLbeAmPhSv7yG0puIWCLF7zHpqlYHVZZcWEQnKy+FkiGUCi\n0aCB6H5cIthcmywFb3A27qPFixdjMplo164dvr6+bNmyhSeeeILhw4ejd7ld7HY7u3fvRlVVCgsL\nOXbsGImJiQQFBRHvoRnGnqREoLmUUNi/HwYMOE8LqwW4tc8DB4r5rOvXh+xsjO5qUNUz/lhJxWgx\nBatLuSsmFNw5+BfgrXfBUCYDycdHNInKysLoe4EHms8FT2rvRqORl156if3796OqKrGxsTz44IM8\n9NBD2j7Hjx8v0SX11Vdf5dVXX+XKK68stznf+abIfZRRQig4neUM4JCUwH1uSgQyQ0LA6cRUKISB\np4J0korRUlLzxGjZ0pZCVFSZse2SYrRqVTRIS8PtBo28CC0FT3ZJHTZsGMOGDat0n9jY2FrXJbW8\nop8jR0Rx1sUuFN555x1effVVUlNT6dChA2+99RaXlWh9WpI33niD+fPnk5KSQlhYGL6+Q0lKegFw\nBV5cDySjVTygZPaR99HcR3nlWwrSdVQ5rVuLGdGqWqxzgdsNGmXymLV7Uba5uBjRso9yckTfHhcH\nDoifF3OAbunSpUybNo1Zs2axY8cOOnTowHXXXYfFYil3/8WLF/P4448za9YskpKS+Oijj1CUpSxb\n9mTRTq4HksklFKSl4H0091GOVWwoZSlczNewJ2jZUuiE6enFNrotBb3nLAUpFGoJmvuoHKGg10Ns\n7HlcnJeZO3cuEydOZPTo0SQkJDB//nwCAgL46KOPyt1/06ZN9OnTh9tvv52YmBj69+9P8+YjSEnZ\nXLST21Jwaa1SKHgfzVLItYLBoPmK3Omo0lKoHLc3oMQMsGJZdLIhXh1DCzTn5pYRCjEx52eoeE1g\nt9vZtm0b/fr107bpdDr69+/Ppk2byn1Pr1692LZtG1u2bAHg4MGDZGSsRlVvLNrJFZcxubRWKRS8\nj5aSmpNX1L4cmY5aVdyde8oTCka98eKLKUgqR4sp5OQUK2kUQuFijidYLBacTicREREltkdERLDX\n3VazFCNGjMBisdCnTx9UVcXpdHLVVfewYcN0rFaXguq2FHKFUJAxBe+jWQrZeTId9RyoVw/CwsoR\nCikpmPQR0lKoazgUh6gELSgoYylczEKhIiqrN/nll1+YM2cO8+fPZ8eOHXz11Vf8998qYHbRDRUU\nBHq9cGUgLYWawP3QMmXnynTUcyQ+vhL3kbQU6hZ2xY7R4cqWclkKqiqEwsVceBsWFobBYCAtLa3E\n9pMnT5axHtzMnDmT0aNHM27cOADatm3L0aO53H//RJKTn+LSSxGui3r1hCuDojoFd0VzcWR1s2fQ\n3EdZOSVaocp01KrTvHlRcglQItB8Qfc+kngeh+LA5BYKLkvBYhHepItZwzKZTHTp0oX169cz0NUb\nXFVV1q9fz4MPPljue6xWq1ak6KZBAz2gkpysAi4LIyREuDJ8ZEVzTaC5j7JyZDrqOdK8ealuqV4I\nNEuhUEuwO+0Y7a5BMC6h4NYYLmahADB16lTGjBlDly5d6NatG3PnzsVqtTJ27FgARo8eTXR0NHPm\nzAHg5ptvZu7cuXTs2JHu3buzf/9+nn56JvXrD+LAgWIup+BgEVNoKGMKNYGWkpqVC7HNtO3JycX6\n+UgqJT4ejh0TXmQ/P4RQyM/HqOql+6iu4VAcGAtdQsHlPqorQmHYsGFYLBZmzpxJWloaHTt2ZO3a\ntYSHhwNw9OjREi6fGTNmoNfrmTFjBseOHSM8PJyBAwdy+PBsLagJFLmPGsqYQk3gUBzo0GHIyi5h\nKZjNMGTIeVxYLaJ5c+E2Nptd/c5cVq3JqV54lsKeMr2JL25q+vs6FAemciyF8PASceeLlkmTJjFp\n0qRyXytdDe8WCO7ZHG6mT4dly4ptCA7G5I4pSKHgdbS06mKdCfPyICPj4q6z8STNm4ufBw64hILr\n5jc51QvHUggLCyMgIICRI0d6Yj21Cj8/P4Jr6IlsV+wYXX16ilsKF7uV4Eni44WGVVjoqusIDsaY\nJcabSqHgfRyKa854dram4ZrN4jUpFKpGkybi2tUykNxCwXEBWQoxMTHs2bMHi8VCVlYWq1atwmQy\n4XOxVlMVIygoiMDAQGw27w9ocSgOTDbXH72YpSCFQtWJiwNFEf2i4uOB4GAMR4+iQydjCjWAXRED\n5osXYEqhcHYYDOI6LisUlAsr+ygmJoaYmBjy8vI4dOgQ2dnZnjhsrSAnJweAevXq4eulKTeqqoqY\ngs0hrgo/P0AIhWKFvpIz4K4IPXy4SCiQk4NRb5SWQg2guY/sds3aNZvFJd2kyXleXC2iRFqqWyjY\nlQvHfVScwMBAbr/99hrRnC80fH19CQwM9MqxnaqIJRhtheJm0unIy4PUVGkpnA1Nm4ryhEOHXBtc\nQsFkMGnnWOI9tAJMKGEpREeDUaa8VJnmzeHXX12/uM6j0e64cNxHpQkMDPTaw7GuouV3F9i1i+Dw\nYfGaO/AkOTO+vqJIyn3uilsK7htKjuP0HnbFjhGXUChmKUjX0dkRHw8ff+xqoe22FAqdF6alIPEO\nJWbbFruZQN5QZ0uzZmWFgkkfIovXagCH4sDk7qxT7DqW1u7Z0bw5WK2ikWBEhBH8/DAVOrAjex/V\nGdwPLGO+rYTZLX2xZ09cXCn3kcPh0Q6TkoqxO+2YKOs+korN2VE8LRUQqdU2h5ynUJfQ3EelhEJ0\ntBAMkqpTxlIATBhwKjKm4G3sih2j6qooDwqisBCOH5dC4WxxC4XiGUimArvHkiWkUKgFFA08L9DM\n7pQUeTOdC82aiQdRQQFFQTr0HgvSSSrGoTgwuYVCcDBHjwq/uLyOz47AQGjUiBIdf402u2ydXZfQ\nLAWrTZrd1cSdlpqSQjFLQS9TUmsAu9OO0T0WPShIxsWqQbNmRXFFgoMx5RfiUByoqlrtY0uhUAvQ\nYgrFLAUpFM6NZs3Ez0OHKLIUVFm8VhM4FAcmRQcmE/j6ag+1mJjzu67aSGxsKaFQIMoAPKHcSKFQ\nC9Cyj/LyIThY88XKm+nsadpUxGEOH6bIUlD1sk6hBrArdoyKWkKxiYjQajElZ0FsbMnYmMlaCOAR\nF5IUCrUAzX3kEgrHjklf7LliNIoAfXGhYFQ9czNJKkfMBFGltesBmjUT7VoUBZf7SFgKnrB4pVCo\nBWiB5lyr9MV6AC0t1fVwMik6GVOoAeyKHZNTlXExDxAbKxo7pqYiGjtaCwA8YvFKoVAL0GIKLktB\n+mKrh5aWajBAQADGYr3ohw8fzsCBA/niiy/O5xIvSuxO10hZaSlUG3dszG3xuoWCJywFWdFcC9Dc\nR06EpbBfzFHw9z+/66qtxMXB6tWuX4KDMTlVrU5BVjR7D819FBysdauVQuHccJ83sxl6BQcLhREZ\naK4zaIFml/9Q1ihUj2bNRIsAqxWhZXlwQImkYuyKa6RsUBCpqcL9Ia/jcyM4GBo0KLIUTLlSKNQp\nSlgKLveRvJnOneIttAkO9mgveknFaNMDi7lA5XV87mi1CsHBwi2HFAp1Bi2moKAFmuXNdO6U8cfa\nFZl9VAPYnXZMhU6ZLOEhtLTU4GCtKFAKhTqCln2kgBIo3EcyyHzuNGki6qc0S8GuyN5HNYBDcYiR\nsi6hEBKijWqWnAOapRAUJIVCXUNzHymQYQvCZpMaVnUwGIRQdVc1G+1OaSnUAHbFjsnmkC5QD+Gu\nalaDpKVQ5ygeaDafEjne8oaqHrGxRf2PjHaHjCnUAHanHaPNLl2gHiI2FvLz4ZRdCoU6R/GYwqGT\nYqqdvKGqR0xMkVAw2Tw3ylBSMQ7Fgclml5aCh3DHxo5kSqFQ59DcR34BmI/oCQwU6WiScycmpljm\nRqFDiynI4jXvYXfYMCqgBkpLwRO4z9+hDM8KBVm8VgvQAs2BRTUKOt15XlQtJzYWTpwAh78YUOJ2\n0cniNe/hcNoxOSFXF0xurhQK1aVBA1GvcDAtiEtdQkE2xKsjaO6jAKlheQp39tZpZz2MhZ6bWiWp\nGLujEJMCqbmizYW8jquHTudKSz1iwOgrWs1K91EdwaE4MKg6dMH1pFDwEG6hcDI/GJMTHI7C87ug\nOoDDNWTnaLZMlvAU7loFk78QtFIo1BHsTtdsW1eAri7WKLzzzjvExcXh7+9Pjx492LJlS6X7Z2Vl\ncd9999GkSRP8/f1JSEhgzZo12utNm4qfJ3KFP9Yh21x4HdElFVIygvDzEyMlJdXDXatgDPCcUJAx\nhVqAe7at3S+IzMy6p2EtXbqUadOm8f7779OtWzfmzp3Lddddx759+wgLCyuzv91up3///kRGRvLV\nV1/RpEkTzGYz9evX1/bx9xcPpWNZQcJSkELB69gVB0YFDluCiImRcTFP4LYUDJcI60sKhTqCmFil\nI09fN83uuXPnMnHiREaPHg3A/Pnz+f777/noo4949NFHy+y/YMECMjMz+euvvzAYDADElGNexcSI\nug+jAnandB95GzGOE/anBte5a9hbxMZCTg7gI91HdQqHS8PKVupegM5ut7Nt2zb69eunbdPpdPTv\n359NmzaV+57vvvuOnj17MmnSJCIjI2nXrh0vvPACiqKU2C82Fg6lB2FSwOGUgWZvY1edmJyw71hg\nnbqGvYm7VqFQJ4VCncKtYZ22B2M0QuPG53tFNYfFYsHpdBIREVFie0REBKmpqeW+5+DBgyxbtgxF\nUfjhhx+YMWMGr732GnPmzCmxX0wMJKe5YgpyRrPXceDEaDRxKMUghYKHcJ/HfFWkUUuhUEewO+0Y\nnSoWWzDR0aJ3T11HVVV0FTilFUUhIiKC999/n06dOjFs2DCefPJJ3n333RL7xcTA3mOimZhDVjR7\nFUVVUFAxmvywWOqWtetNGjUCX1/Is8uYQp3CPbEqLS+ozt1MYWFhGAwG0tLSSmw/efJkGevBTePG\njfHx8SkhNNq0aUNqaioOhwOjUVz2sbFgKQgUgWa1qKLZ/bqbESNGMGLECE9+rTqHuzhQZxDjAuva\ndewtdDqh3GTZpFCoUzgUO0anwrHsYGI7nO/V1Cwmk4kuXbqwfv16Bg4cCAgrYf369Tz44IPlvqd3\n795l2lTs3buXxo0bl3jgx8SAih69wQeHKm4mWdHsHbSHlU4UWUmh4DliYsByLBiDIt1HdQZ7YQFG\nJxw5XfcsBYCpU6fy/vvvs3DhQpKSkrjnnnuwWq2MHTsWgNGjR/PEE09o+997771kZGQwefJk9u/f\nz/fff88LL7zA/fffX+K47oQkncEPOyWD0BLP4m6/4FD9MRggKuo8L+giIiZGVImLLLrqu0GlpVAL\ncCB6PUAAACAASURBVBTmY1JEN8T2dbBwbdiwYVgsFmbOnElaWhodO3Zk7dq1hIeHA3D06NESFkB0\ndDQ//vgjU6ZMoUOHDkRFRTFlypQy6athYaJeQcUPyK7Jr1TncGuwdiWAqCgwyiePx4iJEfU2Rg9Z\nCvJPUwuwF+SLlFTqbn73pEmTmDRpUrmvbdiwocy27t27s3HjxkqP6fbHOvHzyBolFePWYG32gDp7\nDXuL2Fj4LcdVhOmwVft40n1UC3AUCqGQS910H3mTmBgodPif72Vc9Lg12FybrFHwNDEx4tlgVMBR\nYK328aRQqAU4CgswOSGHYK1nj8QzxMZCgSPgfC/joscdU8ixSkvB00ihUAexFxZgVMAvNAh/qdR6\nlJgYsBZIoeBt3O6jTKu0dj1NdLRQGI0KOGz51T6eFAq1AIfdhkmBBjHB53spFx0xMZBnk0LB27jd\nRzanFAqext8ffBq4LQUpFOoEdrsYYxgeF3S+l3LRERMDNqVIKMhxnN7B7T4qUKRQ8AYhUS6hUFh9\noSCzj2oBDocNvaInOs50vpdy0REbC4VKoPa7LF7zDo7CAgAKlOA6OQ/E2zSMcQkFW0G1jyUthVqA\n3WEHp1HeTF4gKgpsirTAvI09NwsAo3+wjIt5gbBmbktBCoU6gc1WCIpRmt1ewNcXDH6BZ95RUi0c\neTkABDaUcTFv0Dg+AKMChVIo1A1sdjuq4iOFgpfwD5HuIm9jdwmFeuHyXHuDmGZ69IqegnwpFOoE\nhXY7qmKSQsFLBNaX7iNv4xYKDRqHnOeVXJzExIBeMZBvrf4EQSkUagF2xY6q+lBsxLDEgwSHS5eG\ntynMywUgvKkUCt4gJgZQDBTkyzYXdQKH4sSg95GDzr1Ew0jp0vA2menCUohsJoWCNwgPB51ixFZ4\nAVgKdnshGamZ1V6IpGIcODAafc/3Mi5aQqOlUPA2mRbRfiGqpTR3vYFOB3qM2O0XgFAYMr49Vz0T\nXe2FSCrGiROTjxQK3qJRUykUvE12hnAfxbWSrjpvodcZcTgugHkKJpMvCnLouTdx6pz4+sr2zt4i\numV92CL+7x7HKUdwepbcTCuEQlhDWYDpLUYnPIaPqfr1yNU+gq+fL06cFBaCj0+11yMpRXY2KHoF\n3wApFLxFwyZFloKsaPYO1lzhPjIZpFDwFvdMn+aR41TbfeQf4Ieid3L0qCeWIymN2QxOvUJgkCwD\n9RYmP9kQz9vYrFb0Cuh1MrflQqfaf6GAID8Ug4L5sOqJ9UhKkXLQgVMPQfWkpeAtjHrZAszb2Avy\nMaoyfa42UG2hEFTPD4cejhyoftRbUpYT+3OxGyAwRGqz3kK6NLyLqoLTbsWoSKFQG6i2UPALCMCh\nh7TkHE+sR1KKkwdycOjBV3YR8xrSUvAumZmgw4ZRlkXVCqr9VzL6+mPXQ/qhXE+sR1KKjMM52PVg\nlE3bvEZxoZArL2OPYzaDUZ+PCcP5XoqkClRbKJj8hKVwOkVaCt4g82guDj0YZTDUaxh0RQ+rI0fO\n40IuUsxm0BtsGGWQuVZQfUvBJRSyjkkVyxvknhDuI5O/tBS8hU6nw+DKk5BCwfOYzWDQ2/CRbrpa\ngQeEQiB2A1jTclAUTyxJ4qawEApOZaPowegvO3l6E7e/+5ln5DhOT2M2g8Fow6STQqE2UP2KZv9A\nEQi153DyJERGemJZEhBaa4BeTKwyBUih4E1M6LGhcO21S3j9dVm85knMZojSF2LUy2SJ2kD1LQV/\nYSkEkkNKiieWJHFjNkOgSygYfeUN5U2MrriCdB95HvNhFXSFmKT7qFZQfaHgI4qqgnTZmM3VXo+k\nGCkpRZaCUebSexWDKzNGKjaeJ81cgFMvr+HaQvWzj/TiD93AL1veUB7GbIbwoGyg6DzXVd555x3i\n4uLw9/enR48ebNmypUrvW7JkCXq9niFDhlS6n9vfLdu1eBarFQosIq3aZJDN0WoD1bcUXCZho/pZ\n0lLwMGYzhAaLVN+6XGC1dOlSpk2bxqxZs9ixYwcdOnTguuuuw2KxVPo+s9nMI488whVXXHHGzzDq\nhaWQdtyJvfrdhyUuUlIgCFGVbzJKoVAbqL6l4DIJw4JypFDwMGYzNAyUQmHu3LlMnDiR0aNHk5CQ\nwPz58wkICOCjjz6q8D2KojBy5EieffZZ4uLizvgZ7vPrT560FjyI2QzBiLRqoxQKtQKPWQrSfeR5\nUlIg2FcIhbran8dut7Nt2zb69eunbdPpdPTv359NmzZV+L5Zs2bRqFEjxo0bV6XPcfu7g8iVyo0H\nMZuhni5XuI9MclBUbaDa6qdbKAT55mA+UO31SFwoihAK/p1EUWBdtRQsFgtOp5OIiIgS2yMiIti7\nd2+57/nzzz/5+OOPSUxMrPLnFBcKUrnxHGYzNAvNoUAPRikUagUeCzT7G3I4fRpyZLcLj5CWJorX\n/HRCKNT1QHNpVFVFpyvbdTM3N5dRo0bxwQcf0KBBgyofz2gQQrdpfWkpeBKzGZqFuWIKJtn+vTbg\nMUvBR5cHCO22bdvqHlXifjAZEee1rloKYWFhGAwG0tLSSmw/efJkGesB4MCBA5jNZm6++WZUVfSu\nUFyl9j4+Puzdu7fcGIPRlRmTXDidAx9GUDy5SY7mPHfMZriifg479GDykbU2tQGPCQWDIjRas1kK\nBU/gFgo6Z912H5lMJrp06cL69esZOHAgIKyE9evX8+CDD5bZv02bNuzatavEtieffJLc3FzefPNN\nmjZtWu7nuF0b49pOZWPI7axc6eEvUkcxm6FxQi52ox5/o7R2awPVb3Ph8sXqHHkYDEjT20OYzRAS\nAqpNWAp1NdAMMHXqVMaMGUOXLl3o1q0bc+fOxWq1MnbsWABGjx5NdHQ0c+bMwcfHh0suuaTE++vX\nr49Op6NNmzYVfobR9cCKDpGV+Z7CbodjxyCicw52H4N0gdYSPGYpOPJziY6WFaGe4vBhiI0VYwyh\n7loKAMOGDcNisTBz5kzS0tLo2LEja9euJTw8HICjR49iNFbv/BiNwlKIqJdHSoqYFlZOyEJyFhw7\nJhImwnxzcJj0dfoark1U31JwSX9HQT6xsdJS8BRmMzSLUXDskkIBYNKkSUyaNKnc1zZs2FDpez/+\n+OMzHt9tiTXyy6WgAE6ehHJCFpKzwP0saGDKxW6UlkJtwWN1Co7CApo1dUqh4CHMZmjRxIrD9ReS\nN5R3cQ/aaehbFBuTVA/3OQwmB4dRV+cVm9qCx4SC3QAtGudJ95EHUFXhPmoZmYPdNRRM3lDexX1+\nQ4xCKMjruPqYzRAeDsYCEWiuy3Gx2oTH2lw49NA8PIfjx5G9Y6rJqVOQlyeKfjRLQd5QXsV9fv3s\neQQFSUvBE5jNIi5GTg4Og05au7UEz1kKeogNzUVRZKfJ6uJ+IDVtkKsJBWkpeBf3+dXl5crYmIfQ\nhEKuKF6T13DtwHMxBb1I5wNpeleXw4fFz6h6ouUwyBvK27jP7/BffyU9fSB//inHcVaX4paCaJ0t\nLYXagMfaXDj0EBkkg3SewGwGf38I0efIQHMN4RYKS1q3/v/2zjuu6uqN4597LxsBQRBRQRFxDzBN\nnLnQLHPkSEtLzcrUzEFqWq4iR26x3Jpb82dKWaGSI0nTVFDDwRQVQRCEy7zr+f3x3HvhspErSp73\n6+UL+Y7zPd8v55znPOM8B2++GQi1WqxgrggaDbdjd3cAGazxiolN1cCojmYLpRxOTkJTqCi6GZYk\nQziaKwv9983MRL16og1XlAcPOHdX/fpgTUGiERObKoJRHc3IyICbm9AUKkpsbF5nEo7mykEvFORy\n1KsHkdyxguhMoPXrgzUFCYk2XEUwqk9B16GEUKgYBrZYKwtIIIFUUuE/laAE9LPYDHY0A6IdVwS9\nUKirAnJyoIRGaLtVBOOZj6ws9B1KqN4Vw1AomIsZViWgW7yGzEy4ufF/hVB4cmJiAEdH3p8CAFTC\nfFRlMJ6mYGUOyOVwc4M+d4yg/KSns+mifn3+RWVpLjpTJZDffORSi2BiIiY3FSG/CRQAlKQWmkIV\nocJCQSqRQiqRQmlprtcUsrOBpCRjVO/FQzc71WsKlmaiM1UC+m9MBJkyB66uQlOoCHqhkMGagpLU\nQuOtIhjFUG0iNYHKMk9TAMQs60kpJBQszERnqgQMvrHwjVWYmBhtOKpcDo0EIJCY3FQRjCIUTKWm\nUFmYCSedEYiNBUxNARcXcPSRhdAUKgOZVJb3i4iiqxBqNU8K9eGoYq1NlcJomoLSwgyQy1GjBmBl\nJTrUk3LnDuDmBki10VxKc1PRmSoB/YpmAP3HjoVcvldou09IfDygUuULRxVh1VUK42gKMlOozE0B\nuRwSCauNMTHGKPnFQx95BLCmYG4iOlMloBO8+wAE+vujX78RiI8HcnOfbb2qIrpwVJ35SCzArFoY\nz6dgYap3Kgmh8OToHXQAkJ4OpZmJ6EyVgME3lsvh7s4RdELjLT+6vq9PhmfKw4zQeKsGxjMfmZno\nw88aNACio41R8otHQU1BaWYiOlMlUNCn0KAB/1dMbspPbCxQsyabkSGXQ2VjDUBoClUF4zmazU0K\naQpirUL5yMzkbSDd3bUH5HKozGSiM1UCBoJXLkfduoCJiZjcPAkG2m5GBpRaoSDMoFUD42kKpjID\nTSEnB0hIMEbpLw66WWmDBmBPXU6O2LGqktAJXjLnKDqZjDU2IRTKjz4cFeCJTTUrAMJ8VFUwnk/B\nTKspEOlVb9GhyofuezVoAL2AVZmKDc8rA/3KfNtqBpMbYT4qP4U1BRYKQuOtGhgv+shExgHKOTn6\nBiE6VPmIjgYsLIBatZCXHsBEKjpTJaAXCjbWwjdWAVQq4O7dfEJBLofKWqspCI23SmBE85G2qIwM\nVKvGjibRocpHdDQPRBIJOAkSAKWJ6EyVgYFQ0PrGGjQAoqKEb6w83LvHc0O9+Sg9XWgKVQzjOZpN\ntEVpZ1kiLLX86IQCgDzzkUwqzEeVgG7Aei/uAfofPoy9e/fC3T0vQaGgbBjsowAYCAXRjqsGRhHd\nJlKTPKGQb5YlNIXyER0N+Ppqf9GZj6QiZ0xloNPGNrRrCQ8bZ2DECFy6xOdiYgAHh2dYuSqETijo\ncqAhLQ1Ka2cAQuOtKhjPfKQL8xb22CdCo+HBp5CmIJWIzlQJ6M1H1SwN2jAg2nF5iIlhn5ilpfZA\nejqU1hYAhKZQVTCeo1km4V/yrVW4f1+kCSgrCQkcxltQKAhNoXLQbbKjtLbSt2F7e8DOTgiF8mAQ\neQRohQJLCDG5qRoYT1PQlZRvliXSBJQdg3BUgL+jhQWUpBIzLADr1q2Du7s7LC0t4ePjg4sXLxZ7\n7ebNm9G1a1c4ODjAwcEBvr6+JV4P5N8sysJgc2ah8ZaPqCigYUPtL0RAejoUVuYAhKZQVTDeOgVd\nSWlpAPKiD4SzuWzoBp78URuwsYFKo3rhZ1j79+/H9OnTsWDBAly5cgWtW7dGnz59kJycXOT1p0+f\nxttvv41Tp07h/PnzcHV1Re/evfHgwYNin6EbsNTVLPWaAiDWKpSXyEjAw0P7S1YWoFZDqRMKL3g7\nrioYL/qI1IC1tV4oiDQB5SM6mm2xVlbaA3I5YGMDpVoJE8mLbT5auXIlPvroI7z77rto0qQJ1q9f\nDysrK2zdurXI63fu3Inx48ejVatWaNSoETZv3gyNRoPg4OBin6Hfa1y7WZQOd3fRhsuKXA4kJubT\nFHRh1RZmAAAzmdkzqpmgPBjPfKRRsgFWKxRMTDgCQcyyyoZBOCqQJxQ0yhd6hqVUKnHp0iX07NlT\nf0wikaBXr144d+5cmcrIzMyEUqmEQwkhRLqEeCori0Kawp07HHsvKBmd8NQLBe1YoBMKwnxUNTCe\n+UijYqGgnR0Awh5bHooTCiqN6oV2NCcnJ0OtVsPZ2dnguLOzMxLKmFxr5syZqFOnDnr16lXsNTrB\nq7IwZ4+/SgWA/yYqFS/KEpRMZCT/1JuPdJqCpVYovMCTm6qE8aKPdEJBOzsAhFAoD4WEQloaYGcH\npVopZlhFQESQSCSlXrd48WIcOHAAhw8fhplZ8eYLneBVa+3f+aPoANGOy0JkJGBrCzg6ag/oNAVz\n/raiHVcNjLN4TWICpVoJ2FU3EAru7sD+/RyEUIb++8KSlQU8eFBAKDx+DLi6vvCOZkdHR8hkMiQm\nJhocf/jwYSHtoSDLli3D0qVLERwcjObNm5d4rU4ozFn/I1YDwNChgKUlNBoAGIHo6BHo3v3J3+NF\nQBd5pO/rOk3B3BQyiaxMQlzw7HmqmkLDhvzro0fGeMp/F90q0CI1BY3yhTYfmZqa4qWXXjJwEhMR\ngoOD0bFjx2Lv+/bbb+Hv74+goCB4e3uX+hydM/+LWWMQCCBw9WoEBgbil18C4eo6AlFRFX6V/zwG\nkUdAnlAwFenfqxLG9ynkEwqNGvHP27eN8ZT/LjpbrDAfFc20adOwceNG7NixAzdv3sT48eORlZWF\n0aNHAwDeffddzJ49W3/90qVL8eWXX2Lr1q1wc3NDYmIiEhMTkZmZWewz9OsULLTmo3y+MU9PICLC\n+O/1XyMyMp+TGeA2bGUFBalf+DZclTBa7qOC0UdAXgOJiABKmNS98EREcChq7dr5DmqFwovuaAaA\nYcOGITk5GXPnzkViYiK8vLwQFBQEJycnAMC9e/dgYpL3jb7//nsolUoMGTLEoJx58+Zh7ty5RT4j\nb/GaVig8fqw/16gR8Ndfxnyj/x45OeyMNxAK6el6bVdoClUHo4w2ptKizUdWVrxeQWgKJXP7Ns9G\n9SZXIv6O1atDmSY6FABMmDABEyZMKPLcH3/8YfB7zBPEQeujjyy1QqGAxrtjB+enkhpFt/7vodt+\n18B8lJYG2NoKbbeKYbx1CurCmgLAHUqo3iUTEZFnagPAkS8ajV5TEB3q6aNfp2BmwiN/AU0hKwuI\nj39WtXv+0ZlAC2kKtrZCU6hiGN+nkJtrkAXP01NoCqVx+3YBoaATrFqfwotuPqoM9Cuade04n1Dw\n9OSfoh0XT1QUZ0Z1ccl3UGc+EppClcL40UdAIdU7IkLsXlUcmZmcTbZYoSBmWZWCbtBSaVRA9eoG\nQsHdHZDJhFAoichIDpQwMK/pzEcapUhxUYUwfpoLoJBQEKp38ejUbt1sFIB+QCJhPqo09IvXNGoW\nCvnasKkpD3hCKBSPQXZUHfk1BTGxqTIYLyFeMZqCUL1LRvdditIU1LbVAIi9bSsDnU9h3cx16B8X\nh72hoQbnRVhqydy+XYRQyKcpiIlN1cH4PgWg0KpmmUx0qOK4fZu3eqxRI99BXXqAatq9bcUs66kj\nlXBXGOs/FoFdumBE9eoG5xs1EhOb4sjJ4eijpk0LnNA6mhVqhWjDVQjjRx8BBkLBzIx3YhIdqmgK\nRR4B/P1kMn14pNAUKg+9T6GIKLroaECpfEYVe46JjGSfYePGBU7kX6cgNIUqg3Edzba2fKCIDiWE\nQtHo1igY8PgxdybiTJ2iQ1UeRTmaAW7DKlVeShJBHjdv8s8mTfIdVKs506/wKVQ5jOZTUJMaGhMZ\nr1gTaxXKTKFwVMAgxQUgNiepTFRFhKQCwjdWEjdvsvlTnx0V4DZMBNjbC02himEUoaAbtBRqRZEL\n2Dw9OTpBm6JeoCUlhZMFFicUFGoFACEUKpPiNIW6dQELCzG5KYpbtwpoCQCQmso/7e2FplDFqBSh\n0KgR22Lv3DHG0/473LrFP4VQeH5QqBUsFLKyDBwIUqlYiFkcN28W4U9ISeGfDg5CU6hiGEUomJuw\nQzRXlVvkLEsXlXDjhjGe9t8hPJwHm0IdSutTEEKh8lGqldyGgUKTm8aN8+znAoZIaAr/NYwjFGQs\nFBRqBcdX6mYJWurUAWxseBAU5BEezouiLC0LnNBqCrlqThcihELlkavOzYuiKzC5adYM+PffZ1Cp\n55gHD9ifXKJQEJpClcIosY66QStXnctCoYCdSCIRHaoo/v2Xv0shUlMBBwe9pqDTxARPn5+/+Rl3\nrK5iBIARBYRCixbAw4dAUhKgzdr9wqPTnAppu6mpvEDJxgZKtUhzUZUwqvlIoVZwGEIRW601by40\nhYKEh/N3KcSjR0CNGsJ89Azo7tcdgdu3YwRQyHyk+1uJyU0eN25wGhDdXtZ6UlPZDCeR8OI1oSlU\nGYzqaM5V5RZpPgJ4RnzjBrR73grS04G7d4vQFIj4++XTFIRQqDwMzEc6E4gWT08eAIVQyOPaNfYZ\nmhYc87VtGIBI6ljFML5PQacpFEiL2qwZZwS9e9cYT6z66JzuhYRCRgZHvQhN4ZmgX5kvkRSa3Jia\ncqSYEAp5XLsGtGxZxInUVMDeHgBE6uwqxtPxKSiVLAGqVdNfoxv8/v0XqFfPGE8tP/HxwP/+x86x\nevWAwYMLLLipRMLDedwp5KDTmd4cHKBQ5wDIE7qCp0+uOpdt4Q4ORZpBW7R4tkJBowF++w04e5ZT\nyPTtC/j4PJu6EAHXrwP9+xdxMr9QEJpCleLp+BSAQh3K1RWwtn42fgUiYPVqVv/9/IC9e4GJE3nr\nwB9+qPz6APwd3N15AbgButlpjRpsjoPQFCoT3TdHjRpAcnKh882b80D4LPYHiYgA2rYF+vUD9uwB\nvv8e6NABGDiwUKBUpRAXx2bQFi2KOCk0hSqL8Rev6YRCAdVbKuUOdfWqMZ5YPmbMAKZMAcaNAxIT\nOaNjfDwwaBAwejSwdGnl16nYyCOdMBXmo2eCQsPfHI6OxQZMpKRwO6pMwsNZI8jMBP78kwP8EhKA\nffuAM2eAjh2LlGFPlWvX+Gex5iOtTyFXnSsi6KoQRvUp6B3NQJEdyssLCAszxhPLzpo1wLJlrCms\nXp23LqlmTWDbNuCLL4CZM4Eff6zceoWFAa1aFXEi30pQIRQqH903L05T0M2KK9OE9OABm4lq1wbO\nnwc6d+bjUinw1lvAuXNc1f79AYWi8up17Rq7X1xdiziZT1PIVeUKE2gV4ulpCkUIBW9vnvHk28I5\nj6wsoydHCg1lc9GUKcDkyYXPSyTAwoXA8OHAmDFPIa+NSgVkZxc6/PAhaypeXkXc8+gRYGIC2NhA\noVZAKpHqN4ARPH305iNHxyKFgocHYG7OJqRCaDRsTzEiRMD77/Ng/9tv+nHWgMaNgZ9/Bv75B5g7\n16iPZ+TyIg9fu8ZCUiIp4mRKSp5QEJpClcK4aS7Uubx02cQE5xL/wYnoEwbXeXnxOFlolrVtG0/h\n69c3mn1JoQBGjmQTzeLFxV8nkQCbN7Pm8OGHRrQVh4TwLuZOTsChQwandNpSQaEQeCsQ55NDWbBq\n47vFDKtyya8ppKcnYc3fa5CjytGfl8nYhFRI433wgP+gdnbA558brT7btrEw2LyZk/IVR/v2wFdf\nsSn077+N9HCFgqMxbG2BN94oNJsrKvIoXh6PLRfWQ50h16/wy1HlwMLEwkiVEjxtjK8pSCRQ1bBH\nx9Rl8N3pa9ChWrbkQdhgp8OoKOCjj9jAX6MGT9uNsJPJunUc9rl9O8/sSsLaGti4ETh1Cti5s8KP\n5tniW2+xZ7tbN+Ddd1k90BIays/08Mi7JS0nDQP2DUAPzTa9CU6hVgjTUSUTvSka/fv3x95797DG\nNR6f/v4ptlzeYnBNmzbA5csFbvzkE/4bT5vGs5DDhytcl0ePgOnT2e/1+uulX+/nB7RuDUyaZKT1\nQF9/zSrI7NnA77+zHVaLQsGrmQs6mWcHz8a43z7Gr54AnJygIQ1UGpWY3FQhjCIUpBIpTKQmetU7\nyi0vFPXKgyv6/1tbc5z3lSv5bl62jFX1bdt4BL95E9i6tUL1SUoCFizgmX+RJpoi6NULGDKEfQw5\nOaVfXyIBAWx62LcP2LGDjb9r1uhPh4Zy55Xm+/qn75wGAGRLVEiuxZsV5apzhVCoZGq+VxOBgYEY\n0asXLtTghnAm7ozBNW3asLarbycRERzr/M033J59fYEvv6zwyPz117xXzZIlZbteJuOm988/3JUq\nRHIyv4ufH+DvD0yYAKxYoTeH3rjBWn9Bv9jVRNb0Q9wA1KypHxOE+ajqYBShALC2oFO9b9XJawA3\nkg1To3p759MUcnI4PnTsWI7N9PZmjWHNmiez44SFAd98g4MT/gAR+wvKg78/EH+fcHRyEHfwJ8mT\nrFBw/UePBtzceNb/9tusgmgHidDQwsLqZnJe+s0bLhy+JzSFykeXhBA1auB6Tf5vWIKhrahNGx4Q\n9X6FzZvZfj5iBKvC8+bxyd9/L38FsrKATZuQNG8ttgdkYNYsNm2WlU6dWEnd8OU9qBYvAw4eZMlS\nXjZs4D44bRr/Pnky+wm0GtClS/yq3t55txARIlMiAQCRDgCcnPSWAmE+qjoYRSjs3bsX5jJzfYeK\ncJTCWi1D/er1EZ5kuDCheeschF5T8Pj422+cX+bdd/MumDiRvdFnz5avEocPA23bgr76Ch8f7Imf\nXvq63EnLGnkSgppNweBNr4IWLgReeoltSuXh2DGOV5w4Me/YqFEc1P3XX8jOBm7cUqFla0OnemRK\nJDwdeHuvuw7sWM4vFPbu3Vu+egieCN3ERlPDAXfsgOa2DRHzOAZqTd7A2qoVIDXPZhMSEQ+8w4bl\npbvt2JFVwfJqvJmZQJcuwPjxcPh6Gi5QW0x9t3DARmksGnoZv8W3guTLOcDQoTwpKY/WQsR1HzEi\nb3Wnhwfw8susEYGFQuOmyvzrU5GclQy5Qg5HqQ2i7QE4OenHBHOZuWjDlYAxvrHRhEJ+TSHBVgaX\nHBM0dWyK24/yZtvZymyspSbIGNYJkVEaICiI7Un5d5np3p1n2OV5ufv3eeDt3x8zPkrHN+bz0ePk\nlyx0ysOPP6Ln9TWYIluLlXMecScYMaLISKpi2buXPZH5PXA+PuwvCQrCP6E5oA+9sTzjJf12mwAQ\nlRoFr1pesFNIcLc6h3Mo1Aq92i06VOWgUHEbTrUxhUYKdLBuAoVagfvy+/prVl9aDJpph5//Z9jH\n6AAAIABJREFUDeZd66OjDY3+Eglrv4GB5Vs8MHkycPMmUo//Ay+Tf1HbIgWW779dPq05IwPufoPx\n2MEDrZwSoNj9I3DgAK90Kyv//MPv9M47hscHDmTtR6HA0Yff4eYwM/x862f9aZ2W0EPaAHF2ACwt\nDcxHog0/fZ4boQDwH13XAJKrSeCYSfCw90BUapT+mkM3DuGh4g5Q5x/sCwkBjh8HfH2h1qix4NQC\nHAw/yB1q2DCefZU1RNXPD7CywqOlW7BuoylyPpvLToKJE4uJfy2CtDT20L35JjJGT8K331kjd8su\ntqEuWFC2MrKygCNHWJAA2BG2A0vOLgFJpVyfY8ew569TgPN1RMqv6v0IAHeohvYecH0M3LXi9xbm\no8pHN7NNsuKB2EfmBgCISslrx3uu7QFJlQhRrOOJh5kZ0L07QuJCMOP4DGQoMjhgQqPhdlwWdL60\nZcsQEOKNKFkjqDZtZ82zrGUA7FSIjwf278eNBHvszB4CjB/PEVFFJKoskn37AGdnoFs3xKXFwe+Y\nHw/4vXoBmZlQ/nUBd+qw0zngYoD+Np1Q6JjtiBRL3tpUmI+qHk/Fp5BsroZTmgoe9g0QnRoNDbHq\neuH+BTR0aAhpjgNOXz3As5HevbEjbAfmn56PoXOH4l76PTaKJiUh4tddaLquKaYHTTd4ljxXjiVn\nl+BS/CWeqe3fD3z1FdbttYaq3nHUcNnGdv3YWGDrVqg0KoQmhPL+u/lQqBW4/OAy1y8ggKOG1qzB\nB5NTkKD5HDuDa7LA2bgRuHcPZ+POYvlfy5GtzFt7QEQYe2QsvDd44+6hbWwCGD4c1x9ex3uH38Os\nVbNwNOIo0KcPcPEizscEwTTXGbVtauNY1DEAHBt/N+0uGlrVRS054aE51zNHlaOP2rh//z6MgTFm\nEsaa8T1v5QD8tyAiJJlyW26b7QAJJPoBL0uZhfCkcNhL3JBqfwLKoGNA587QWFth6I9D8e2Gb/HV\n6a/YEdC7N7B7Nz759RN4rfdCTGqMwbN+vvUz1v69ltvfihWAiwty3h6LVbvD0bLLYtiNeI01kDlz\nAJUKdx7fwf30wu0gOjUaKdkpnExx2TLg/ffRoFcDdBx+Fl/4rwXNX8B+heXLkaHIwNKQpbhw/4JB\nGX/d/Qseazzw3YV13J+GDgVkMswOno3l55aj/+z+7ECwtcWl/x0C7GPQunoXhMSF6DXeyJRIuFRz\nQYPHEpCEzUn5zUfPUxs2VjnPU10A44wTxtMU8vkUkkwUcMzQwMO8FnJUOXggfwAACE0MRRuXNnBR\ndEN0zjHWCl55BXuu74FPXR/I/pVh25VtbMtv0AAzQ+bjZvJNrDi/Aufvndc/a+HphZgVPAu9dvZC\n8prFnCdo2CgsCh8H5fDemLdhGlSNPXm2tmgRRh18G94bvDHsx2EgrSquIQ1e3fUqXtr4EiYc+QBY\nuRJ4/31k13TAyNPtgeqLMSPYD5pJkwFLS9xftRC+O33hd9wPnwfnxaH/GfcntoVuQ2hCKOZdWAq0\nawd4eGDvtb1wsHSAzW0b/BD2A4emEuGBKgj18Ap86vroO2bs41gQCA00dnDMApJl/B2zVdmwNGU7\n9fPUoZ63jmBss4Sa1EjO4bTZdZJz4WrnipjHPKCHJYRBTWqMajQFMJfj6u0QoHNn/BP/Dx5kPIBd\nhB22h21nH8Tbb+P03bMIuBiAsMQw+B330z/jwv0L6L+vPyb/Phkrjy/kKLXJk+G/5zpS3mqFC7Gf\n4/fI31lLjYjAX9sXwnOtJxoFNDLw0x26cQgN1zRE44DGuBfwDU9sPv8cJ2NOIqRxFySYTMXeC2qO\nHlq7FlN/noiZJ2bCd6cvHmbmhUnPPTkX0anRmPr7VCQ+vg8MH45MRSYO3zyM5k7NcePkDcTI7wKv\nvIKLEexAn9P9M2QqM3HtIee7iEyNREOHhqiZzNrBw8yHBuaj56kNG6uc56kugHHGiTJlSSUiyItZ\n1QgAKpUKMoUMGfIMpKen42FOBnzSAOfHMiAHuBp3Fdau1rgSewXTOkxDpq0FgqSH8bBJI6iUmTh1\n8xT8e/ojzjIOuy7uwmSvyUgd2Bs/Yz2+8VmITWHbsPLUSmzqvwkp2Sn47ux3GN18NA78ewCLw3/A\n3DFTsWxnGHLq7cBrNYfj16x9CDgTgLFTp+Li6b3Yd+UuXm/0On4K/QkHGh5AX8++OHTjEE7ePIlB\nTQdhw99bMaiaFB0+/hjfn1mD6AfRcDSrg2S31Vjx0zv4cMwYLL6+FmbtLTG+zXgE/BmAj1t+DBcb\nF6w6vQoNrRpimMcArPprOfwHjoFVWhr2X96Pvq59cdHqIo5eO4qkHuugcnZEkt1N9HAYCw+bNKwJ\nX4O0tDRcv3sdyAEck9SwTQOuZqcjPT0d6WnpMFWaIj09HUSEdCOsllWpVBUuxxhlPG/l6O/PBZJS\nkhD3MA6SHECWkAi3Wm64df8W0tPT8WfEnzBVmuKTToOxJtQPZ2wew7NlSxy8fBDVUR2NHRrj70d/\nI/hGMHy6d8fmVlK459phku8X8Dvuhxsdb6CObR0sOrEIHlYe6OLWBf4nl+BtCymsho/AygUfwsq+\nHszNU/HJT5/gwgcXIO3ti6kXv4W7pztUGhXG/288fnn7FyjUCnx65FO0c2yH6JQoTL22HFtGjYLc\nQorRW0ejcbXGuKWJxMz/+aPfrEm4v2Ultv+zC9M6TMN3F7/DmjNrMKPTDFx/eB3BN4KxvPdyzDk2\nA+s72WFq8+Y4eHk/MuWZ2DRsEzqt6oT9l/djgo8PLp05CvMkT3Su3RaSXAlCIkLQ0Lohbt2/hSaO\nTWB5PwxwB2ISYljTzQFU2arnqg0bq5znqS4ASv3GNjY2kBS5BD0PCVHpXqz09HTY6TYeEQgEAkGV\nJC0tDba2tiVeUyahUJqmAACv7X4NdWzqYN3r6+C01AnrjgIjp2xBk4Qv8E7Ld9C6VmuMOjQKtz+5\njWo5ZmjwfX2MSBkI6l0dZ+6cwZXxV6BQK+C5xhNjvcfiVOwpOIbexo+PfZG07ls0CWgCv45+2HBp\nA4Y1H4al3b/BfZ/maDU4Ee1rDEDIo8P4uMEqLH5rDG4l38LLm15G1/pdcSb2DPYeBF6bsRHnO9ZD\nn1190MG1A87dPYeQ90PQ4sg5hKz2w2vvAI0dGyMyJRKXPrwEd3t3TPlhC7bFT0N7R1+EJQXj6o9O\ncL7wL2ae+gL7/92Pd1q+g61XtuLmpJuwGzoSvVpcga3Xy/By9sLmK5sR8UkEzGRmaP5dc7zR6A2k\n/nQTQU6nED0nCUm5KWgc0Bg739yJi/cv4sitI7gqm4SNB2bic18pkmck4429b8DZ2hlbBmwp8dsL\nKk56ejpcXV2BqcBtv9tYeW4lgs/vwcUT7vj2m35Yd3EdYqfE4uVNL6OLWxcs77McYz7sjJAa4Tgx\nMwwtv2+BLQO2YEizIZgeNB2/Rf6GBd0WYFzgOFzeAHgc/Qufxm1EUFQQ+jfuj33X9yF8Yjiq/bAX\nH57yw5mXayIzwR05smQ8WHARJjIZRhwcgdDEUJhKTeEW+xg/n6sHnDqNHjt6IlOZiUfZj9DTvSc2\n9lgJResWeGm0Ag/N2bm7os8KvN/mfcQ/TkLTta3gquiJJJtj+PR0Lma/uxE3erSCz2YffNH1CywN\nWYrZXWZjakYLHJsxBEOHAT+99ROG/jgU/j39Mb7teGy+tBmfHf8Mfwz4G90Ot8OMlLcw59uN+ODn\nDxCVEoX/Dfsf6q+qj20DtuLNrh+h1nRgbq+F8LD3wLAfh+HmpJtwsXF51n/mF56yaAplMh9JJJJS\npYutrS2UJkooTBSABeAGc9imp8OztifuKe7BMsMStRxrwbO2J3DqFNonA3/ayKF4cBkDWw7Ulz/E\newhWXFkBADjs+R5sF+yDrdU2jHx5JBb/sxiWJpb4wvcL2P5+ArYRCfi46XCsjdkH89wWWDVmAsxM\nTNHOth0+6foJ1l5Yi+Fth+Otq2mQrFqF3u9fw3vt38MPYT/gsx6foWPdNsDKYejb7R0Mb6vGvuv7\nMM93HlrXaw0AWPfRROycHYC/M45jQZuP4bnkeyAoCDP6zsDGfzci4GoA/Dr7wVUlA/78ExOHjMHo\n+K0Ijg/GRy99BCcHXijRr2U/BMcEQ25vgR7xgP29e7D38oJzDWfckt9CvDIeHi4esI1Ig6tldajM\nUiCxkEBpqoStrW2p315gRMwBMyszpEvSUcvaDrYPH6JZ3WZIvZAKOeS4nXEbMxvOhK2tLQYnZuNQ\nUzXWXtgOEysTvOn1JmwtbDHq5VHYHL4Z446NQ+eGneCNcCAwEFM+nYIfbv6ADdc3YG7Xuaht7wx8\n/z3mdewLL/wBRc2/4VcnEA7aRHJL+y1Fhy0dICEJjvZdDrv1HwDnz2PtoLXw3ekLeyt7LHtjGWzX\n7wRS07GqXwDePDkevRr1wpRXpuj7bV/7L/Gb8nPUtq6LWXaNYbtuHdqPu4KBXgPx9YWv4WjniCmv\nTIHtB5Mw0KIJatZIwaAjg2BuaY6xPmNha2WLoW2GYvqZ6fjy/HLAAhiZoYKtrS18GvggMDYQ9xX3\nAQugla0bbJVK1LRxghxySC2kgAXg5OAEW0vRjqsEZCSGHBhCvXf2prCEMMJ80LmXaxPNmkVjDo+h\ndhvbUb89/ejVXa/yxYsX08JXzAjzQZgPCooM0pdzKf4SWflbUZetXUh9N45IIiHatIkeZz+m+Sfn\n08mYk0QaDZGPD1G3bvTvDSXBI4jWbHpkUB+NRkPRKdGk1qiJ/vqLCCDasoU0Gg3dT7/PFy1bRiSV\nEt26RUq1kmJTYwu9l//KhyT1OEl37miIfH2J2rQh0mjo6O2jNO/kPMpWZhP5+xOZm1N20gNq9X0r\nsl1kSxGPIvRlHLl5RP+u37eVEq1bR0REfXb2oX57+pH3em8ad2Qc0ZgxdOK1JoT5oMhHkdT6+9Y0\n8ehEY/2JBCWQlpZGAAizQOEPw6n3zt40eJE3kUxG5++EEOaDVp1bRZgPuppwlSgri1KsZST9UkaY\nD/Ld4asvS6PRUN9dfcn8K3M6HXua6MMPierVI1Kr6cD1AzT/5HzKVeUSHTzI7fLiRRow9jbV8gol\npdKwXilZKZSSlcJtvkMHolatiBQKSstJ47aXkEBka0s0kdtJfHo8ZSoyDctI0ZBFk5M09csEohMn\n+JnHj1NSZhJ9duwzCokLIUpOJrKwIPL3p+8ufEeYD5p9YrZBOd7rvQnzQS6fVCdN0yZERHQq5hRh\nPsgvyI8wH5RxkfvaSyua0AeBH9Duq7v5eG6G8f9ogqeC0YTCez+9Rx23dKTg6GAe1Hq3JXrnHfr6\n9NfksMSBnJY60ZzgOXzxwIEU3r4jYUYNarG6HQ/c+cjIzSCVWsW/9O3LHUGjybvg+HFu2L/8QhMm\nENWsSZSdXUoF33mHqEYNovh4/j0yksjammjSpBJvS08nsrMjmjGDiIKC+LknT+ZdoFAQ1alD9P77\nRESUq8qltJw0gzKyFFnkuqQJYYobJbb2Jho1ioiIZh2fRc7fOpP5V+a0+vxqop49KXSkL2E+6Pzd\n89RobSPyC/Ir5cUExiC/ULhw7wJ5r/emj9b2IQIoKeZfwnzQSxteIit/K1KqlUQhIUQANRz6Nknm\nyeiP6D8MylNr1DxoExGdPs3t5sSJvAtUKqIWLYh69qR794hMTIhWrCilkpcu8SRm8WL+XaMhevtt\nInt7HtRLYPJkbv5ZmRoiLy+iPn0ML1iyhMjcnOjhQyIiSspMKlSGTli8O/h9nqw9fkyPsx+zoFjm\nQm4r3Yh+/pkIoFc3d6dB+wbRpkubCPNRqI8Lnl+MFpJqbWqNTEUmkjKTAACOLh5AbCyaODZBSnYK\nkrKS0Mm1E6/OPH8eDbt0hdm6OIxWh0AqMayGtZl13h4CM2ZwOu3AQP5dreasje3aIcXnNWzfztF2\nFqWtjVm+nNOl9uzJ4X+9e/OuJf7+Jd5mY8OJ9TZsADI6+PJKZX//vFWmO3bwimrthg1mMjPYmhuq\nyZamlngr9Qpq7o+EU5fOvFMKAG8XbyRmJiJXnYvWzq2Bu3fhVKsBAI7xzlbmhaQ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"text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p = plot(g.fourier_series_partial_sum(5, 1/2), -1,1, color='blue',legend_label='n=5')\n", "p += plot(g.fourier_series_partial_sum(11, 1/2), -1,1, color='red',legend_label='n=11')\n", "p += plot(g.fourier_series_partial_sum(31, 1/2), -1,1, color='green',legend_label='n=31')\n", "\n", "p.show(figsize=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "入力波が$v_{Rin} = V sin(2\\pi f_{Rin} t)$とすると、以下のように$v_{mix}$には、$f_{Rin}$、$f_{Rin} + f_{LO}$と$f_{Rin} - f_{LO}$成分が含まれます。\n", "\n", "これにローパスフィルターを掛けることによって$v_{mix}$の$f_{Rin} - f_{LO}$成分のみが取り出されます。\n", "\n", "$$\n", "\\begin{eqnarray}\n", "v_{mix} & = & v_{Rin} \\times v_{LO} \\\\\n", "& = & \\frac{V}{2} sin(2 \\pi f_{Rin} t) + \\frac{V}{2\\pi} \\left \\{ -cos(2\\pi(f_{Rin} + f_{LO})t) + cos(2\\pi(f_{Rin} - f_{LO})t) \\right \\} + ...\n", "\\end{eqnarray}\n", "$$ " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 7.5.1", "language": "", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 0 }