{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 12wk-2: 순환신경망 (3) – `RNN`, `LSTM`\n",
"\n",
"최규빈 \n",
"2024-05-22\n",
"\n",
"![](\"https://colab.research.google.com/assets/colab-badge.svg\")
\n",
"\n",
"# 1. 강의영상\n",
"\n",
"\n",
"\n",
"# 2. Import"
],
"id": "6627a70b-2b21-4745-88fb-242b49a08018"
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"import torch\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt"
],
"id": "ae13ade3-992a-40fa-a77c-dd7af67f2ee1"
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"soft = torch.nn.Softmax(dim=1)"
],
"id": "420cfa15-75f5-4a1a-a411-bbfbe2110c72"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 3. `AbAcAd` – `RNN` + GPU\n",
"\n",
"## A. Data\n",
"\n",
"`-` 데이터 정리"
],
"id": "d1c1de28-5528-4e17-a69c-5861c1a84f62"
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"txt = list('AbAcAd'*50)\n",
"txt[:10]"
],
"id": "f976566e-f085-44cd-a05f-af9031671d53"
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"df_train = pd.DataFrame({'x':txt[:-1], 'y':txt[1:]})\n",
"df_train[:5]"
],
"id": "59efc62f-6b6b-4da4-b979-73c28782e9f4"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## B. 구현1 – RNNCell (지난시간)\n",
"\n",
"ref: \n",
"\n",
"`-` 데이터정리"
],
"id": "79e1e8cf-ffb8-4f40-872b-b044a297c4d8"
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"x = torch.tensor(df_train.x.map({'A':0,'b':1,'c':2,'d':3}))\n",
"y = torch.tensor(df_train.y.map({'A':0,'b':1,'c':2,'d':3}))\n",
"X = torch.nn.functional.one_hot(x).float()\n",
"y = torch.nn.functional.one_hot(y).float()"
],
"id": "80e6fd64-0138-4784-9655-2c1626fd3cd0"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`-` Net설계 및 가중치 설정 (구현1과 동일하도록 가중치 초기화)"
],
"id": "8c378c62-320f-46e7-b77d-751a33f7f9ad"
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"torch.manual_seed(4) # 이거를 고정해야함 \n",
"rnncell = torch.nn.RNNCell(4,2)\n",
"cook = torch.nn.Linear(2,4)"
],
"id": "ee4a2dbc-be4b-4041-b383-4bd64b8690bf"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`-` 손실함수 및 옵티마이저 설정"
],
"id": "9a358631-9acf-4916-8384-0509f0e9c218"
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"loss_fn = torch.nn.CrossEntropyLoss() \n",
"optimizr = torch.optim.Adam(list(rnncell.parameters())+list(cook.parameters()),lr=0.1)"
],
"id": "ef704847-ca89-4f11-b2dc-575fde24a9d8"
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"L = len(X)\n",
"for epoc in range(200):\n",
" ## 1~2 \n",
" loss = 0 \n",
" ht = torch.zeros(2) # 첫 간장은 맹물 \n",
" for t in range(L):\n",
" Xt,yt = X[t],y[t]\n",
" ht = rnncell(Xt,ht)\n",
" ot = cook(ht)\n",
" loss = loss + loss_fn(ot,yt)\n",
" loss = loss/L\n",
" ## 3 \n",
" loss.backward()\n",
" ## 4 \n",
" optimizr.step()\n",
" optimizr.zero_grad()"
],
"id": "b74d4894-d3f1-4f2b-8fc2-fbb773dd084c"
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"h = torch.zeros(L,2)\n",
"water = torch.zeros(2)\n",
"h[0] = rnncell(X[0],water)\n",
"for t in range(1,L):\n",
" h[t] = rnncell(X[t],h[t-1])\n",
"yhat = soft(cook(h))\n",
"yhat"
],
"id": "1dc8a9a4-bfaf-476f-839e-1f3d06b5da80"
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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V3B/Zmhs9uugJaqcysAY4wwVIIrgASQQXIIngAiQRXIAkgguQRHABkgguQBLBBUgiuABJ\nBBcgieACJBFcgCSCC5BEcAGSCC5AEsEFSCK4AEkEFyCJ4AIkEVyAJLsV3NbW1iiVSnH55ZfXaByA\n+jXo4D755JOxZMmSmDFjRi3nAahbgwru1q1b4/zzz4877rgj9ttvv1rPBFCXBhXchQsXxhlnnBEf\n/vCHd7lvV1dXlMvlfjeAvdGoah/ws5/9LFatWhVPPvnkgPZvbW2NG264oerBAOpNVWe47e3tcdll\nl8Xdd98dY8aMGdBjFi9eHB0dHX239vb2QQ0KMNyVKpVKZaA7//KXv4wFCxbEyJEj+7Zt27YtSqVS\njBgxIrq6uvp97d2Uy+Vobm6OjpEjo6lUGvzke5BSz/8reoTdN7YzonNcRERsrWyJxmgseKAa6ekp\neoLaGlX1P0r3XKNHFz1BzZQrlWjeti06Ojqiqalph/tV9eydcsop8fTTT/fbduGFF8aRRx4Z11xz\nzS5jC7A3qyq448ePj+nTp/fb1tjYGPvvv/87tgPQn//TDCDJbl8Qevjhh2swBkD9c4YLkERwAZII\nLkASwQVIIrgASQQXIIngAiQRXIAkgguQRHABkgguQBLBBUgiuABJBBcgieACJBFcgCSCC5BEcAGS\nFPaZy/+z9J8xduyOP054OKl8bPh/3HtnRIzbfmfc+Ii3Chymlnp7i56AHenuLnqC2imXIyZM2OVu\nznABkgguQBLBBUgiuABJBBcgieACJBFcgCSCC5BEcAGSCC5AEsEFSCK4AEkEFyCJ4AIkEVyAJIIL\nkERwAZIILkASwQVIIrgASQQXIIngAiQRXIAkgguQRHABkgguQBLBBUgiuABJBBcgieACJBFcgCSC\nC5BEcAGSCC5AEsEFSCK4AEkEFyCJ4AIkEVyAJIILkERwAZIILkASwQVIIrgASQQXIIngAiQRXIAk\ngguQRHABkgguQBLBBUgyqqgDnzm/Ek1NlaIOX1OlqId1dEbEuLd/uXVLRDQWOUztNNbJOrbr6Ch6\nAt5NT8+AdnOGC5BEcAGSCC5AEsEFSCK4AEkEFyCJ4AIkEVyAJIILkERwAZIILkASwQVIIrgASQQX\nIIngAiQRXIAkgguQRHABkgguQBLBBUgiuABJqg7uK6+8Ep/+9Kdj//33j7Fjx8bMmTNj5cqVQzEb\nQF2p6mPS33zzzTjppJPi5JNPjt/+9rcxadKk+Pvf/x4TJkwYovEA6kdVwf3Od74TLS0tceedd/Zt\nO/TQQ2s9E0BdquqSwn333RezZ8+OT37ykzFp0qQ49thj44477tjpY7q6uqJcLve7AeyNqgru+vXr\n47bbbovDDz88Hnjggbjooovi0ksvjbvuumuHj2ltbY3m5ua+W0tLy24PDTAclSqVSmWgO48ePTpm\nz54djz76aN+2Sy+9NJ588sl47LHH3vUxXV1d0dXV1Xe/XC5HS0tLdPzrX9HU1LQbo+85SiNKRY+w\n+8Z2RnSOi4iIrZUt0RiNBQ9UI411so7tOjqKnoB3US6Xo/k974mOjo6ddq2qM9wDDzwwpk6d2m/b\nUUcdFRs2bNjhYxoaGqKpqanfDWBvVFVwTzrppHjuuef6bVu3bl0ccsghNR0KoB5VFdwrrrgiHn/8\n8fjWt74Vzz//fCxbtiyWLFkSCxcuHKr5AOpGVcE97rjjYvny5XHPPffE9OnT45vf/Gbccsstcf75\n5w/VfAB1o6qfw42ImD9/fsyfP38oZgGoa95LASCJ4AIkEVyAJIILkERwAZIILkASwQVIIrgASQQX\nIIngAiQRXIAkgguQRHABkgguQBLBBUgiuABJBBcgieACJBFcgCRVf6ZZrTRPKEVEqajD11SlDtbR\nGRHjtt8ZNz7irQKHqaXe3qInYG8wamApdYYLkERwAZIILkASwQVIIrgASQQXIIngAiQRXIAkgguQ\nRHABkgguQBLBBUgiuABJBBcgieACJBFcgCSCC5BEcAGSCC5AEsEFSCK4AEkEFyCJ4AIkEVyAJIIL\nkERwAZIILkASwQVIIrgASQQXIIngAiQRXIAkgguQRHABkgguQBLBBUgiuABJBBcgieACJBFcgCSC\nC5BEcAGSCC5AEsEFSCK4AEkEFyCJ4AIkEVyAJIILkERwAZKMKurAjY0RpVJRR6+tff5TKXqE3VYZ\n1RkR496+s3VLRDQWOU7t9PQUPUFtjR1b9AS1091d9ATpnOECJBFcgCSCC5BEcAGSCC5AEsEFSCK4\nAEkEFyCJ4AIkEVyAJIILkERwAZIILkASwQVIIrgASQQXIIngAiQRXIAkgguQRHABkgguQBLBBUhS\nVXB7enria1/7WkyZMiX23XffeN/73hc33nhj9Pb2DtV8AHVjVDU7f+c734nbb789li5dGtOmTYun\nnnoqLrzwwmhubo7LLrtsqGYEqAtVBfexxx6Ls846K84444yIiDj00EPjnnvuiaeeempIhgOoJ1Vd\nUpgzZ0489NBDsW7duoiIWLNmTaxYsSI++tGP7vAxXV1dUS6X+90A9kZVneFec8010dHREUceeWSM\nHDkytm3bFjfddFOcd955O3xMa2tr3HDDDbs9KMBwV9UZ7r333ht33313LFu2LFatWhVLly6N7373\nu7F06dIdPmbx4sXR0dHRd2tvb9/toQGGo6rOcK+++uq49tpr49xzz42IiKOPPjpeeumlaG1tjQsu\nuOBdH9PQ0BANDQ27PynAMFfVGe5bb70VI0b0f8jIkSP9WBjAAFR1hnvmmWfGTTfdFAcffHBMmzYt\nVq9eHTfffHN87nOfG6r5AOpGVcG99dZb47rrrouLL744Nm3aFJMnT44vfvGL8fWvf32o5gOoG6VK\npVLJPGC5XI7m5uZobOyIUqkp89BD5j//KXqC3VcZ2xnbOsZFRMTWypZojMaCJ6qRnp6iJ6itsWOL\nnqB2uruLnqBmyuVyNE+YEB0dHdHUtOOueS8FgCSCC5BEcAGSCC5AEsEFSCK4AEkEFyCJ4AIkEVyA\nJIILkERwAZIILkASwQVIIrgASQQXIIngAiQRXIAkgguQpKrPNKuljedcEU2jRxd1+Nq6/faiJ9ht\nnT0R47bfGTc+4q0ip6mhevtE6Tr6WJq9kTNcgCSCC5BEcAGSCC5AEsEFSCK4AEkEFyCJ4AIkEVyA\nJIILkERwAZIILkASwQVIIrgASQQXIIngAiQRXIAkgguQRHABkgguQBLBBUgiuABJBBcgieACJBFc\ngCSCC5BEcAGSCC5AEsEFSCK4AEkEFyCJ4AIkEVyAJIILkERwAZIILkASwQVIIrgASQQXIIngAiQR\nXIAkgguQRHABkgguQBLBBUgiuABJBBcgieACJBFcgCSCC5BkVPYBK5VKRESUu7uzD81OdFYiovz2\nr8uViG2FTlND5XLRE7AXKP/v99n2vu1IqbKrPWrs5ZdfjpaWlsxDAqRob2+Pgw46aIdfTw9ub29v\nbNy4McaPHx+lUmlIjlEul6OlpSXa29ujqalpSI6RyXr2XPW0lgjrGaxKpRJbtmyJyZMnx4gRO75S\nm35JYcSIETv9G6CWmpqa6uKbZjvr2XPV01oirGcwmpubd7mPF80AkgguQJK6DG5DQ0Ncf/310dDQ\nUPQoNWE9e656WkuE9Qy19BfNAPZWdXmGC7AnElyAJIILkERwAZIILkASwQVIIrgASQQXIMn/B5Z7\n1S0GfxA4AAAAAElFTkSuQmCC\n"
}
}
],
"source": [
"mat = torch.concat([h,yhat],axis=1).data[:10]\n",
"plt.matshow(mat,cmap='bwr',vmin=-1,vmax=1)\n",
"plt.axvline(x=1.5,color='lime')\n",
"plt.xticks(range(6),[r'$h_1$',r'$h_2$',r'$P_A$',r'$P_b$',r'$P_c$',r'$P_d$']);"
],
"id": "886ae12d-fedb-4490-80d6-fd3ced8dc0ac"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## C. 구현2 – RNN\n",
"\n",
"ref: "
],
"id": "12b7e859-a465-4546-a589-fb915c7bf22e"
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"x = torch.tensor(df_train.x.map({'A':0,'b':1,'c':2,'d':3}))\n",
"y = torch.tensor(df_train.y.map({'A':0,'b':1,'c':2,'d':3}))\n",
"X = torch.nn.functional.one_hot(x).float()\n",
"y = torch.nn.functional.one_hot(y).float()"
],
"id": "fdc8c1a5-92a3-4f33-be0e-5584fd81fc5e"
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"torch.manual_seed(4) \n",
"rnncell = torch.nn.RNNCell(4,2)\n",
"cook = torch.nn.Linear(2,4)"
],
"id": "1f126ff1-45a0-411e-bf5d-7083379d075e"
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"rnn = torch.nn.RNN(4,2)\n",
"rnn.weight_ih_l0.data = rnncell.weight_ih.data\n",
"rnn.bias_ih_l0.data = rnncell.bias_ih.data\n",
"rnn.weight_hh_l0.data = rnncell.weight_hh.data\n",
"rnn.bias_hh_l0.data = rnncell.bias_hh.data"
],
"id": "45948ef6-303f-40f5-a58f-58efe6a35542"
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"loss_fn = torch.nn.CrossEntropyLoss() \n",
"optimizr = torch.optim.Adam(list(rnn.parameters())+list(cook.parameters()),lr=0.1)"
],
"id": "395f1a1e-c721-42d0-94cd-99a7d641d012"
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"Water = torch.zeros(1,2) # 첫 간장은 맹물 \n",
"for epoc in range(200):\n",
" ## 1\n",
" h,hL = rnn(X,Water)\n",
" netout = cook(h)\n",
" ## 2 \n",
" loss = loss_fn(netout, y)\n",
" ## 3 \n",
" loss.backward()\n",
" ## 4 \n",
" optimizr.step()\n",
" optimizr.zero_grad()"
],
"id": "14b78f0c-7191-4e54-9660-d7558e103a8c"
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"h,_ = rnn(X,Water)\n",
"yhat = soft(cook(h))\n",
"yhat"
],
"id": "d9aaa513-824a-4f37-ae31-e64e9e4c5201"
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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V3B/Zmhs9uugJaqcysAY4wwVIIrgASQQXIIngAiQRXIAkgguQRHABkgguQBLBBUgiuABJ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\n1S0GfxA4AAAAAElFTkSuQmCC\n"
}
}
],
"source": [
"mat = torch.concat([h,yhat],axis=1).data[:10]\n",
"plt.matshow(mat,cmap='bwr',vmin=-1,vmax=1)\n",
"plt.axvline(x=1.5,color='lime')\n",
"plt.xticks(range(6),[r'$h_1$',r'$h_2$',r'$P_A$',r'$P_b$',r'$P_c$',r'$P_d$']);"
],
"id": "e0f71e50-8478-4350-be24-aceb62b84cb9"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## D. 구현3 – RNN + GPU"
],
"id": "3a642509-c15c-4a08-9b9d-742f55ff747b"
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"x = torch.tensor(df_train.x.map({'A':0,'b':1,'c':2,'d':3}))\n",
"y = torch.tensor(df_train.y.map({'A':0,'b':1,'c':2,'d':3}))\n",
"X = torch.nn.functional.one_hot(x).float()\n",
"y = torch.nn.functional.one_hot(y).float()"
],
"id": "88ed3725-d932-44d3-b972-1f86fe09c400"
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"torch.manual_seed(4) \n",
"rnncell = torch.nn.RNNCell(4,2)\n",
"cook = torch.nn.Linear(2,4)"
],
"id": "527edf36-792e-4a00-a4b7-be2fbd2c0fac"
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"rnn = torch.nn.RNN(4,2)\n",
"rnn.weight_ih_l0.data = rnncell.weight_ih.data\n",
"rnn.bias_ih_l0.data = rnncell.bias_ih.data\n",
"rnn.weight_hh_l0.data = rnncell.weight_hh.data\n",
"rnn.bias_hh_l0.data = rnncell.bias_hh.data"
],
"id": "f683d18f-84b2-4e24-a294-9788f8a54ae4"
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"loss_fn = torch.nn.CrossEntropyLoss() \n",
"optimizr = torch.optim.Adam(list(rnn.parameters())+list(cook.parameters()),lr=0.1)"
],
"id": "944ce9c9-0737-43bd-8a3f-5c7e00219015"
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"X = X.to(\"cuda:0\")\n",
"y = y.to(\"cuda:0\")\n",
"rnn.to(\"cuda:0\") \n",
"cook.to(\"cuda:0\")\n",
"Water = torch.zeros(1,2).to(\"cuda:0\")\n",
"for epoc in range(200):\n",
" ## 1\n",
" h,hL = rnn(X,Water)\n",
" netout = cook(h)\n",
" ## 2 \n",
" loss = loss_fn(netout,y)\n",
" ## 3 \n",
" loss.backward()\n",
" ## 4 \n",
" optimizr.step()\n",
" optimizr.zero_grad()"
],
"id": "e6f0edcc-b379-4085-ab01-dcf45b090c21"
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"h,hL = rnn(X,Water)\n",
"netout = cook(h)\n",
"yhat = soft(netout)\n",
"yhat"
],
"id": "0168429e-84ea-4b9e-992a-1019798965a6"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- 살짝결과다름"
],
"id": "a1b5fcb6-7cf9-4935-ac24-0062dbc5c546"
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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}
}
],
"source": [
"mat = torch.concat([h,yhat],axis=1).data[:10].to(\"cpu\")\n",
"plt.matshow(mat,cmap='bwr',vmin=-1,vmax=1)\n",
"plt.axvline(x=1.5,color='lime')\n",
"plt.xticks(range(6),[r'$h_1$',r'$h_2$',r'$P_A$',r'$P_b$',r'$P_c$',r'$P_d$']);"
],
"id": "f986f897-ed60-4523-8c5d-e1c411571722"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## E. 구현4 – RNN + GPU + 맹물X"
],
"id": "2e7d09fa-8dac-4bfa-8b95-a92cea502154"
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"x = torch.tensor(df_train.x.map({'A':0,'b':1,'c':2,'d':3}))\n",
"y = torch.tensor(df_train.y.map({'A':0,'b':1,'c':2,'d':3}))\n",
"X = torch.nn.functional.one_hot(x).float()\n",
"y = torch.nn.functional.one_hot(y).float()"
],
"id": "0bd76e8a-d000-443b-830d-85e540dd52aa"
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"torch.manual_seed(4) \n",
"rnncell = torch.nn.RNNCell(4,2)\n",
"cook = torch.nn.Linear(2,4)"
],
"id": "dcca37f0-9e81-4b6c-9ef8-93b009e59236"
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"rnn = torch.nn.RNN(4,2)\n",
"rnn.weight_ih_l0.data = rnncell.weight_ih.data\n",
"rnn.bias_ih_l0.data = rnncell.bias_ih.data\n",
"rnn.weight_hh_l0.data = rnncell.weight_hh.data\n",
"rnn.bias_hh_l0.data = rnncell.bias_hh.data"
],
"id": "8a736532-c7da-4b59-9733-e45282bcc74d"
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"loss_fn = torch.nn.CrossEntropyLoss() \n",
"optimizr = torch.optim.Adam(list(rnn.parameters())+list(cook.parameters()),lr=0.1)"
],
"id": "b5aa2a0d-2da6-43b0-a7b9-c66ef21ba062"
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"X = X.to(\"cuda:0\")\n",
"y = y.to(\"cuda:0\")\n",
"rnn.to(\"cuda:0\") \n",
"cook.to(\"cuda:0\")\n",
"Water = torch.zeros(1,2).to(\"cuda:0\")\n",
"for epoc in range(200):\n",
" ## 1\n",
" h,_ = rnn(X)\n",
" netout = cook(h)\n",
" ## 2 \n",
" loss = loss_fn(netout,y)\n",
" ## 3 \n",
" loss.backward()\n",
" ## 4 \n",
" optimizr.step()\n",
" optimizr.zero_grad()"
],
"id": "6f7194ba-b0e3-4923-80df-268293eac90d"
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"h,_ = rnn(X)\n",
"netout = cook(h)\n",
"yhat = soft(netout)\n",
"yhat"
],
"id": "ed7a920e-6c5a-4918-a2dd-271f4a51412e"
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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3R7bqRo0qeoLqKQ+sAc5wAZIILkASwQVIIrgASQQXIIngAiQRXIAkgguQRHABkgguQBLB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\nL9YdZb8AAAAASUVORK5CYII=\n"
}
}
],
"source": [
"mat = torch.concat([h,yhat],axis=1).data[:10].to(\"cpu\")\n",
"plt.matshow(mat,cmap='bwr',vmin=-1,vmax=1)\n",
"plt.axvline(x=1.5,color='lime')\n",
"plt.xticks(range(6),[r'$h_1$',r'$h_2$',r'$P_A$',r'$P_b$',r'$P_c$',r'$P_d$']);"
],
"id": "76ced2b1-7cd7-401d-9b52-e231b408a105"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## F. 은닉노드 비교실험"
],
"id": "b7e06e1f-a9be-498c-afcc-77c44804a6d8"
},
{
"cell_type": "code",
"execution_count": 146,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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P3vb+++8bSWbBggWtVsOLdZA8XsqB19Y7L2USyeXG+uulXuC1OuTA++gFya1D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ZqlFStWqE+fPq4ODPAqcoBsRwYAcgCQAcSS8Hkua2tr9eyzzyocDmvYsGHN3i8SiSgSiUSvhzhn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\nUHOc3FdFNgAAAABJRU5ErkJggg==\n"
}
}
],
"source": [
"x = torch.tensor(df_train.x.map({'A':0,'b':1,'c':2,'d':3}))\n",
"y = torch.tensor(df_train.y.map({'A':0,'b':1,'c':2,'d':3}))\n",
"X = torch.nn.functional.one_hot(x).float().to(\"cuda:0\")\n",
"y = torch.nn.functional.one_hot(y).float().to(\"cuda:0\")\n",
"fig,ax = plt.subplots(5,5,figsize=(10,10))\n",
"for i in range(5):\n",
" for j in range(5):\n",
" rnn = torch.nn.RNN(4,2).to(\"cuda:0\")\n",
" cook = torch.nn.Linear(2,4).to(\"cuda:0\")\n",
" loss_fn = torch.nn.CrossEntropyLoss()\n",
" optimizr = torch.optim.Adam(list(rnn.parameters()) + list(cook.parameters()), lr=0.1)\n",
" for epoc in range(200):\n",
" ## 1\n",
" h,_ = rnn(X)\n",
" netout = cook(h)\n",
" ## 2 \n",
" loss = loss_fn(netout,y)\n",
" ## 3 \n",
" loss.backward()\n",
" ## 4 \n",
" optimizr.step()\n",
" optimizr.zero_grad()\n",
" h = rnn(X)[0].data.to(\"cpu\")\n",
" yhat = soft(cook(rnn(X)[0])).data.to(\"cpu\")\n",
" mat = torch.concat([h,yhat],axis=1)[:8]\n",
" ax[i][j].matshow(mat,cmap=\"bwr\")\n",
" ax[i][j].axvline(x=1.5,color=\"lime\")\n",
" ax[i][j].set_xticks(range(6),[r'$h_1$',r'$h_2$',r'$P_A$',r'$P_b$',r'$P_c$',r'$P_d$'])\n",
"fig.suptitle(\"RNN -- # of hidden nodes = 2\",size=20)\n",
"fig.tight_layout()"
],
"id": "a1ebda43-f6f5-4e0a-9cd8-5826653f7252"
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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cqVNbW2uKiopMRUWF2b17t9m2bZu56qqrTH5+vtm2bVubrBNUL2heEMuxK1kw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\nAAAAwWPyCgAAAAAIHpNXAAAAAEDw/h8d8+HLEuOUQQAAAABJRU5ErkJggg==\n"
}
}
],
"source": [
"x = torch.tensor(df_train.x.map({'A':0,'b':1,'c':2,'d':3}))\n",
"y = torch.tensor(df_train.y.map({'A':0,'b':1,'c':2,'d':3}))\n",
"X = torch.nn.functional.one_hot(x).float().to(\"cuda:0\")\n",
"y = torch.nn.functional.one_hot(y).float().to(\"cuda:0\")\n",
"fig,ax = plt.subplots(5,5,figsize=(10,10))\n",
"for i in range(5):\n",
" for j in range(5):\n",
" rnn = torch.nn.RNN(4,3).to(\"cuda:0\")\n",
" cook = torch.nn.Linear(3,4).to(\"cuda:0\")\n",
" loss_fn = torch.nn.CrossEntropyLoss()\n",
" optimizr = torch.optim.Adam(list(rnn.parameters()) + list(cook.parameters()), lr=0.1)\n",
" for epoc in range(200):\n",
" ## 1\n",
" h,_ = rnn(X)\n",
" netout = cook(h)\n",
" ## 2 \n",
" loss = loss_fn(netout,y)\n",
" ## 3 \n",
" loss.backward()\n",
" ## 4 \n",
" optimizr.step()\n",
" optimizr.zero_grad()\n",
" h = rnn(X)[0].data.to(\"cpu\")\n",
" yhat = soft(cook(rnn(X)[0])).data.to(\"cpu\")\n",
" mat = torch.concat([h,yhat],axis=1)[:8]\n",
" ax[i][j].matshow(mat,cmap=\"bwr\")\n",
" ax[i][j].axvline(x=2.5,color=\"lime\")\n",
" ax[i][j].set_xticks(range(7),[r'$h_1$',r'$h_2$',r'$h_3$',r'$P_A$',r'$P_b$',r'$P_c$',r'$P_d$'])\n",
"fig.suptitle(\"RNN -- # of hidden nodes = 3\",size=20)\n",
"fig.tight_layout()"
],
"id": "a334fe0f-a1af-4058-b833-a56c6ae7dad3"
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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wJkyYoOXLl6t79+76yU9+0mrruOpl8eLFikQiKisrSzy2adMmSVKXLl1aZR1X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0UmWmzP8bJly5SVlaX+/fsnHvv444+1Y8eOxKciLuts375dV1xxhaZMmZJ2naKiIi1fvlzr16/X\ntGnTtG3btpRqPP/88+rVq5d69erV4DzVfdF80KBB9T7nrrvu0sSJEyVJffr00apVq1KuE4/HtXv3\nbo0fP16SVFZWdshPjBqrM2PGDJ188skaNmyYJKlTp07KyclJucaIESPUt29fSdJxxx1nfdE+E5CJ\n+pEJMlGHTOxDJshEnZbKhIs8JFOnNWbCRR6SrUMmyER9XGTCp21EsnWCZuLgV20my5cvV+/evdWu\nXbvEY0uXLlVRUVFKx4UnUycej2vs2LGaMGGCTjnllMD9dOnSRWVlZZo3b54uuOCCpGs88sgjmj59\nup599llVVVVpz549Kiws1N13323VX7JkiY455hgVFRUdstf58+frjTfe0MUXXyxJqqqq0iWXXHLQ\n8xqrs3LlSvXt29f6zsGhVqDG6qxYsUJDhgw55P+l0suBr71kyRKNHTu2wZphQybIxNd7IRNkgkzY\nvZAJfzLhIg/J1GmNmXCRh2R7IRNkoikz4dM2Itl+Amcipf3MLaCxwyAaU1tbay666CJzzz33BOpj\n69atprKy0hhjTGVlpenbt69Zvnx52vUaOgyiMSNGjDBvvvlm4v4bb7xhzjzzzLR66Nu3r9m9e7fZ\ntm2bGTx4sPnss89SrvPb3/42cZa6vXv3mu3bt6dc49e//rW5+eabjTHGvPrqqyYrK8vEYrGU62QC\nMnEwMpHZyMTByERm8yETrvNgTHgy4SIPxpCJVJCJg7nIhE/bCGPcZKLF9hwn49vf/raWLFmi6upq\ndevWTTNmzEjqU4UDvfnmm3r66adVVlammTNnSpL++Mc/WocqJGPTpk26+uqrZYyRMUY33HBDixy6\n8pe//EWRSMT6xOrYY4895KFBjVmxYoXOP/98DRkyRLW1tfrNb36jww47LOU6V155pS688EKVlpaq\nTZs2euSRR3TiiSemVOOyyy7T6NGjdcIJJ6i0tFQ9e/ZM6uQJmYZMHIxMZDYycTAykdl8yYQveZD8\ny4SLPEhkIllk4mCuMuHTNkJyk4mIMfWcJg0AAAAAgAzRopdyAgAAAADABwyOAQAAAAAZj8ExAAAA\nACDjMTgGAAAAAGQ8BscAAAAAgIzH4BgAAAAAkPG8GxzH43Hde++9isfjoanjUy+u6vjUS9j5tqzD\nuP6EcZ7CzLdlHcb1J4zzFGa+Leswrj9hnKcw82lZ+9SLqzo+9eKyjuThdY5jsZii0agqKytVWFgY\nijo+9eKqjk+9hJ1vyzqM608Y5ynMfFvWYVx/wjhPYebbsg7j+hPGeQozn5a1T724quNTLy7rSB7u\nOQYAAAAAoLkxOAYAAAAAZLyc5n7B2tpabd68WQUFBYpEIgf9fywWs/5Nl091fOrFVZ3m7MUYo507\nd6pr167Kygrf5zlkomV7cVWHTLjRWB4kv37vrur41IurOmTCDTLR8r24qkMm3GhtmfCpF1d1fOol\n2TrJZqLZv3O8adMmlZSUNOdLIiQqKirUrVu3lm7DOTKBdIUxE+QBQZAJwEYmAFtjmWj2PccFBQWS\npI4dKxSJBPvC9NNPB+/noYeC15Ckacv7pT1tdbtadV28WZK02XyiDuoQvKGiouA1vvwyeA0HYrGY\nSrp3T6w7YVM3XxWHHabCoJ/uuthYLFsWvIYkDRmS9qTV7WrU9fmFkqTNf1unDsoL3s+xxwavUVER\nvIYk7d4daPLYzp0qOfroUGaibp6+8Y0KZWcH20Z8+GHwfu68M3gNSXrvvWDT782t1kuPdpXkaDtx\n+OHBppekLVuC15AkB3u1YrGYSnr0CHUmKiZPVmH79oFq/XDO2MD9/HvuHYFrSNIpb/xroOlr21Vr\n9f85zETnzsGml6TPPgteQ3KXiZC+d0pk4uSTVZgTcChz7bWB+/nbyDGBa0jS/2/v7qOkqg683/9O\nd0NB013VgkIklEqMGqBBHXAiGt8SJLdHHeMYR40a4stMjKhR4iTTyc3EmMQ2d54x3oxPWGJ8SByX\nYt5AZyXigrmCJhkygKAGXxGURhEDalV3EQvoOvcP7IYdaKhTe1ez65zvZ61aUm2dXbu669tVu+p0\nnQ9/2G77sLGg0sYPmujptG9i+HC77SVv1hJS+U0M+OK4d/eHIEirrs7uic8wB2vIQYPsx5Bktaip\nr5f0wbciHabdLI772c0kEs8+AbG/XWdqXe/tStfV2S+O6+tdTMh+DEmyeMCqbwh2NzGoOX5NWC6O\ne8Wxid7bVF+ftl4cu/j2DBliP4Zk/1gTDKp3+zjhUw8Od/mMcxPpoUOVbrR7oXDwYPufWTqVsh5D\nkn3fDTRRjlg30dBgvzi2bEqSBjn6uVv/qII9muiJWRMOHaiJeP0RAgAAAAAAFWBxDAAAAABIvIoW\nxz/60Y80duxYDRkyRJMnT9ZTTz3lel5ATaEJwEQTgIkmABNNwEeRF8cPP/ywbrrpJn3jG9/QqlWr\ndNppp6mtrU0bNmyoxvwA79EEYKIJwEQTgIkm4KvIi+M777xTV199ta655hqNGzdOd911l7LZrGbP\nnl2N+QHeownARBOAiSYAE03AV5EWx9u3b9fKlSs1ffp04+vTp0/X73//+31uUywWlc/njRMQFzQB\nmKI2QQ+IO5oATDQBn0VaHG/ZskU9PT0aNWqU8fVRo0bprbfe2uc2HR0dymQyfScO2o04oQnAFLUJ\nekDc0QRgogn4rKIP5PrL40OFYdjvMaPa29uVy+X6Tp2dnZVcJeA1mgBM5TZBD0gKmgBMNAEfRTpy\n9qGHHqr6+vq9XtV5++2393r1p1cqlVLK0QHjAd/QBGCK2gQ9IO5oAjDRBHwW6Z3jwYMHa/LkyVq0\naJHx9UWLFumUU05xOjGgFtAEYKIJwEQTgIkm4LNI7xxL0qxZs3TFFVdoypQpmjp1qubMmaMNGzbo\n2muvrcb8AO/RBGCiCcBEE4CJJuCryIvjiy++WFu3btVtt92mTZs2qbW1Vb/5zW905JFHVmN+gPdo\nAjDRBGCiCcBEE/BV5MWxJF133XW67rrrXM8FqFk0AZhoAjDRBGCiCfiook+rBgAAAAAgTlgcAwAA\nAAASr6Ldql145x37Maaesu/jyEYx//DD7SciKdj0ZuUbNxYkNe369/Dh0jb726WeHvsxtm+3H0OS\nBg92M07cvf229RCpdzZZj9Hg6Mf10Xzl25Z27NHEoYdJ2xxMqFRyMIgb4WC7Q1LYbl8LVrySUfpg\nT0KS7jzEzThdXVabFxrD3iKkpmb7JjzqwYm6+L/Wf/ytF6iuzq6KVz9ytvU8Dlmx6MAXKsO72+x+\nj9EE7vnbX2voULsmrv87++fcQ8eMsR5Dknbs3Gi1fWGndjeRznjRRCgHaxpJgUIn45Qj/o8mAAAA\nAAAcAItjAAAAAEDisTgGAAAAACRe5MXxk08+qfPOO0+jR49WEARasGBBFaYF1AZ6AEw0AZhoAjDR\nBHwWeXFcKBR0/PHH6+67767GfICaQg+AiSYAE00AJpqAzyJ/WnVbW5va2tqqMReg5tADYKIJwEQT\ngIkm4DP+5hgAAAAAkHhVP85xsVhUsVjsO5/PWxz8FIgBmgB2owfARBOAiSYwkKr+znFHR4cymUzf\nKZvNVvsqAa/RBLAbPQAmmgBMNIGBVPXFcXt7u3K5XN+ps7Oz2lcJeI0mgN3oATDRBGCiCQykqu9W\nnUqllEqlqn01QM2gCWA3egBMNAGYaAIDKfLiuLu7W2vXru07v379eq1evVrDhw/XEUcc4XRygO/o\nATDRBGCiCcBEE/BZ5MXxihUrdNZZZ/WdnzVrliRpxowZ+slPfuJsYkAtoAfARBOAiSYAE03AZ5EX\nx2eeeabCMKzGXICaQw+AiSYAE00AJpqAzzjOMQAAAAAg8VgcAwAAAAASr+qfVt2f739fGjrUcpAv\nB/YT2bTJfgxJoSqfS0FSU++Zd96RNMzBjBwYMsTNOKWSm3Fi7tBBOQVB2moMFz+yXN5BV5Iyr1W+\ny1TYuMe/u7sVOmgikINduOrcvJ4YWDbh5LZ4LqOcJLseXAgHjXIyTrBzh90AO/d4pOjukhePE456\n4DGiPEOHSvX1loO8/LL1PN59z81jhPXvsQaaSLqvftV+jBscPJ4O32Y/D0l6x3qE3U24eu5kK6hz\n8/tiIJvgnWMAAAAAQOKxOAYAAAAAJB6LYwAAAABA4rE4BgAAAAAkXqTFcUdHh0466SQ1Nzdr5MiR\n+sxnPqOXXnqpWnMDvEcTgIkmABNNACaagM8iLY6XLl2qmTNnatmyZVq0aJF27typ6dOnq1AoVGt+\ngNdoAjDRBGCiCcBEE/BZpEM5LVy40Dg/d+5cjRw5UitXrtTpp5/udGJALaAJwEQTgIkmABNNwGdW\nf3Ocy+UkScOHD3cyGaDW0QRgognARBOAiSbgk0jvHO8pDEPNmjVLn/jEJ9Ta2trv5YrFoorFYt/5\nfD5f6VUCXqMJwFROE/SAJKEJwEQT8E3F7xxff/31evbZZ/XQQw/t93IdHR3KZDJ9p2w2W+lVAl6j\nCcBUThP0gCShCcBEE/BNRYvjG264QY8++qieeOIJjRkzZr+XbW9vVy6X6zt1dnZWNFHAZzQBmMpt\ngh6QFDQBmGgCPoq0W3UYhrrhhhs0f/58LVmyRGPHjj3gNqlUSqlUquIJAj6jCcAUtQl6QNzRBGCi\nCfgs0uJ45syZevDBB/XII4+oublZb731liQpk8lo6NChVZkg4DOaAEw0AZhoAjDRBHwWabfq2bNn\nK5fL6cwzz9Thhx/ed3r44YerNT/AazQBmGgCMNEEYKIJ+CzybtUAdqMJwEQTgIkmABNNwGdWxzkG\nAAAAACAOWBwDAAAAABIv0m7VLl37tYzSB+vKqyCQzS4iBUlNu/7Z1CxtczChUsmPMVC2P/1JSltG\nEdQF1vOwuy/vIW+x7c7d/wyamhQ4aCIs2d+uwFEToex+Trbb14KcMkoHB/92Bm97+HvQxeMEjxE1\nZ+1ayTaJYPvr1vP4yEesh5Akvb3MbvuCpL7POKaJRMrJj7VE12tunjc1p+0C32M14ea5k4P7s4vn\nXq6U+9yJd44BAAAAAInH4hgAAAAAkHgsjgEAAAAAicfiGAAAAACQeJEWx7Nnz9akSZOUTqeVTqc1\ndepUPfbYY9WaG+A9mgBMNAGYaAIw0QR8FmlxPGbMGN1xxx1asWKFVqxYoU9+8pM6//zztWbNmmrN\nD/AaTQAmmgBMNAGYaAI+C8IwtPqM7eHDh+tf//VfdfXVV5d1+Xw+r0wmo5zkxcevu2J1+JvGglTY\n9eHr3cOkYb4cyskT+XxemZYW5XI5pW2PdTQAKm3ivffsb59Xh3KyUYUmnBzKydH3xvZQTPl8Xi0t\nmVg2YTxG+HAop9CT36Wum4jRY4QU78eJ3iYGDcopCOxu2/btVptLcncop2XWh3IqaOxhNNGfJDTh\ny1qiK+/JoZwapabCrn/70oRPh54s97lTxcc57unp0c9//nMVCgVNnTq138sVi0UVi0VjYkAc0QRg\nKqcJekCS0ARgogn4JvIHcj333HNqampSKpXStddeq/nz52v8+PH9Xr6jo0OZTKbvlM1mrSYM+IYm\nAFOUJugBSUATgIkm4KvIu1Vv375dGzZs0Hvvvadf/vKX+vGPf6ylS5f2e4fe16s92WzWm10hXGG3\n6urxfdcgV02wW/Ue2K16v3zfrTpKE/t9jGC36t3YrXq/4vQ40V8T7FZtYrfq/UtCE76sJditun+1\nuFu19d8cT5s2TUcffbTuueeesifm098JuMLiuHp8/wX/lyptgsXxHlgc75fvi+O/FKUJ/ua4HyyO\n9yvOjxP8zfG+sTjevyQ04ctagsVx/2pxcWx9nOMwDI1Xc4CkownARBOAiSYAE03AF5E+kOvrX/+6\n2tralM1m1dXVpXnz5mnJkiVauHBhteYHeI0mABNNACaaAEw0AZ9FWhxv3rxZV1xxhTZt2qRMJqNJ\nkyZp4cKFOvvss6s1P8BrNAGYaAIw0QRgogn4LNLi+L777qvWPICaRBOAiSYAE00AJpqAz6z/5hgA\nAAAAgFrH4hgAAAAAkHiRdqt2atgwyfIwHUF3l/U0wjn3Wo8hSeE/Vn5bCpKaes90d0ka5mBGHqnj\nNZhyHHaYdRIqtrZazyP848H/2P09mwi7uxU6aMKLQ1R9wPaQWwf/J1R9GeWk0IeDdLhheziLWD9O\n8BhRli06VGnb+hvsD80SrNthPYYkffSjdtuHjZI2fXCGJhLp5HE51dfbPU40OFgJrbI8BFMv++cp\nux8pXDx3cvG8ydlzLwdNlPtToj4AAAAAQOKxOAYAAAAAJB6LYwAAAABA4lktjjs6OhQEgW666SZH\n0wFqG00AJpoAdqMHwEQT8E3Fi+Ply5drzpw5mjRpksv5ADWLJgATTQC70QNgogn4qKLFcXd3ty67\n7DLde++9OuSQQ1zPCag5NAGYaALYjR4AE03AVxUtjmfOnKlzzjlH06ZNcz0foCbRBGCiCWA3egBM\nNAFfRT6617x58/T0009r+fLlZV2+WCyqWCz2nc/n81GvEvAaTQCmKE3QA+KOxwjARBPwWaR3jjs7\nO/XlL39ZDzzwgIYMGVLWNh0dHcpkMn2nbDZb0UQBH9EEYIraBD0gzniMAEw0Ad8FYRiG5V54wYIF\nuuCCC1RfX9/3tZ6eHgVBoLq6OhWLReP/Sft+tSebzSo3bJjSQWA3+e4uq+0lKZxzr/UYkqR//MeK\nNy00Sk2FXf/uDrs0TMPczMkXdXZHDMtLykjK5XJKp9NOpuSKyyYGDcopCOxuX/HYiVbbS5L++Ef7\nMSzt2URX2O2kiUBl/6qrPpro+3/99SDlJPl122yEsnu8i/XjhGUPkr9NOH3eNGiQ9fMmlUp220sK\ndu6wHkOSbH9MYWNBXZuaJNHEviShiXHjcqqvt7ttDZH3od3bqtWWXX7A+nlKY0Eq7GrCxXOnOD1v\nkspvItJd4lOf+pSee+4542tXXnmlPvaxj+lrX/vaXndmSUqlUkqlUlGuBqgZNAGYojZBD4gzHiMA\nE03Ad5EWx83NzWptbTW+NmzYMI0YMWKvrwNJQBOAiSaA3egBMNEEfGf/HjUAAAAAADXOek/7JUuW\nOJgGEB80AZhoAtiNHgATTcAnvHMMAAAAAEg8FscAAAAAgMRjcQwAAAAASDwHR/eqUKEgWR6vL/z/\nnrCeRvDJf7AeYxebcQqSdh2XTE3N0jYH03FwLENnbOeSz0stLU6m4rMtOzL2R3V1cIhiV8e1sz2u\na6+gqUmBJ004u000cUA5OejBhRNPdDLM2SPsuuoZ4vhxIk6PEVIimsjs2CLbY3//6lf28wj/zs3v\nQeXtNi/s7CuCJvYlAU0sWz/K/tjf779vPQ9nz5tu/bbV9oVB2/uacPLcyaPnTSrZf4/DfF5qyRzw\ncrxzDAAAAABIPBbHAAAAAIDEY3EMAAAAAEi8SIvjW2+9VUEQGKcPfehD1Zob4D2aAEw0AZhoAjDR\nBHwW+QO5JkyYoMWLF/edr6+vdzohoNbQBGCiCcBEE4CJJuCryIvjhoYGXt0B9kATgIkmABNNACaa\ngK8i/83xK6+8otGjR2vs2LG65JJLtG7dumrMC6gZNAGYaAIw0QRgogn4KtI7xx//+Md1//3369hj\nj9XmzZv13e9+V6eccorWrFmjESNG7HObYrGoYrHYdz6ftzywHeARmgBMUZugB8QdTQAmmoDPIr1z\n3NbWpgsvvFATJ07UtGnT9Otf/1qS9NOf/rTfbTo6OpTJZPpO2WzWbsaAR2gCMEVtgh4QdzQBmGgC\nPrM6lNOwYcM0ceJEvfLKK/1epr29Xblcru/U2dlpc5WA12gCMB2oCXpA0tAEYKIJ+CTyB3LtqVgs\n6oUXXtBpp53W72VSqZRSqZTN1QA1gyYA04GaoAckDU0AJpqATyK9c3zLLbdo6dKlWr9+vf7whz/o\ns5/9rPL5vGbMmFGt+QFeownARBOAiSYAE03AZ5HeOd64caMuvfRSbdmyRYcddphOPvlkLVu2TEce\neWS15gd4jSYAE00AJpoATDQBn0VaHM+bN69a8wBqEk0AJpoATDQBmGgCPrP6QC4AAAAAAOKAxTEA\nAAAAIPGsPq3aRkuQUxCkrcYofdLRZBwIFVS8bUFSU++Z7i5Jw+wnVOfgdY9SyX4MDKhAofUYNvfl\nqvCqCfvvL8qTUU6S3WOEC0NecDPO4MF224eNe5xx0QSPETUnp4x1EcHfOXiM+Pu/tx5DkoKfPWw5\nwh7PnmgimTIZ+5+bg0/BDl9z87wpuNWyz8aC9PXbd/3bmybcPG9y8fy23DF45xgAAAAAkHgsjgEA\nAAAAicfiGAAAAACQeCyOAQAAAACJF3lx/MYbb+jyyy/XiBEj1NjYqBNOOEErV66sxtyAmkATgIkm\nABNNACaagK8ifVr1u+++q1NPPVVnnXWWHnvsMY0cOVKvvvqqWlpaqjQ9wG80AZhoAjDRBGCiCfgs\n0uL4+9//vrLZrObOndv3taOOOsr1nICaQROAiSYAE00AJpqAzyLtVv3oo49qypQpuuiiizRy5Eid\neOKJuvfee/e7TbFYVD6fN05AXNAEYIraBD0g7mgCMNEEfBZpcbxu3TrNnj1bxxxzjB5//HFde+21\nuvHGG3X//ff3u01HR4cymUzfKZvNWk8a8AVNAKaoTdAD4o4mABNNwGdBGIZhuRcePHiwpkyZot//\n/vd9X7vxxhu1fPly/fd///c+tykWiyoWi33n8/m8stmsgiCnIEhbTF0qlaw2dypUUPG2hUapqbDr\n391hl4ZpmP2E6hx8ELkn3+B8Pq9MS4tyuZzSabv7jGsum8hJsr11gcrOuV8292VXfG0iLNl/fyX7\nn1OcmuivBzkpwt6QIW7GGTzYbvuwsaCuTU2SHDURo8cIKRlNePMY8fcXW48hScHPHrYboLEgFWii\nP4loYtQopW1/bqmU3faS9Npr9mPIQZ8eNuHL8yap/CYi3erDDz9c48ePN742btw4bdiwod9tUqmU\n0um0cQLigiYAU9Qm6AFxRxOAiSbgs0iL41NPPVUvvfSS8bWXX35ZRx55pNNJAbWCJgATTQAmmgBM\nNAGfRVoc33zzzVq2bJluv/12rV27Vg8++KDmzJmjmTNnVmt+gNdoAjDRBGCiCcBEE/BZpMXxSSed\npPnz5+uhhx5Sa2urvvOd7+iuu+7SZZddVq35AV6jCcBEE4CJJgATTcBnkY5zLEnnnnuuzj333GrM\nBahJNAGYaAIw0QRgogn4ysFH8wEAAAAAUNtYHAMAAAAAEi/ybtWuhOGuk9UYDo7H+thvHB1/629s\nxilI2nVcMjU1S9scTMijY+1h4Lg4TGPg6Jh0dvxswsVx9iT7310+HIu62nLKeHCUY0lTPuFmnN/+\n1mrzws6+Itw0wWNEzTl5XE719XZVhD96ynoewemWxyf+gO3vsT0eJWgioTKbX5bt0b+dPJ6uXWs/\nhqTwGLsncYUgdNqEi2MUu3reNJB45xgAAAAAkHgsjgEAAAAAicfiGAAAAACQeJEWx0cddZSCINjr\nxEG7kVQ0AZhoAjDRBGCiCfgs0gdyLV++XD09PX3n//jHP+rss8/WRRdd5HxiQC2gCcBEE4CJJgAT\nTcBnkRbHhx12mHH+jjvu0NFHH60zzjjD6aSAWkETgIkmABNNACaagM8q/pvj7du364EHHtBVV12l\nIIj/YUWAA6EJwEQTgIkmABNNwDcVH+d4wYIFeu+99/SFL3xhv5crFosqFot95/P5fKVXCXiNJgBT\nOU3QA5KEJgATTcA3Fb9zfN9996mtrU2jR4/e7+U6OjqUyWT6TtlsttKrBLxGE4CpnCboAUlCE4CJ\nJuCbihbHr7/+uhYvXqxrrrnmgJdtb29XLpfrO3V2dlZylYDXaAIwldsEPSApaAIw0QR8VNFu1XPn\nztXIkSN1zjnnHPCyqVRKqVSqkqsBagZNAKZym6AHJAVNACaagI8iv3NcKpU0d+5czZgxQw0NFf/J\nMhAbNAGYaAIw0QRgogn4KvLiePHixdqwYYOuuuqqaswHqDk0AZhoAjDRBGCiCfgq8ks106dPVxiG\n1ZgLUJNoAjDRBGCiCcBEE/BVxZ9WDQAAAABAXLA4BgAAAAAk3oD/BfzuXSjsD+Dt4hDg27Z5cCDx\nsNB3Y/Kh1ONizBgdIL33YO9x3f2m93a5+ImFYUx+7jFvIlRgtX2cm3DZgxM7dx7sGUiSCqHcNuFR\nDy4koYmeHgfPmwoF6zFc1Wk7Ck3sXxKa8GUtoa4uF6NIlj8r102EDpoI5M/9r9wmBnxx3NV3B7I/\ngHfGegRJn3Uyip0/q+/G9H8I9IhaWlyN5I2uri5lMh78vBzrbcLJIe3DmHx/aKIscWzCaQ8uLFt2\nsGewi+smYtiDFO8mXn7ZwfOmNushnLH+KdFEWeLchDdriRNPdDGKvW1y3ES87je9DtREEA7wS0ql\nUklvvvmmmpubFQR7v3uSz+eVzWbV2dmpdDpd8fX4NI5Pc3E1zkDOJQxDdXV1afTo0aqri99fAtAE\ntynqOHFu4kA9SH793F2N49NcXI1DE27QxMGfi6txaMKNWmvCp7m4GsenuZQ7TrlNDPg7x3V1dRoz\nZswBL5dOp62+ST6O49NcXI0zUHOJ26uee6IJP+biahyasFNuD5JfP3dX4/g0F1fj0IQdmvBnLq7G\noQk7tdqET3NxNY5PcylnnHKaiNdLSQAAAAAAVIDFMQAAAAAg8bxbHKdSKX3rW99SKpWKzTg+zcXV\nOD7NJe58+17H8f4Tx9sUZ759r+N4/4njbYoz377Xcbz/xPE2xZlP32uf5uJqHJ/m4nIc6SB8IBcA\nAAAAAL7x7p1jAAAAAAAGGotjAAAAAEDisTgGAAAAACQei2MAAAAAQOKxOAYAAAAAJB6LYwAAAABA\n4rE4BgAAAAAkHotjAAAAAEDisTgGAAAAACQei2MAAAAAQOKxOAYAAAAAJB6LYwAAAABA4rE4BgAA\nAAAkHotjAAAAAEDiHfTF8Ve+8hWdd955sRrH1VyQTD7dl12NQxOw4dN92dU4NAEbcbwv0wRs+HQ/\n9GkuiO6gL45Xr16t448/PlbjuJrL6aefriAIFASBBg0apOOOO04PPvhgTY/jai5x5tN92dU4NFH9\nucSZT/dlV+PQRPXnEmdxvC/HsQmf5hJ3Pt0PfZqLFM/7clWbCA+yESNGhD/72c9iNY6LMUqlUtjc\n3Bx2dHSEmzZtCtetWxdeddVVYUNDQ7hu3bqaHMfVXOLOp/uyq3FoorpziTuf7suuxqGJ6s4l7uJ2\nX3Y1ThzvyzRRHp/uhz7NJY735Wo3cVAXxxs2bAglhb/4xS/CadOmhUOHDg2PPfbYcNmyZTU7jqu5\nvPTSS6Gk8Kmnnur72tq1a0NJ4YIFC2pyHFdziTOf7suuxqGJ6s8lzny6L7sahyaqP5c4i+N9OY5N\n+DSXuPPpfujTXMIwnvflajdxUHerXr16tSTp3//939Xe3q5nnnlGRxxxhP75n/+5ZsdxNZeVK1cq\nCAJNmjSp72sbN26UJI0aNaomx3E1lzjz6b7sahyaqP5c4syn+7KrcWii+nOJszjel+PYhE9ziTuf\n7oc+zUWK53256k1YL68t3HbbbeEhhxwSbt68ue9rd999dzhhwoQwDMPwM5/5TNjS0hJeeOGFFY+z\nYcOG8IwzzgjHjRsXTpw4cb+7J+xvnHw+H06ZMiU8/vjjw9bW1nDOnDkV3aYwDMNCoRAeccQR4Ve+\n8pV+53LLLbeEH/nIR/rOv/jii+GUKVPCE044Iezp6en7+gUXXBCeccYZFY/zn//5n+H111/f7/ZR\n5+NyjNNPPz1cv359WWPHBU3QBE2YaIImaMLkUxMueijnNoVh7TXhoodKxqGJXWhiFxdN+PQYUck4\nUZs46O8cn3/++Ro5cmTf19atW6ePfvSjkqQbb7xR999/v9U4DQ0Nuuuuu/T8889r8eLFuvnmm1Uo\nFCKP09jYqKVLl2r16tX6wx/+oI6ODm3dujXybZKk733ve/r4xz++39u0cuVKvfbaa2pqatKQIUN0\nwgknaMKECVq4cKHq6nb92FatWqW33npLL774YsXjPPvsszrxxBP3O5dy5+N6jNdee01HHXVUWWPH\nBU30jyZoohdN7EITNNHrYDXhoodybpNUe0246KGScWhiF5rYxUUTPj1GVDJO1CYO+uJ46tSpxtdW\nrVqlE044QZJ01llnqbm52Wqcww8/vG+8kSNHavjw4XrnnXcij1NfX6/GxkZJ0vvvv6+enh6FYRj5\nNr3yyit68cUX9Td/8zf7vU2rVq3SP/3TP2n16tVat26dtm3bpp/85CfG7gLf/OY3dccdd2jYsGHa\nsmVLReM8++yzeuGFFzR58mRNmDBBL7/8ckXjvP766zr33HP77qBvvPFG5DHWrFmjk08+Wccff7zu\nvPNOZbPZ/X6P4ogm+kcTNNGLJnZvQxM0IR28Jlz0UM5tqsUmXPRQzjg0QRP746IJnx4jyhnHuomy\n32N2LJ/Ph0EQhP/zP/9jfP2QQw4J58+f33f+iSee2O9uEOWOE4ZhuHz5cmN3hKjjvPvuu+GkSZPC\noUOHhnfffXdFY/zt3/5t+NJLL4Vz587tdzeIV199NZQULl68uL+bHS5btiycNm1aGIZheM4554RL\nly6taJxx48aFP/zhD8MwDMPZs2eHX/ziFyOPUywWwwkTJvTNYevWreGOHTsijbFt27awtbU1XLNm\nTRiGYXjeeeeFX/rSl/qddxzRBE3siSZogiZMNOFXEy56KHecWmvCRQ/ljEMTNFHtJnx6jChnHBdN\nHLR3jlevXq26ujpNnDix72uvv/663n333b5XRVyOs3XrVn3+85/XnDlzKh6npaVFzzzzjNavX68H\nH3xQmzdvjjTGI488omOPPVbHHnvsfm9T7x+aT548ud/LfPOb39Rtt90mSRo3bpyef/75yOMUi0Vt\n375dM2fOlCRNmjRpn68YHWic+fPn6+STT9bpp58uSRo+fLgaGhoij3HmmWdq/PjxkqTjjjvO+EP7\nJKCJ/tEETfSiiV1ogiZ6HawmXPRQzji12ISLHsodhyZooj8umvDpMaLccWyb2PtaB8gzzzyjj33s\nYxoyZEjf11atWqWWlpZI+4WXM06xWNQFF1yg9vZ2nXLKKdbzGTVqlCZNmqQnn3xSF110Udlj3HPP\nPZo3b55+/vOfq7u7Wzt27FA6nda//Mu/GOM//fTT+uhHP6qWlpZ9zvWpp57Sb3/7W1166aWSpO7u\nbn3uc5/b63IHGmfNmjUaP3688TcH+7oDHWic5557TieddNI+/1+Uuex53U8//bQuuOCC/Y4ZNzRB\nE385F5qgCZow50IT/jThoodyxqnFJlz0UO5caIImqtmET48R5c7HuolI7zMfBAfaDeJASqVSeMkl\nl4Tf+ta3rObx1ltvhblcLgzDMMzlcuH48ePDZ555puLx9rcbxIGceeaZ4e9+97u+87/97W/DT33q\nUxXNYfz48eH27dvDzZs3h1OmTAn/9Kc/RR7nhz/8Yd+n1O3cuTPcunVr5DH+7d/+LbzpppvCMAzD\nxx9/PKyrqwvz+XzkcZKAJvZGE8lGE3ujiWTzoQnXPYRhfJpw0UMY0kQUNLE3F0349BgRhm6aOGjv\nHJfj05/+tJ5++mkVCgWNGTNG8+fPL+tVhT397ne/08MPP6xJkyZpwYIFkqT/+I//MHZVKMfGjRt1\n9dVXKwxDhWGo66+//qDsuvJf//VfCoLAeMXqmGOO2eeuQQfy3HPP6cILL9RJJ52kUqmkH/zgBzr0\n0EMjj/OFL3xBF198sVpbWzVo0CDdc889+uu//utIY1x++eVqa2vTX/3VX6m1tVVjx44t68MTkoYm\n9kYTyUYTe6OJZPOlCV96kPxrwkUPEk2Uiyb25qoJnx4jJDdNBGHYz8ekAQAAAACQEAf1UE4AAAAA\nAPiAxTEAAAAAIPFYHAMAAAAAEo/FMQAAAAAg8VgcAwAAAAASj8UxAAAAACDxWBwDAAAAABLPu8Vx\nsVjUrbfeqmKxGJtxfJqLq3F8mkvc+fa9juP9J463Kc58+17H8f4Tx9sUZ759r+N4/4njbYozn77X\nPs3F1Tg+zcXlOJIUhGEYWo/iUD6fVyaTUS6XUzqdjsU4Ps3F1Tg+zSXufPtex/H+E8fbFGe+fa/j\neP+J422KM9++13G8/8TxNsWZT99rn+biahyf5uJyHMnDd44BAAAAABhoLI4BAAAAAInXMNBXWCqV\n9Oabb6q5uVlBEOz1//P5vPHfSvk0jk9zcTXOQM4lDEN1dXVp9OjRqquL3+s5NHFw5+JqHJpw40A9\nSH793F2N49NcXI1DE27QxMGfi6txaMKNWmvCp7m4GsenuZQ7TrlNDPjfHG/cuFHZbHYgrxIx0dnZ\nqTFjxhzsaThHE6hUHJugB9igCcBEE4DpQE0M+DvHzc3NkqR0ulNBYPcH0xdfbD+ff0393/aDSFr4\nie9WvO379QXNOHu0JOnN8A0N0zD7CY0YYT/Gn/5kP4YD+Xxe2aOO6rvvxE3v7brllk6lUnZNfPXf\nRlnP5/yTN1uPIUnjx1e+7c7BBc35tuMmWlrsx3jvPfsxJKlUsto8zk303qaGBvvHiC0//bX1fIZf\ncY71GJK0YoXd9n8OCjpl7AdN7HjdvgkXT5bfest+DEnavt16iHxXl7JHHx3rJjqPPVbp+nq7wd55\nx35CqZT9GJL17+RCqkejF6+R5Ohx4sMftttektavtx9Dkhy805vv6lJ27NhYN3HXXZ0aOtTucWLD\nBvv5fPX/OdR+EEnHjdhitX1paEFvr3b43GmU/XNKdXbajyFJDfZL1nKfOw344rh394cgSFs/8Rk8\n2H4+aUe/5BsbK78tdfX10gebp8O0m4VAP7uZROLZJyD2t+tMreu9XalUWkOG2H3P0w6+Rw0Nbn7u\nNmnVDY55E5aL415xbMLlY0S6sdHBfNz8zG2fn9YHezSxw0ETPvXgYHHcK85NpOvr7RfHLnavdbWL\nruVtqW+Q28cJn5pwuBt0nJsYOjRtvTgeMsR+Pi6ee0lSXZ3l/afO8XMnn5pwsDjudaAm4vVHCAAA\nAAAAVKCixfGPfvQjjR07VkOGDNHkyZP11FNPuZ4XUFNoAjDRBGCiCcBEE/BR5MXxww8/rJtuuknf\n+MY3tGrVKp122mlqa2vTBhc77QM1iCYAE00AJpoATDQBX0VeHN955526+uqrdc0112jcuHG66667\nlM1mNXv27GrMD/AeTQAmmgBMNAGYaAK+irQ43r59u1auXKnp06cbX58+fbp+//vfO50YUAtoAjDR\nBGCiCcBEE/BZpI/+2rJli3p6ejTqLz7ae9SoUXqrn0M6FItFFYvFvvO2B3kGfEITgClqE/SAuKMJ\nwEQT8FlFH8j1lx+BHYZhvx+L3dHRoUwm03fioN2II5oATOU2QQ9ICpoATDQBH0VaHB966KGqr6/f\n61Wdt99+e69Xf3q1t7crl8v1nTpdHQwa8ABNAKaoTdAD4o4mABNNwGeRFseDBw/W5MmTtWjRIuPr\nixYt0imnnLLPbVKplNLptHEC4oImAFPUJugBcUcTgIkm4LNIf3MsSbNmzdIVV1yhKVOmaOrUqZoz\nZ442bNiga6+9thrzA7xHE4CJJgATTQAmmoCvIi+OL774Ym3dulW33XabNm3apNbWVv3mN7/RkUce\nWY35Ad6jCcBEE4CJJgATTcBXkRfHknTdddfpuuuucz0XoGbRBGCiCcBEE4CJJuCjij6tGgAAAACA\nOGFxDAAAAABIvIp2q3ZhQy4j68+a+9/7Po5sJB/+sP0Yks79X/+r4m0LjZIKH5xpapa2OZhQqeRg\nEE/UJeM1nK9+z76J+rrQeh49z+77EFRR/fTyzRVvW9zzN1Mcm7C9TyegiR07HAxywQX283AwDUma\n9b/t7n87Bku644MzLYfYN+FTD4MH+zGG5zIvLJPsnzl5I3zN8jlc4x7/dvE44VMTLjQctKf4A+aS\nLzpYS1x5pfU8gu1F6zEkKXzTrolCo9TUe8ZBE2HJ/jllIPsxnCnzuVP8n2EBAAAAAHAALI4BAAAA\nAInH4hgAAAAAkHgsjgEAAAAAiRd5cfzkk0/qvPPO0+jRoxUEgRYsWFCFaQG1gR4AE00AJpoATDQB\nn0VeHBcKBR1//PG6++67qzEfoKbQA2CiCcBEE4CJJuCzyJ/z3tbWpra2tmrMBag59ACYaAIw0QRg\nogn4rOoHQSsWiyoWdx//K5/PV/sqAa/RBLAbPQAmmgBMNIGBVPUP5Oro6FAmk+k7ZbPZal8l4DWa\nAHajB8BEE4CJJjCQqr44bm9vVy6X6zt1dnZW+yoBr9EEsBs9ACaaAEw0gYFU9d2qU6mUUqlUta8G\nqBk0AexGD4CJJgATTWAgcZxjAAAAAEDiRX7nuLu7W2vXru07v379eq1evVrDhw/XEUcc4XRygO/o\nATDRBGCiCcBEE/BZ5MXxihUrdNZZZ/WdnzVrliRpxowZ+slPfuJsYkAtoAfARBOAiSYAE03AZ5EX\nx2eeeabCMKzGXICaQw+AiSYAE00AJpqAz/ibYwAAAABA4lX906r7k1FOUtpqjLBluP1ENm60H0NS\nIJtXwAqSmnb9s7tL0jAHM3KgztFrJ6WSm3FizkkTpcB+Ip+7yX4MSTNuP67ibQtDS/riZR+coYlE\nyimjdGB3f551k/33+Qc/sB5CklT3/9ptHzZKuuODM740QQ8DKqeM5SOEX+rr7N45DOscP3f6xS/s\ntvfNtm0HewZV5+R502OHW88jlIPnXrJdS0iu1xP281FNPk7wzjEAAAAAIPFYHAMAAAAAEo/FMQAA\nAAAg8VgcAwAAAAASL9LiuKOjQyeddJKam5s1cuRIfeYzn9FLL71UrbkB3qMJwEQTgIkmABNNwGeR\nFsdLly7VzJkztWzZMi1atEg7d+7U9OnTVSgUqjU/wGs0AZhoAjDRBGCiCfgs0qGcFi5caJyfO3eu\nRo4cqZUrV+r00093OjGgFtAEYKIJwEQTgIkm4DOrvznO5XKSpOHDHRxvGIgBmgBMNAGYaAIw0QR8\nEumd4z2FYahZs2bpE5/4hFpbW/u9XLFYVLFY7Dufz+crvUrAazQBmMppgh6QJDQBmGgCvqn4nePr\nr79ezz77rB566KH9Xq6jo0OZTKbvlM1mK71KwGs0AZjKaYIekCQ0AZhoAr6paHF8ww036NFHH9UT\nTzyhMWPG7Pey7e3tyuVyfafOzs6KJgr4jCYAU7lN0AOSgiYAE03AR5F2qw7DUDfccIPmz5+vJUuW\naOzYsQfcJpVKKZVKVTxBwGc0AZiiNkEPiDuaAEw0AZ9FWhzPnDlTDz74oB555BE1NzfrrbfekiRl\nMhkNHTq0KhMEfEYTgIkmABNNACaagM8i7VY9e/Zs5XI5nXnmmTr88MP7Tg8//HC15gd4jSYAE00A\nJpoATDQBn0XerRrAbjQBmGgCMNEEYKIJ+MzqOMcAAAAAAMQBi2MAAAAAQOJF2q3apZwyStsOMnue\n9TzqP3ex9RiS1GDxMkPYIPX0nmlqlrY5mFCp5McYKJuLJv7hGvtdlX58l/UQkqTwhCWVbzykZ/e/\naSKRhtfnFAR2Rez490HW87hTO63HkCRZ3nUKJamp94yLJuih5mSUk+yfOXkjLAVW23vZhE/y+YM9\ng6rLDTpU6cDufvSDrxat53HLLdZD7OLyLuhJE2HJzS70gQZuV3zeOQYAAAAAJB6LYwAAAABA4rE4\nBgAAAAAkHotjAAAAAEDiRVocz549W5MmTVI6nVY6ndbUqVP12GOPVWtugPdoAjDRBGCiCcBEE/BZ\npMXxmDFjdMcdd2jFihVasWKFPvnJT+r888/XmjVrqjU/wGs0AZhoAjDRBGCiCfgs0qGczjvvPOP8\n9773Pc2ePVvLli3ThAkTnE4MqAU0AZhoAjDRBGCiCfis4uMc9/T06Oc//7kKhYKmTp3qck5ATaIJ\nwEQTgIkmABNNwDeRF8fPPfecpk6dqvfff19NTU2aP3++xo8f3+/li8WiisXdB9jOJ+Cg5EgWmgBM\nUZqgByQBTQAmmoCvIn9a9XHHHafVq1dr2bJl+tKXvqQZM2bo+eef7/fyHR0dymQyfadsNms1YcA3\nNAGYojRBD0gCmgBMNAFfBWEYhjYDTJs2TUcffbTuueeeff7/fb3ak81mlZOUtrliSZo3z3YE1X/u\nYusxJKnO4qBYYWNBPbkmSVL3MGnYNgcTKpUcDOKHfD6vTEuLcrmc0mnre03VHcwm/uEaq5wlST/+\nsfUQkqTwhBMr3rYwpEdN//2cJJrYlzg10V8P9fU5BYHdbduhQVbbS5J27rQfw4FCo9RU2PVvJ03E\nqAcpGU3IzTMnb4QKrLanif1LQhO5QYOUDuzuRz+4o3jgCx3ALbdYDyHJwV2wsSAVHK4nHDRh23mv\nQPbPb8ttouK/Oe4VhqFxh/1LqVRKqVTK9mqAmkETgGl/TdADkogmABNNwBeRFsdf//rX1dbWpmw2\nq66uLs2bN09LlizRwoULqzU/wGs0AZhoAjDRBGCiCfgs0uJ48+bNuuKKK7Rp0yZlMhlNmjRJCxcu\n1Nlnn12t+QFeownARBOAiSYAE03AZ5EWx/fdd1+15gHUJJoATDQBmGgCMNEEfGbxMVIAAAAAAMQD\ni2MAAAAAQOJZf1p1pVoC+8N06HMO5tFiP4YkbR05ruJtC0NLauo9090laZiLKfnD5jhXSXLZZdLg\nwVZD3Ptj+4/Mv7ep6cAXKkPq+a6Ktw0bC1JvFTSRSGedJTVYPkJN2LDDeh77OWT5AItxE/RQlpwy\nMTqQk1RfZ3dolrDOcRO/+IXd9r7Z5uIYiJ7LZKx/f7g4DFNPyc3hijR0qNXmhaFhfNcTA/g4wSMS\nAAAAACDxWBwDAAAAABKPxTEAAAAAIPFYHAMAAAAAEs9qcdzR0aEgCHTTTTc5mg5Q22gCMNEEsBs9\nACaagG8qXhwvX75cc+bM0aRJk1zOB6hZNAGYaALYjR4AE03ARxUtjru7u3XZZZfp3nvv1SGHHOJ6\nTkDNoQnARBPAbvQAmGgCvqpocTxz5kydc845mjZt2gEvWywWlc/njRMQNzQBmMptgh6QBDxGACaa\ngK8aom4wb948Pf3001q+fHlZl+/o6NC3v/3tyBMDagVNAKYoTdAD4o7HCMBEE/BZpHeOOzs79eUv\nf1kPPPCAhgwZUtY27e3tyuVyfafOzs6KJgr4iCYAU9Qm6AFxxmMEYKIJ+C7SO8crV67U22+/rcmT\nJ/d9raenR08++aTuvvtuFYtF1dfXG9ukUimlUik3swU8QxOAKWoT9IA44zECMNEEfBdpcfypT31K\nzz33nPG1K6+8Uh/72Mf0ta99ba87MxB3NAGYaALYjR4AE03Ad5EWx83NzWptbTW+NmzYMI0YMWKv\nrwNJQBOAiSaA3egBMNEEfFfxcY4BAAAAAIiLyJ9W/ZeWLFniYBpAfNAEYKIJYDd6AEw0AZ/wzjEA\nAAAAIPFYHAMAAAAAEs96t+pKvddwqNJBYDVGMV+0nsfnP289xC4/e7HybRv3+HdTs7TNejZSqeRg\nEEds55LPSy0tTqbite5uadAgqyGGDgmtp/HnnsYDX6gMxe2V911okJp6z9DE3hLQxOLF9mP8n/9j\nP8aV1zo6fMj27VabF+S4iTj1ICWiiYxyktIHexrOhCW754CFUoybcCGfP9gzqL4tW6yH6JHd/VCS\nAtk/95Kk4UPttg+H7vFI4aCJsGR/u1x9b1zMJcznpZbMAS/HO8cAAAAAgMRjcQwAAAAASDwWxwAA\nAACAxIu0OL711lsVBIFx+tCHPlStuQHeownARBOAiSYAE03AZ5E/kGvChAlavMcnpdTX1zudEFBr\naAIw0QRgognARBPwVeTFcUNDA6/uAHugCcBEE4CJJgATTcBXkf/m+JVXXtHo0aM1duxYXXLJJVq3\nbl015gXUDJoATDQBmGgCMNEEfBXpneOPf/zjuv/++3Xsscdq8+bN+u53v6tTTjlFa9as0YgRI/a5\nTbFYVLG4+3jE+SQcdw2JQROAKWoT9IC4ownARBPwWaR3jtva2nThhRdq4sSJmjZtmn79619Lkn76\n05/2u01HR4cymUzfKZvN2s0Y8AhNAKaoTdAD4o4mABNNwGdWh3IaNmyYJk6cqFdeeaXfy7S3tyuX\ny/WdOjs7ba4S8BpNAKYDNUEPSBqaAEw0AZ9E/kCuPRWLRb3wwgs67bTT+r1MKpVSKpWyuRqgZtAE\nYDpQE/SApKEJwEQT8Emkd45vueUWLV26VOvXr9cf/vAHffazn1U+n9eMGTOqNT/AazQBmGgCMNEE\nYKIJ+CzSO8cbN27UpZdeqi1btuiwww7TySefrGXLlunII4+s1vwAr9EEYKIJwEQTgIkm4LNIi+N5\n8+ZVax5ATaIJwEQTgIkmABNNwGdWH8gFAAAAAEAcsDgGAAAAACSe1adV28js2CIpbTXGoWPs5/Gn\nrW5eH3h8YVjxtu/XFyQ17TrT3SVpmP2E6hzcrlLJfgyULfPI/bJtIlRgPY+hQyq/L+/p8msq33bH\nYJqAvStvyliPEWwvOpiJC46boIeak1PG8hHCL/V1do81YZ3jJn7xC7vtfbNt28GeQdWNac4pCOyq\nyOft5+HiuZckpbotm9jjV3LY3a3QsomgzsHtcvQ4Ecj+uWm5Y/DOMQAAAAAg8VgcAwAAAAASj8Ux\nAAAAACDxWBwDAAAAABIv8uL4jTfe0OWXX64RI0aosbFRJ5xwglauXFmNuQE1gSYAE00AJpoATDQB\nX0X6tOp3331Xp556qs466yw99thjGjlypF599VW1tLRUaXqA32gCMNEEYKIJwEQT8FmkxfH3v/99\nZbNZzZ07t+9rRx11lOs5ATWDJgATTQAmmgBMNAGfRdqt+tFHH9WUKVN00UUXaeTIkTrxxBN17733\nVmtugPdoAjDRBGCiCcBEE/BZpMXxunXrNHv2bB1zzDF6/PHHde211+rGG2/U/fff3+82xWJR+Xze\nOAFxQROAKWoT9IC4ownARBPwWaTdqkulkqZMmaLbb79dknTiiSdqzZo1mj17tj7/+c/vc5uOjg59\n+9vftp8p4CGaAExRm6AHxB1NACaagM8ivXN8+OGHa/z48cbXxo0bpw0bNvS7TXt7u3K5XN+ps7Oz\nspkCHqIJwBS1CXpA3NEEYKIJ+CzSO8ennnqqXnrpJeNrL7/8so488sh+t0mlUkqlUpXNDvAcTQCm\nqE3QA+KOJgATTcBnkd45vvnmm7Vs2TLdfvvtWrt2rR588EHNmTNHM2fOrNb8AK/RBGCiCcBEE4CJ\nJuCzSIvjk046SfPnz9dDDz2k1tZWfec739Fdd92lyy67rFrzA7xGE4CJJgATTQAmmoDPIu1WLUnn\nnnuuzj333GrMBahJNAGYaAIw0QRgogn4KtI7xwAAAAAAxBGLYwAAAABA4kXerdqVnDJK2w6yNbCf\nSDZrP4akT/9flc+l0Cip8MGZpmZpm4MJlUoOBsFActFEoNB6HmHb31mPIUk/GP+rirct7vmbiSYS\n6Ze/lIYNsxzk0nrreYRy8Dgj6akn7dr8c5306d4zLpqgh5qTUU6yf+bkjbBk11ahJDX1nqGJveXz\nB3sGVbexy8Fa4uabrecR/MD+uZckhdstm2jY3UTQ1KTAsomw5OZ2ueDi+W25eOcYAAAAAJB4LI4B\nAAAAAInH4hgAAAAAkHgsjgEAAAAAiRdpcXzUUUcpCIK9TjNnzqzW/ACv0QRgognARBOAiSbgs0if\nVr18+XL19PT0nf/jH/+os88+WxdddJHziQG1gCYAE00AJpoATDQBn0VaHB922GHG+TvuuENHH320\nzjjjDKeTAmoFTQAmmgBMNAGYaAI+q/g4x9u3b9cDDzygWbNmKQj6Py5XsVhUsVjsO59PwHHXkEw0\nAZjKaYIekCQ0AZhoAr6p+AO5FixYoPfee09f+MIX9nu5jo4OZTKZvlM2m630KgGv0QRgKqcJekCS\n0ARgogn4puLF8X333ae2tjaNHj16v5drb29XLpfrO3V2dlZ6lYDXaAIwldMEPSBJaAIw0QR8U9Fu\n1a+//roWL16sX/3qVwe8bCqVUiqVquRqgJpBE4Cp3CboAUlBE4CJJuCjit45njt3rkaOHKlzzjnH\n9XyAmkQTgIkmABNNACaagI8iL45LpZLmzp2rGTNmqKGh4s/zAmKDJgATTQAmmgBMNAFfRV4cL168\nWBs2bNBVV11VjfkANYcmABNNACaaAEw0AV9Ffqlm+vTpCsOwGnMBahJNACaaAEw0AZhoAr6q+NOq\nAQAAAACIiwHfyb/3VSInh+928YpTqWQ/hqVCqL5vSD6UelwMGqMDpPce7D2urzA6bcLBKPkdOxzM\nQ3r//crnUqwv0MR+xLmJ3tu0bZuD+7JH359Cwe72/LnOcRMx6kFKRhOuHiV8YXtrnD93ooma4fR5\nU7HoYBA/nsG5biL0qIlA9vfjcpsIwgGuZuPGjRy8GxXp7OzUmDFjDvY0nKMJVCqOTdADbNAEYKIJ\nwHSgJgZ8cVwqlfTmm2+qublZQRDs9f/z+byy2aw6OzuVTqcrvh6fxvFpLq7GGci5hGGorq4ujR49\nWnV18ftLAJrgNkUdJ85NHKgHya+fu6txfJqLq3Fowg2aOPhzcTUOTbhRa034NBdX4/g0l3LHKbeJ\nAd+tuq6urqxXsNLptNU3ycdxfJqLq3EGai6ZTMb6OnxFE37MxdU4NGGn3B4kv37ursbxaS6uxqEJ\nOzThz1xcjUMTdmq1CZ/m4mocn+ZSzjjlNBGvl5IAAAAAAKgAi2MAAAAAQOJ5tzhOpVL61re+pVQq\nFZtxfJqLq3F8mkvc+fa9juP9J463Kc58+17H8f4Tx9sUZ759r+N4/4njbYozn77XPs3F1Tg+zcXl\nONJB+EAuAAAAAAB84907xwAAAAAADDQWxwAAAACAxGNxDAAAAABIPBbHAAAAAIDEY3EMAAAAAEg8\nFscAAAAAgMRjcQwAAAAASDwWxwAAAACAxPv/AdSmLtUNlAWVAAAAAElFTkSuQmCC\n"
}
}
],
"source": [
"x = torch.tensor(df_train.x.map({'A':0,'b':1,'c':2,'d':3}))\n",
"y = torch.tensor(df_train.y.map({'A':0,'b':1,'c':2,'d':3}))\n",
"X = torch.nn.functional.one_hot(x).float().to(\"cuda:0\")\n",
"y = torch.nn.functional.one_hot(y).float().to(\"cuda:0\")\n",
"fig,ax = plt.subplots(5,5,figsize=(10,10))\n",
"for i in range(5):\n",
" for j in range(5):\n",
" rnn = torch.nn.RNN(4,4).to(\"cuda:0\")\n",
" cook = torch.nn.Linear(4,4).to(\"cuda:0\")\n",
" loss_fn = torch.nn.CrossEntropyLoss()\n",
" optimizr = torch.optim.Adam(list(rnn.parameters()) + list(cook.parameters()), lr=0.1)\n",
" for epoc in range(200):\n",
" ## 1\n",
" h,_ = rnn(X)\n",
" netout = cook(h)\n",
" ## 2 \n",
" loss = loss_fn(netout,y)\n",
" ## 3 \n",
" loss.backward()\n",
" ## 4 \n",
" optimizr.step()\n",
" optimizr.zero_grad()\n",
" h = rnn(X)[0].data.to(\"cpu\")\n",
" yhat = soft(cook(rnn(X)[0])).data.to(\"cpu\")\n",
" mat = torch.concat([h,yhat],axis=1)[:8]\n",
" ax[i][j].matshow(mat,cmap=\"bwr\")\n",
" ax[i][j].axvline(x=3.5,color=\"lime\")\n",
" ax[i][j].set_xticks(range(8),[r'$h_1$',r'$h_2$',r'$h_3$',r'$h_4$',r'$P_A$',r'$P_b$',r'$P_c$',r'$P_d$'])\n",
"fig.suptitle(\"RNN -- # of hidden nodes = 4\",size=20)\n",
"fig.tight_layout()"
],
"id": "be712d28-10c9-4caa-839b-20b4ddb91811"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 4. `abcabC`\n",
"\n",
"## A. Data\n",
"\n",
"`-` 데이터 정리"
],
"id": "b1370cea-a67f-4691-a408-cc8cf5f8913a"
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"txt = list('abcabC'*50)\n",
"txt[:10]"
],
"id": "da7c76fb-2aeb-4ea3-94cc-81e11af1f066"
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"df_train = pd.DataFrame({'x':txt[:-1], 'y':txt[1:]})\n",
"df_train[:5]"
],
"id": "e67e3959-a183-43db-b9bf-a35a092ff9b4"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## B. RNN\n",
"\n",
"ref: "
],
"id": "3e09bd3a-730e-411a-a59d-4f6e0d036be8"
},
{
"cell_type": "code",
"execution_count": 156,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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/fr169eqlm2++ud3WcdXL6tWrFYlENGTIkNR927dvlyR17969XdZx1UuQ+Wld\ndlWHTGS/lyDz07rsqg6ZyH4vQeanddlVHTKR/V6CzE/rsqs6ZCK7fTTJyRA7Q7feeqvp2rWr2bVr\nV+q+WbNmmYEDBxpjjLngggtMcXGxufDCCzOus23bNjN27FjTv39/M3jw4CYPT2iqTiKRMCNGjDBD\nhw41gwYNMnPmzMlonowxpqqqyvTq1cvceOONjfZy0003mc9//vOpn998800zYsQIM2zYMFNTU9Pk\n8kinzpNPPmmuueYaz3Vc9GKMMeXl5Wb48OFm4MCBpn///uZPf/pTS2c1EMgEmSATNjJBJsiEjUyQ\nCTJhIxPhyURr5KHN9xyff/75KikpSd23efNmnXjiiZKk6667Tg899JCnOnl5eZo5c6Zef/11LV68\nWDfccIOqqqrSrpOfn6+lS5dq3bp1evnll1VWVqbKysq050mS7rjjDp1yyilNztPq1av13nvvqaCg\nQJ06ddKwYcM0cOBALVq0SDk5Lf+zNVfn1Vdf1cknn+y5joteHnjgAZWXl2vRokXauHGjli5dqpqa\nmhbPaxCQicaRCTJRh0wcQibIRB0ycQiZIBN1yMQhQctEa+ShzQfHo0aNsu5bu3athg0bJkkaN26c\nCgsLPdU57rjjUvVKSkrUrVs3ffzxx2nXyc3NVX5+viTpwIEDqqmpkTEm7Xl655139Oabb+qss85q\ncp7Wrl2rH//4x1q3bp02b96s/fv3a+7cualDBv74xz/qlFNO0eDBg3Xeeeepuro6ozqvvvqq3njj\nDQ0fPlwDBw7U22+/nVGdrVu36pxzzkmtpO+//35aNfbt26fbb79d8+fP19FHHy1JOuaYYzRp0qQm\nl1PQkInGkQkyUYdMHJ6GTJAJiUzUn4ZMkAmJTNSfJkiZaJU8pLWf2aFEImEikYh55ZVXrPu7du1q\nFixYkPr5+eefb/IwiJbWMcaYlStXWocjpFtnz549ZsiQIaZz585m1qxZGdU477zzzFtvvWXKy8sb\nPQzi3XffNZLM4sWLG5tts3v37tT/L7/88gYf25I6/fv3N3fffbcxxpjZs2ebq666Ku06yWTSDBw4\n0CxdutQYY0xlZaX59NNP06rx4IMPmosvvrjRPsOATJCJ+sgEmSATNjJBJsiEjUyQiTBlorXy0GZ7\njtetW6ecnBwNHjw4dd/WrVu1Z8+e1KciLutUVlbqu9/9rubMmZNxneLiYq1fv15btmzRvHnztGvX\nrrRq/O1vf1Pfvn3Vt2/fJuep7svmw4cPb/D3xhjNmTNHI0eO1NChQ7VgwQJ16tQp7TrJZFLV1dWa\nMmWKJGnIkCHavXt32nUWLFigU089VWPGjJEkdevWTXl5eWnV2Lhxo/Xl+jAiE40jE+FEJhpHJsKJ\nTDSOTIQTmWhc0DLRWnnIa/4h2bF+/Xr169fP+iOsXbtWxcXFOv74453WSSaT+vrXv65p06Zp9OjR\nnvvp3r27hgwZomXLlumiiy5qcY377rtPjz76qB577DHt27dPn376qYqKinTLLbdY9desWaMTTzxR\nxcXFDfY6d+5cbdq0ScuWLVPnzp3Vu3dvDRgw4IjHNVfntdde04ABA1LH+K9du7bBlaq5Ohs2bNDI\nkSMb/F1La3Tp0kW1tbVN1gg6MkEm6iMTZIJM2MgEmSATNjJBJsKUiVbLg+d9z1nW3GEQzamtrTWX\nXHKJmT59uqc+du7caeLxuDHGmHg8bgYMGGDWr1+fcb2mDoNozo033mgeeOABY4wxM2fOND179sy4\nhwEDBpjq6mqza9cuM2LECPPRRx+lXefuu+9OnaHu4MGDprKyMu0aL7zwgunfv3/q8I5PPvnEPPzw\nw2nXCQMycSQyEW5k4khkItzIxJHIRLiRiSMFLROu8tCmJ+Rqzte+9jVddNFFevrpp9WzZ0+tXLky\n7RovvPCC5s+fr4ULF2rYsGEaNmyYNmzYkHad7du3a8yYMRo6dKhOP/10XXPNNW12KMukSZN02223\naezYsaqsrLQOu0jHhg0bdOGFF2rkyJEaP3687rrrrtQX2NNx2WWX6d1339WgQYM0YsQIbdq0Ke0a\no0eP1tSpUzVu3DgNHjxYY8aMCd3ZFluCTDSMTIQXmWgYmQgvMtEwMhFeZKJhQcuEqzxEjGngFGkA\nAAAAAISIr/ccAwAAAADQGhgcAwAAAABCj8ExAAAAACD0GBwDAAAAAEKPwTEAAAAAIPQYHAMAAAAA\nQo/BMQAAAAAg9Hw3OE4mk5oxY4aSyWRg6vipF1d1/NRL0PltWQdx/QniPAWZ35Z1ENefIM5TkPlt\nWQdx/QniPAWZ35Z1ENefIM6TJEWMMcZzFYcSiYRisZji8biKiooCUcdPvbiq46degs5vyzqI608Q\n5ynI/Lasg7j+BHGegsxvyzqI608Q5ynI/Lasg7j+BHGeJB/uOQYAAAAAoLUxOAYAAAAAhF5eaz9h\nbW2tPvjgAxUWFioSiRzx+0QiYf2bKT/V8VMvruq0Zi/GGO3du1c9evRQTk7wPs8hE23bi6s6ZMId\nMtG2vbiqQybcaC4Pkr/+7q7q+KkXV3XIhBtkou17cVXHj5lo9e8cb9++XaWlpa35lAiIiooK9ezZ\ns63bcI5MIFNkArAFMRPkAV6QCcDWXCZafc9xYWGhJGnx4gp16eLtC9OjRnnvJ66Y9yKSYopnPnHn\nKmlnD0nSB+Z9dVEX7w0VF3uv8fHH3mtIksdPLBOJhEp79UqtO0FTN18VkryeVuNLJ3lYD//p4EHP\nJSRJ/ft76CFapUW/918mzCfel68kReTtM8nQZOKGG1QUjXords893hu65RbvNSTppz/NeNKqzlKP\nnYf+76dM6JNPvNdwIMiZSOVhzBgV5Xl72/Zf4xd47ueOOzyXkCR9UOXt/ZfzTAQoD1JIMiHv75t0\n2WVeK0hz53qvIWnMUG/vMWqiVdr4nMP3TiHNRKsPjusOf+jSpUgFBW1/hj13HXioFMlNTV5kity8\n6WnkMJO0uDoDoqPDeRo7dKa9q5uvInlfH3Nzvf/NXB1L0qFD5tNGOmQhEw4YR5nwOjhO1Ql6JqJR\nFXXq5LWY94Y6d/Zew6PciHyZCWfbCUeCmIlUHvLyPA+OO3Xy/vdytYg9b+/8mAmf5UEKeCYkFXmd\nv44dXTTkvYYcvIfL8+F7p3aYiWB9CQEAAAAAgAxkNDi+99571adPH3Xq1EnDhw/X8uXLXfcFtCtk\nArCRCcBGJgAbmYAfpT04nj9/vq6//nr9/Oc/19q1a3XGGWdo4sSJ2rZtWzb6A3yPTAA2MgHYyARg\nIxPwq7QHx7/73e905ZVX6nvf+5769++vmTNnqrS0VLNnz85Gf4DvkQnARiYAG5kAbGQCfpXW4Li6\nulqrV6/WhAkTrPsnTJigF1980WljQHtAJgAbmQBsZAKwkQn4WVqnPdy9e7dqamrUvXt36/7u3btr\n586dDU6TTCaVTCZTP3u9yDPgJ2QCsJEJwJZuJsgDgo5MwM8yOiHXZ0+BbYxp9LTYZWVlisViqRsX\n7UYQkQnARiYAW0szQR4QFmQCfpTW4Pjoo49Wbm7uEZ/qfPjhh0d8+lNn2rRpisfjqVtFRUXm3QI+\nQyYAG5kAbOlmgjwg6MgE/CytwXHHjh01fPhwPffcc9b9zz33nEaPHt3gNNFoVEVFRdYNCAoyAdjI\nBGBLNxPkAUFHJuBnaX3nWJKmTp2qSZMmacSIERo1apTmzJmjbdu26eqrr85Gf4DvkQnARiYAG5kA\nbGQCfpX24Pjiiy9WZWWlbr31Vu3YsUODBg3S008/rd69e2ejP8D3yARgIxOAjUwANjIBv0p7cCxJ\nP/zhD/XDH/7QdS9Au0UmABuZAGxkArCRCfhRRmerBgAAAAAgSBgcAwAAAABCj8ExAAAAACD0MvrO\nsQsDRsXk/UTsxnOFiIMaktSzZ+bT1naWPnDSRT01Nd5r/Pzn3mtIUn6+t+kPHHDTh8/FFJc8psK8\n3cF7I/36ea8hKbJgQ+YTe1xlGmJqHbxe5EQcdCKpttZNnYCL3TVNXjMhTffch7nO0d+9T5/Mp+1c\nK2mrmz7quFgPcxx9xk4mmhX7fwvkeRvxv97X5amO3jepb19v03eulbTJSSuSyEM7FFNcMh63EXO8\n92FcFJG0Zo3HAq7fO7lYD2fM8F5DcpOtFo4n2HMMAAAAAAg9BscAAAAAgNBjcAwAAAAACL20B8fL\nli3Tueeeqx49eigSiWjhwoVZaAtoP8gEcBh5AGxkArCRCfhZ2oPjqqoqDR06VLNmzcpGP0C7QyaA\nw8gDYCMTgI1MwM/SPlv1xIkTNXHixGz0ArRLZAI4jDwANjIB2MgE/IzvHAMAAAAAQi/r1zlOJpNK\nJpOpnxOJRLafEvA1MgHYyARwGHkAbGQCrSnre47LysoUi8VSt9LS0mw/JeBrZAKwkQngMPIA2MgE\nWlPWB8fTpk1TPB5P3SoqKrL9lICvkQnARiaAw8gDYCMTaE1ZP6w6Go0qGo1m+2mAdoNMADYyARxG\nHgAbmUBrSntwvG/fPm3atCn185YtW7Ru3Tp169ZNvXr1ctoc0B6QCeAw8gDYyARgIxPws7QHx6tW\nrdK4ceNSP0+dOlWSNHnyZM2dO9dZY0B7QSaAw8gDYCMTgI1MwM/SHhyfeeaZMsZkoxegXSITwGHk\nAbCRCcBGJuBnXOcYAAAAABB6DI4BAAAAAKGX9bNVZ5NRpK1bOGx75pNW5UsFdT8UFEr7HfRTW+u9\nxh13eK/hQiLhn16yKK6YirwWOeigkY0bHRTxls8qZSMTDg7hcpEreX/t8tVrn8+5WFYRuTn8z2zx\n0Et+vf/7aTvhKBNoXnzLxyoq/NRTjcjR3tdlZ68/2zp5mz6/3ry4yAR5aHdcvG9y8frubBvhMVvO\n3zu5WJ9nzPBew5VEQrrrrmYfxp5jAAAAAEDoMTgGAAAAAIQeg2MAAAAAQOgxOAYAAAAAhF5ag+Oy\nsjKNHDlShYWFKikp0QUXXKC33norW70BvkcmABuZAGxkArCRCfhZWoPjpUuXasqUKVqxYoWee+45\nHTx4UBMmTFBVVVW2+gN8jUwANjIB2MgEYCMT8LO0LuW0aNEi6+fy8nKVlJRo9erVGjNmjNPGgPaA\nTAA2MgHYyARgIxPwM0/XOY7H45Kkbt26NfqYZDKpZDKZ+jmRSHh5SsDXyARgIxOArblMkAeEDZmA\nn2R8Qi5jjKZOnarTTz9dgwYNavRxZWVlisViqVtpaWmmTwn4GpkAbGQCsLUkE+QBYUIm4DcZD46v\nueYavfrqq3rkkUeafNy0adMUj8dTt4qKikyfEvA1MgHYyARga0kmyAPChEzAbzI6rPraa6/VE088\noWXLlqlnz55NPjYajSoajWbUHNBekAnARiYAW0szQR4QFmQCfpTW4NgYo2uvvVYLFizQkiVL1KdP\nn2z1BbQLZAKwkQnARiYAG5mAn6U1OJ4yZYrmzZunv/3tbyosLNTOnTslSbFYTJ07d85Kg4CfkQnA\nRiYAG5kAbGQCfhYxxpgWPzgSafD+8vJyXXbZZS2qkUgkFIvFFJdU1NInDriqfKngn5d229dF6rLf\nQdHaWgdF/CGRSChWXKx4PK6iIn+tNWQiO7KRCVPb4pe6RkXkvYYkGTW83rRUIpFQcXEs8JmQg1R4\nXdaSP/7ubCeaFuTtRGobsWWLigoLvfVy9FGeppfcZEqS1KmTp8mr8o0KKg+dwdhJJgKUBykkmZD3\n902uXt9d8Jot59uJkGYi7cOqARxGJgAbmQBsZAKwkQn4WcZnqwYAAAAAICgYHAMAAAAAQi+jSzm5\n4JdvWJqObk4NH6lOepi6SlLBof/u2yupi/eGchx87hGw7xqEga++O7P4/zKfOOcfks499H9HmYjk\neP+enIvvLUve/05++jtnU1wxH2wlHH7H0hW2E+Hk4Iy+ZsQIzzUiqxx9B/+Ax1zVX31dZMJHeXDx\nmuO71y2f8tNy+o/festWMs/xeMJHmWhN7DkGAAAAAIQeg2MAAAAAQOgxOAYAAAAAhF5ag+PZs2dr\nyJAhKioqUlFRkUaNGqVnnnkmW70BvkcmABuZAGxkArCRCfhZWoPjnj176q677tKqVau0atUqffnL\nX9b555+v1157LVv9Ab5GJgAbmQBsZAKwkQn4WVpnqz733HOtn++44w7Nnj1bK1as0MCBA502BrQH\nZAKwkQnARiYAG5mAn2V8Kaeamho99thjqqqq0qhRo1z2BLRLZAKwkQnARiYAG5mA36Q9ON6wYYNG\njRqlAwcOqKCgQAsWLNCAAQMafXwymVQyefgawIlEIrNOAZ8iE4CNTAC2dDJBHhAGZAJ+lfbZqk86\n6SStW7dOK1as0A9+8ANNnjxZr7/+eqOPLysrUywWS91KS0s9NQz4DZkAbGQCsKWTCfKAMCAT8KuI\nMcZ4KTB+/HidcMIJuu+++xr8fUOf9hxaqeOSirw8tROmY9RJnUh1svkHNSa/SqoqkCTtM3vVRV28\nN5Tj4CpdtbXeaziQSCQUKy5WPB5XUVHbrzPNyTQTLhIRkac4O2UW/1/G01bl/EMF4w59J8lPmTC1\nbpav178TmQifqnypoOrQ//2UCbYTmWkqE1nNw4gRXisosmql5xqSZBTxNL3zTPgoD16XjXRovSku\njpGJduQ/fuvtvUEyr0o//5HD8YSPMuFCS7cTGX/nuI4xxlphPysajSoadTMABdoDMgHYyARgayoT\n5AFhRCbgF2kNjn/2s59p4sSJKi0t1d69e/Xoo49qyZIlWrRoUbb6A3yNTAA2MgHYyARgIxPws7QG\nx7t27dKkSZO0Y8cOxWIxDRkyRIsWLdJXv/rVbPUH+BqZAGxkArCRCcBGJuBnaQ2OH3zwwWz1AbRL\nZAKwkQnARiYAG5mAnzn4pjUAAAAAAO0bg2MAAAAAQOgxOAYAAAAAhJ7nSzllKq6YL67p6un6xPV4\nuRSYyZH7q9O6uK7YzTd7ryFJ3bp5m/7AATd9+FzMwRX7zJdO8dxH4esve64hSZHxX8l84vwq6Z/X\nrzSKOLnmY8RBJpxdR9rFtQNDwEUmXHCx/klStGPm64/pWCWpwEkfKT66/iSZaJ6TbcQqN+uyC13y\nvb2emvzDmXCynXBwHXtX24hIjoNtnoM+/C5o24ibbvJYIF/Sj1x08k8uthG33uq9histHE+wNQIA\nAAAAhB6DYwAAAABA6DE4BgAAAACEnqfBcVlZmSKRiK6//npH7QDtG5kAbGQCsJEJwEYm4CcZD45X\nrlypOXPmaMiQIS77AdotMgHYyARgIxOAjUzAbzIaHO/bt0+XXnqp7r//fnXt2tV1T0C7QyYAG5kA\nbGQCsJEJ+FFGg+MpU6bo7LPP1vjx4133A7RLZAKwkQnARiYAG5mAH6V9neNHH31Ua9as0cqVK1v0\n+GQyqWTy8LWEE4lEuk8J+BqZAGxkArClkwnygDAgE/CrtPYcV1RU6Ec/+pEefvhhderUqUXTlJWV\nKRaLpW6lpaUZNQr4EZkAbGQCsKWbCfKAoCMT8LOIMca09MELFy7U17/+deXm5qbuq6mpUSQSUU5O\njpLJpPU7qeFPe0pLSxWXVOS1ebW49azL8XDeb5NfJbO3QJK0z+xVF3Vx1JVHN9/spk63bp4mTxw4\noNiMGYrH4yoq8rrWuOUyE3KQCvOlUzxNL0mFr7/suYYk7dvnYeL8KqnqUCb2mn1OMuGn1wtPLxiS\nEpJiEploJUYRJ3WiHTNfB01+lT7d48PthCtkIvW7rG4jHKzLrl5L8/O9TW/yq/SPj9xuJ7xytp3x\nmAeJTLQmV9sIz+tPvfdOvtlO3HprW3eQkjhwQLG77mo2E2kdVv2Vr3xFGzZssO67/PLL1a9fP/30\npz894g2PJEWjUUWj0XSeBmg3yARgIxOALd1MkAcEHZmAn6U1OC4sLNSgQYOs+7p06aKjjjrqiPuB\nMCATgI1MADYyAdjIBPzM+3EbAAAAAAC0c2mfrfqzlixZ4qANIDjIBGAjE4CNTAA2MgG/YM8xAAAA\nACD0GBwDAAAAAEKPwTEAAAAAIPQ8f+e4LTm5rljEzbXJVJv5tcmqaqWCuh8KCqX9Lvqp9V7jrru8\n13AhkZBmzGjrLrIurpjnq/X9/T+8X2Nx7xmOMuFBlQ5nIlJQoIhfMuGI8fB6IUkmkZCKY4668a/O\nnb2/RFft9891XQs6Zj6t6Sh9mirko+2EK157SSSk4mInrQSZi3XZ1TVdddBDICRVHTROtxNeX5ed\ncpHNEGTCxfsmF5lwtY3wmq36752cbCdcrIe33OK9hiuJRIvGNuw5BgAAAACEHoNjAAAAAEDoMTgG\nAAAAAIReWoPjGTNmKBKJWLdjjz02W70BvkcmABuZAGxkArCRCfhZ2ifkGjhwoBYvXpz6OTc312lD\nQHtDJgAbmQBsZAKwkQn4VdqD47y8PD7dAeohE4CNTAA2MgHYyAT8Ku3vHL/zzjvq0aOH+vTpo0su\nuUSbN29u8vHJZFKJRMK6AUFCJgAbmQBs6WSCPCAMyAT8Kq3B8SmnnKKHHnpIzz77rO6//37t3LlT\no0ePVmVlZaPTlJWVKRaLpW6lpaWemwb8gkwANjIB2NLNBHlA0JEJ+FnEGJPxlaurqqp0wgkn6Cc/\n+YmmTp3a4GOSyaSSyWTq50QiodLSUsUlzxfudiLi6GL2mS9GVeVLBVWH/r+vi9TF60W7JTcX7vaJ\nRCKhWHGx4vG4iop8sdY0qq0z8ffl3i9Ef/oZjjLhQdAzYeRtGScSCRUXxwKfic6d44pEvM1f1X7v\n63NE3nMlSQUFmU9r8qtUtetQgSBmwqsgbScay4N88s7J6+tXSseOniavyjcq2POpJDeZMLXec+7q\ntcKFMGTCRSL89Dfzmi3n750CtI2QWp6JtL9zXF+XLl00ePBgvfPOO40+JhqNKhqNenkaoN0gE4CN\nTAC25jJBHhA2ZAJ+4uk6x8lkUm+88YaOO+44V/0A7RqZAGxkArCRCcBGJuAnaQ2Ob7rpJi1dulRb\ntmzRyy+/rG984xtKJBKaPHlytvoDfI1MADYyAdjIBGAjE/CztA6r3r59u771rW9p9+7dOuaYY3Tq\nqadqxYoV6t27d7b6A3yNTAA2MgHYyARgIxPws7QGx48++mi2+gDaJTIB2MgEYCMTgI1MwM88fecY\nAAAAAIAgYHAMAAAAAAg9T5dy8iLml+v1dXBzavhIdbL5BzWqStI/L4C5b6+kLt4bynHwuUfArm8W\nBmPHeq9R6+iaf14uYWk6Hs6E2bdPxkEmIjner83p4jqYkvfrKvrpuozZtPMfMR9sJaQPP3RT55iS\nzNfBqtrUVoLtREjF5T0PLl47XL3+mGqPr8n138E6yISLbQR5aH+cXbfbgf/vd96ylcxzPJ4I6TaC\nPccAAAAAgNBjcAwAAAAACD0GxwAAAACA0GNwDAAAAAAIvbQHx++//76+853v6KijjlJ+fr6GDRum\n1atXZ6M3oF0gE4CNTAA2MgHYyAT8Kq2zVe/Zs0ennXaaxo0bp2eeeUYlJSV69913VVxcnKX2AH8j\nE4CNTAA2MgHYyAT8LK3B8a9//WuVlpaqvLw8dd/xxx/vuieg3SATgI1MADYyAdjIBPwsrcOqn3ji\nCY0YMUIXXXSRSkpKdPLJJ+v+++9vcppkMqlEImHdgKAgE4CNTAC2dDNBHhB0ZAJ+ltbgePPmzZo9\ne7a+8IUv6Nlnn9XVV1+t6667Tg899FCj05SVlSkWi6VupaWlnpsG/IJMADYyAdjSzQR5QNCRCfhZ\nxBhjWvrgjh07asSIEXrxxRdT91133XVauXKlXnrppQanSSaTSiaTqZ8TicQ/V+q4pKKMG3fFdIw6\nqROpTjb/oMbkV0lVBZKkfWavuqiL94ZyHJyIvLbWew0HEomEYsXFisfjKipq+3WmPpeZcJGI3JwW\nx7lRrv7sHTtmPq3Jr9Knew5lYq/Z5yQTkZyI5xqm1vvylaSIvNUhE63row/d/N2PKcl8HazKlwqq\nDv2f7cSRgpSJbObB62uPS0beXpOdZyJAeZDIRHv0//3OWz6TeVWadq3D8URIM5HWXB933HEaMGCA\ndV///v21bdu2RqeJRqMqKiqybkBQkAnARiYAW7qZIA8IOjIBP0trcHzaaafprbfesu57++231bt3\nb6dNAe0FmQBsZAKwkQnARibgZ2kNjm+44QatWLFCd955pzZt2qR58+Zpzpw5mjJlSrb6A3yNTAA2\nMgHYyARgIxPws7QGxyNHjtSCBQv0yCOPaNCgQbrttts0c+ZMXXrppdnqD/A1MgHYyARgIxOAjUzA\nz9K6zrEknXPOOTrnnHOy0QvQLpEJwEYmABuZAGxkAn7l4DRkAAAAAAC0bwyOAQAAAAChl/Zh1a7E\nFfPF9fo8XZ+4Hi+XAjM5cn/lQRfXFbv5Zu81JKlbN2/THzjgpg+fizm4Yp8xDj7v6uTo2t8H/pH5\nxPVemSIyTrLu4hrFLq6VLMlX1/3zMxeZcMF4uD6xpaAg82nzjaQqN33UcbEeurgOpkQmWsDJNsLj\ntYUlh9dKzvP4FjTPSKpx0ook8tAO+WYb4SBXkjR1qscC+ZKuddHJP7lYD2+91XsNV1o4nmDPMQAA\nAAAg9BgcAwAAAABCj8ExAAAAACD00hocH3/88YpEIkfcuGg3wopMADYyAdjIBGAjE/CztM6GsHLl\nStXUHD75wcaNG/XVr35VF110kfPGgPaATAA2MgHYyARgIxPws7QGx8ccc4z181133aUTTjhBY8eO\nddoU0F6QCcBGJgAbmQBsZAJ+lvF3jqurq/Xwww/riiuuUCTi6DIXQDtGJgAbmQBsZAKwkQn4TcYX\nmVu4cKE++eQTXXbZZU0+LplMKpk8fC3hRCKR6VMCvkYmABuZAGwtyQR5QJiQCfhNxnuOH3zwQU2c\nOFE9evRo8nFlZWWKxWKpW2lpaaZPCfgamQBsZAKwtSQT5AFhQibgNxkNjrdu3arFixfre9/7XrOP\nnTZtmuLxeOpWUVGRyVMCvkYmABuZAGwtzQR5QFiQCfhRRodVl5eXq6SkRGeffXazj41Go4pGo5k8\nDdBukAnARiYAW0szQR4QFmQCfpT2nuPa2lqVl5dr8uTJysvL+CvLQGCQCcBGJgAbmQBsZAJ+lfbg\nePHixdq2bZuuuOKKbPQDtDtkArCRCcBGJgAbmYBfpf1RzYQJE2SMyUYvQLtEJgAbmQBsZAKwkQn4\nVcZnqwYAAAAAICgYHAMAAAAAQq/VvwFfdwiFm8t3++ci4F6ODDGmKjUrCZNQjWrcNOVVvQuue3Lg\ngKfJE/+cPqiH3xyeL+/rc8LFMnK2nD3MTxYyYRTxXMN7hX9KePtbJ/45PZloHc668PD3qqo1/txO\nuEImGuV0G+G5gsMqHv9WVSbAmfCYh0MlyERrcdeFx0p+HE94HAO4lPjnuKa5TLT64Hjv3r2SJDeX\n7445qeKCp9eeKqVmpYc+56KdQNq7d69iMf/8zV2py4SLVDhZOq4+FPHSzT8U7EwUFzspQyZah7Ml\nXFXlYVqRiRYIYiZ8t41wVcXr+/a9Cm4mHOVBIhOtwd3S9Vgp6O+dHGkuExHTyh8p1dbW6oMPPlBh\nYaEikSP3wyQSCZWWlqqiokJFRUUZP4+f6vipF1d1WrMXY4z27t2rHj16KCcneN8EIBPMU7p1yIR/\n/u6u6vipF1d1yIQbzeVB8tff3VUdP/Xiqg6ZcINMtH0vrur4MROtvuc4JydHPXv2bPZxRUVFnhaS\nH+v4qRdXdVqrl6B96lkfmfBHL67qkAnvyIQ/enFVh0x409I8SP76u7uq46deXNUhE96QCf/04qqO\nnzIRrI+SAAAAAADIAINjAAAAAEDo+W5wHI1GNX36dEWj0cDU8VMvrur4qZeg89uyDuL6E8R5CjK/\nLesgrj9BnKcg89uyDuL6E8R5CjK/Lesgrj9BnCepDU7IBQAAAACA3/huzzEAAAAAAK2NwTEAAAAA\nIPQYHAMAAAAAQo/BMQAAAAAg9BgcAwAAAABCj8ExAAAAACD0GBwDAAAAAEKPwTEAAAAAIPQYHAMA\nAAAAQo/BMQAAAAAg9BgcAwAAAABCj8ExAAAAACD0GBwDAAAAAEKPwTEAAAAAIPTafHB844036txz\nzw1UHVe9IJz8tC67qkMm4IWf1mVXdcgEvPDTuuyqDpmAF35al13VIRNto80Hx+vWrdPQoUMDVcdV\nL2PGjFEkElEkElGHDh100kknad68ee26jqtegsxP67KrOmQi+70EmZ/WZVd1yET2ewkyP63LruqQ\niez3EmR+Wpdd1SET2e2jUaaNHXXUUebPf/5zoOq4qFFbW2sKCwtNWVmZ2bFjh9m8ebO54oorTF5e\nntm8eXO7rOOql6Dz07rsqg6ZyG4vQeenddlVHTKR3V6Czk/rsqs6ZCK7vQSdn9ZlV3XIRPb6aEqb\nDo63bdtmJJnHH3/cjB8/3nTu3Nn07dvXrFixot3WcdXLW2+9ZSSZ5cuXp+7btGmTkWQWLlzYLuu4\n6iXI/LQuu6pDJrLfS5D5aV12VYdMZL+XIPPTuuyqDpnIfi9B5qd12VUdMpHdPprSpodVr1u3TpJ0\nzz33aNq0aVq/fr169eqlm2++ud3WcdXL6tWrFYlENGTIkNR927dvlyR17969XdZx1UuQ+WlddlWH\nTGS/lyDz07rsqg6ZyH4vQeanddlVHTKR/V6CzE/rsqs6ZCK7fTTJyRA7Q7feeqvp2rWr2bVrV+q+\nWbNmmYEDBxpjjLngggtMcXGxufDCCzOus23bNjN27FjTv39/M3jw4CYPT2iqTiKRMCNGjDBDhw41\ngwYNMnPmzMlonowxpqqqyvTq1cvceOONjfZy0003mc9//vOpn998800zYsQIM2zYMFNTU9Pk8kin\nzpNPPmmuueYaz3Vc9GKMMeXl5Wb48OFm4MCBpn///uZPf/pTS2c1EMgEmSATNjJBJsiEjUyQCTJh\nIxPhyURr5KHN9xyff/75KikpSd23efNmnXjiiZKk6667Tg899JCnOnl5eZo5c6Zef/11LV68WDfc\ncIOqqqrSrpOfn6+lS5dq3bp1evnll1VWVqbKysq050mS7rjjDp1yyilNztPq1av13nvvqaCgQJ06\nddKwYcM0cOBALVq0SDk5Lf+zNVfn1Vdf1cknn+y5joteHnjgAZWXl2vRokXauHGjli5dqpqamhbP\naxCQicaRCTJRh0wcQibIRB0ycQiZIBN1yMQhQctEa+ShzQfHo0aNsu5bu3athg0bJkkaN26cCgsL\nPdU57rjjUvVKSkrUrVs3ffzxx2nXyc3NVX5+viTpwIEDqqmpkTEm7Xl655139Oabb+qss85qcp7W\nrl2rH//4x1q3bp02b96s/fv3a+7cualDBv74xz/qlFNO0eDBg3Xeeeepuro6ozqvvvqq3njjDQ0f\nPlwDBw7U22+/nVGdrVu36pxzzkmtpO+//35aNfbt26fbb79d8+fP19FHHy1JOuaYYzRp0qQml1PQ\nkInGkQkyUYdMHJ6GTJAJiUzUn4ZMkAmJTNSfJkiZaJU8pLWf2aFEImEikYh55ZVXrPu7du1qFixY\nkPr5+eefb/IwiJbWMcaYlStXWocjpFtnz549ZsiQIaZz585m1qxZGdU477zzzFtvvWXKy8sbPQzi\n3XffNZLM4sWLG5tts3v37tT/L7/88gYf25I6/fv3N3fffbcxxpjZs2ebq666Ku06yWTSDBw40Cxd\nutQYY0xlZaX59NNP06rx4IMPmosvvrjRPsOATJCJ+sgEmSATNjJBJsiEjUyQiTBlorXy0GZ7jtet\nW6ecnBwNHjw4dd/WrVu1Z8+e1KciLutUVlbqu9/9rubMmZNxneLiYq1fv15btmzRvHnztGvXrrRq\n/O1vf1Pfvn3Vt2/fJuep7svmw4cPb/D3xhjNmTNHI0eO1NChQ7VgwQJ16tQp7TrJZFLV1dWaMmWK\nJGnIkCHavXt32nUWLFigU089VWPGjJEkdevWTXl5eWnV2Lhxo/Xl+jAiE40jE+FEJhpHJsKJTDSO\nTIQTmWhc0DLRWnnIa/4h2bF+/Xr169fP+iOsXbtWxcXFOv74453WSSaT+vrXv65p06Zp9OjRnvvp\n3r27hgwZomXLlumiiy5qcY377rtPjz76qB577DHt27dPn376qYqKinTLLbdY9desWaMTTzxRxcXF\nDfY6d+5cbdq0ScuWLVPnzp3Vu3dvDRgw4IjHNVfntdde04ABA1LH+K9du7bBlaq5Ohs2bNDIkSMb\n/F1La3Tp0kW1tbVN1gg6MkEm6iMTZIJM2MgEmSATNjJBJsKUiVbLg+d9z1nW3GEQzamtrTWXXHKJ\nmT59uqc+du7caeLxuDHGmHg8bgYMGGDWr1+fcb2mDoNozo033mgeeOABY4wxM2fOND179sy4hwED\nBpjq6mqza9cuM2LECPPRRx+lXefuu+9OnaHu4MGDprKyMu0aL7zwgunfv3/q8I5PPvnEPPzww2nX\nCQMycSQyEW5k4khkItzIxJHIRLiRiSMFLROu8tCmJ+Rqzte+9jVddNFFevrpp9WzZ0+tXLky7Rov\nvPCC5s+fr4ULF2rYsGEaNmyYNmzYkHad7du3a8yYMRo6dKhOP/10XXPNNW12KMukSZN02223aezY\nsaqsrLQOu0jHhg0bdOGFF2rkyJEaP3687rrrrtQX2NNx2WWX6d1339WgQYM0YsQIbdq0Ke0ao0eP\n1tSpUzVu3DgNHjxYY8aMCd3ZFluCTDSMTIQXmWgYmQgvMtEwMhFeZKJhQcuEqzxEjGngFGkAAAAA\nAISIr/ccAwAAAADQGhgcAwAAAABCj8ExAAAAACD0GBwDAAAAAEKPwTEAAAAAIPQYHAMAAAAAQo/B\nMQAAAAAg9Hw3OE4mk5oxY4aSyWRg6vipF1d1/NRL0PltWQdx/QniPAWZ35Z1ENefIM5TkPltWQdx\n/QniPAWZ35Z1ENefIM6TJEWMMcZzFYcSiYRisZji8biKiooCUcdPvbiq46degs5vyzqI608Q5ynI\n/Lasg7j+BHGegsxvyzqI608Q5ynI/Lasg7j+BHGeJB/uOQYAAAAAoLUxOAYAAAAAhF5eaz9hbW2t\nPvjgAxUWFioSiRzx+0QiYf2bKT/V8VMvruq0Zi/GGO3du1c9evRQTk7wPs8hE23bi6s6ZMIdMtG2\nvbiqQybcaC4Pkr/+7q7q+KkXV3XIhBtkou17cVXHj5lo9e8cb9++XaWlpa35lAiIiooK9ezZs63b\ncI5MIFNkArAFMRPkAV6QCcDWXCZafc9xYWGhJOnb365Qx47evjD9xz967+fjIWd6LyLp9INLMp62\nJlql1/+vhyTpA/O+uqiL94aKi73X+OQT7zUcSCQSKu3VK7XuBE3dfFVEoypq5BPQFqup8dzPvLt3\ne64hSd/+QSzjaas6Sz12Hvo/mThSWDIhVSgS8XhiDQc7TDp29F5DknZ27JXxtFWdjXq8degT8ffN\nB04yESnOPKMpjjJh5O21L5FIqFev0kBmIrWNWL1aRQUFnmqdNPZYz/3s3Om5hCQpPnuep+mrcpPq\ncfH1khxtJwK0jZCCvZ1IZaKoyPv7plde8dxP7CTvuZKk0aO9TV/TqUovL3A4nghpJlp9cFx3+EPH\njkWeB8de8yBJRbm53otIyjUe5iUvV/rn5EWmyM1AwAWfnQGxsUNn2ru6+SqKRLy/yDtYRp07u/m7\ne6mSGxGZaIGgZyISKfI8OHaxiFwtZi/5zs2R80w4mS1HmfA6OK4TxEykthEFBSryONDJyfHPa1hR\n586eps/Ny/HfdsJn2wgp4Jlw8b7JyYcHbv7ueR5HZRE/jifaYSaC9SUEAAAAAAAykNHg+N5771Wf\nPn3UqVMnDR8+XMuXL3fdF9CukAnARiYAG5kAbGQCfpT24Hj+/Pm6/vrr9fOf/1xr167VGWecoYkT\nJ2rbtm3Z6A/wPTIB2MgEYCMTgI1MwK/SHhz/7ne/05VXXqnvfe976t+/v2bOnKnS0lLNnj07G/0B\nvkcmABuZAGxkArCRCfhVWoPj6upqrV69WhMmTLDunzBhgl588cUGp0kmk0okEtYNCAoyAdjIBGBL\nNxPkAUFHJuBnaQ2Od+/erZqaGnXv3t26v3v37trZyLn9y8rKFIvFUjeuS4YgIROAjUwAtnQzQR4Q\ndGQCfpbRCbk+ewpsY0yjp8WeNm2a4vF46lZRUZHJUwK+RiYAG5kAbC3NBHlAWJAJ+FFaV9Q6+uij\nlZube8SnOh9++OERn/7UiUajikajmXcI+BiZAGxkArClmwnygKAjE/CztPYcd+zYUcOHD9dzzz1n\n3f/cc89p9OjRThsD2gMyAdjIBGAjE4CNTMDP0tpzLElTp07VpEmTNGLECI0aNUpz5szRtm3bdPXV\nV2ejP8D3yARgIxOAjUwANjIBv0p7cHzxxRersrJSt956q3bs2KFBgwbp6aefVu/evbPRH+B7ZAKw\nkQnARiYAG5mAX6U9OJakH/7wh/rhD3/ouheg3SITgI1MADYyAdjIBPwoo7NVAwAAAAAQJAyOAQAA\nAAChl9Fh1S7859yYijzWuK+Ra2amo8O6Ws81JOmLX8x82pqOTlqw1TqYrxxHn5246CUMDhzwXCIi\n47mGucx7rnzJxXp4++3ea0hSdbW36ZNJN334nDGHbl7U1HpfnyMHvedKkiL792Q+cXWVpAInfaT4\naDsR8diLi9c+vzvhtGOVk+PtndO+fd77MHKzjYh+39vfzORXSZde5aQXSb7KA++bWqhXLyk311OJ\n0i8d57kNV5nQMm+TV+U73kqENBPsOQYAAAAAhB6DYwAAAABA6DE4BgAAAACEHoNjAAAAAEDopT04\nXrZsmc4991z16NFDkUhECxcuzEJbQPtBJoDDyANgIxOAjUzAz9IeHFdVVWno0KGaNWtWNvoB2h0y\nARxGHgAbmQBsZAJ+lvalnCZOnKiJEydmoxegXSITwGHkAbCRCcBGJuBnWb/OcTKZVLLeNTkTiUS2\nnxLwNTIB2MgEcBh5AGxkAq0p6yfkKisrUywWS91KS0uz/ZSAr5EJwEYmgMPIA2AjE2hNWR8cT5s2\nTfF4PHWrqKjI9lMCvkYmABuZAA4jD4CNTKA1Zf2w6mg0qmg0mu2nAdoNMgHYyARwGHkAbGQCrYnr\nHAMAAAAAQi/tPcf79u3Tpk2bUj9v2bJF69atU7du3dSrVy+nzQHtAZkADiMPgI1MADYyAT9Le3C8\natUqjRs3LvXz1KlTJUmTJ0/W3LlznTUGtBdkAjiMPAA2MgHYyAT8LO3B8ZlnniljTDZ6AdolMgEc\nRh4AG5kAbGQCfsZ3jgEAAAAAoZf1s1U3Jqa4pCJPNXIi3vuo2fiW9yKS1K9fxpNW5UsFdT8UFEr7\nHfRTW+uPGmgxF5kwfT7vvZEt3ktIUkRePhWuUioVjjJhah18Sv2LX3qvIa/LRlIiIf3mN0568bO4\nYh4T4WBZSzIRN58jH3NU5q+pJl+q/Of/IwUFivhkO+EkV3Lzdwq6d3d7z4MLzv5W1R6nr/8O1sV2\ngvdN7U5sw9/l9X2TC64ykedxVGbyHL938lEmjLwP+lpagz3HAAAAAIDQY3AMAAAAAAg9BscAAAAA\ngNBjcAwAAAAACL20BsdlZWUaOXKkCgsLVVJSogsuuEBvveXohFZAO0QmABuZAGxkArCRCfhZWoPj\npUuXasqUKVqxYoWee+45HTx4UBMmTFBVVVW2+gN8jUwANjIB2MgEYCMT8LO0Thq+aNEi6+fy8nKV\nlJRo9erVGjNmjNPGgPaATAA2MgHYyARgIxPwM0/fOY7H45Kkbt26OWkGaO/IBGAjE4CNTAA2MgE/\nyfhy08YYTZ06VaeffroGDRrU6OOSyaSSyWTq50QikelTAr5GJgAbmQBsLckEeUCYkAn4TcZ7jq+5\n5hq9+uqreuSRR5p8XFlZmWKxWOpWWlqa6VMCvkYmABuZAGwtyQR5QJiQCfhNxBhj0p3o2muv1cKF\nC7Vs2TL16dOnycc29GnPoZU6Lqko3ae25Di4EFXN647OjtevX8aTVuVLBf88B8G+LlKX/Q76qa11\nUMQfEomEYsXFisfjKiryts5ki18yYfp83tP0kqQtW7zXkBRR2i8th+VXSVUFktxlwtR66McxT8tG\n4cmE90R4X9aSZCJurnp4zFGZvy6b/CpVbnWbCRfbCaOIg0bIRH3ZzIMLLjLlhOvtRIDeN0nhyISL\n901+kpfx8byHmPwq1cSDmQkX25pEIqHi4lizmUjrz2CM0bXXXqsFCxZoyZIlzb7hkaRoNKpoNJrO\n0wDtBpkAbGQCsKWbCfKAoCMT8LO0BsdTpkzRvHnz9Le//U2FhYXauXOnJCkWi6lz585ZaRDwMzIB\n2MgEYCMTgI1MwM/SOlZs9uzZisfjOvPMM3XcccelbvPnz89Wf4CvkQnARiYAG5kAbGQCfpb2YdUA\nDiMTgI1MADYyAdjIBPzMzVlGAAAAAABoxxgcAwAAAABCz+NJwzMXP/vbKurQwVONyMIF3hvxcAmm\n+rxd2qBK0qFTr2vfXkldvDfk4jpXPjqFexjEOxytoojHU9Vvqfbch6vLdJhOmZ9Uo6qTqUuEzL59\nMg4yEclxcMkZR5nwekkCV5fP8buYXy7T8Ze/OCnz0b9m/neryk9tJXy2neDwyNbimzw44vV1rN47\nJzeZ4H1TuxNXzHsiOnb03EekOtn8g1rg4EGvBer9P2CZcPHetKU12HMMAAAAAAg9BscAAAAAgNBj\ncAwAAAAACD0GxwAAAACA0EtrcDx79mwNGTJERUVFKioq0qhRo/TMM89kqzfA98gEYCMTgI1MADYy\nAT9La3Dcs2dP3XXXXVq1apVWrVqlL3/5yzr//PP12muvZas/wNfIBGAjE4CNTAA2MgE/S+tSTuee\ne6718x133KHZs2drxYoVGjhwoNPGgPaATAA2MgHYyARgIxPws4yvc1xTU6PHHntMVVVVGjVqVKOP\nSyaTSiYPX/8rkUhk+pSAr5EJwEYmAFtLMkEeECZkAn6T9gm5NmzYoIKCAkWjUV199dVasGCBBgwY\n0Ojjy8rKFIvFUrfS0lJPDQN+QyYAG5kAbOlkgjwgDMgE/CpijDHpTFBdXa1t27bpk08+0V/+8hc9\n8MADWrp0aaMrdEOf9pSWlip+9tkq6tDBW/MLF3iaXpKMIp5rSFJEaS1GW36VVFUgSdpn9qqLunhv\nKMfBichra73XcCCRSChWXKx4PK6ioqK2bucIzjLRoYOKIh7Xx+pqb9PL47pcj+nUOeNpq/KNCioP\nLaO9Zp+TTERyHGTdUSa8vu4kEgkVF8cCnwkpLqnt58/81fu2RpL0r/+a8aRV+VJB1aH/+2k7YWrd\nvF54fd0J0nbC73lwxevroPNMBOh9kxSOTDhJRMeOXisoUp1s/kGtwfV4IqSZSPuw6o4dO+rEE0+U\nJI0YMUIrV67Uf/7nf+q+++5r8PHRaFTRaDTdpwHaDTIB2MgEYEsnE+QBYUAm4FeePxIwxlif5gBh\nRyYAG5kAbGQCsJEJ+EVae45/9rOfaeLEiSotLdXevXv16KOPasmSJVq0aFG2+gN8jUwANjIB2MgE\nYCMT8LO0Bse7du3SpEmTtGPHDsViMQ0ZMkSLFi3SV7/61Wz1B/gamQBsZAKwkQnARibgZ2kNjh98\n8MFs9QG0S2QCsJEJwEYmABuZgJ85OA0ZAAAAAADtG4NjAAAAAEDopX0pJ2eeespzCRfXKHZ2TddI\n5p8zVEWMCpx0UY+Privm5DppYfDpp55LuFifXV37Wwc8TFtvlYnIuMmpi0zcfrv3GpIiBw96m54z\neraYk/X50syv2V2ft/W4SnK9pXCQCVfbULYTzYsr5vmarqeN9v73euFFN9uI3BxvvZgcx5ngfVO7\nc8WFcXXo4C0Vj/y91HMfZruj900eOd9KhDQTpA8AAAAAEHoMjgEAAAAAocfgGAAAAAAQegyOAQAA\nAACh52lwXFZWpkgkouuvv95RO0D7RiYAG5kAbGQCsJEJ+EnGg+OVK1dqzpw5GjJkiMt+gHaLTAA2\nMgHYyARgIxPwm4wGx/v27dOll16q+++/X127dnXdE9DukAnARiYAG5kAbGQCfpTR4HjKlCk6++yz\nNX78+GYfm0wmlUgkrBsQNGQCsJEJwNbSTJAHhAWZgB/lpTvBo48+qjVr1mjlypUtenxZWZl+9atf\npd0Y0F6QCcBGJgBbOpkgDwgDMgG/SmvPcUVFhX70ox/p4YcfVqdOnVo0zbRp0xSPx1O3ioqKjBoF\n/IhMADYyAdjSzQR5QNCRCfhZWnuOV69erQ8//FDDhw9P3VdTU6Nly5Zp1qxZSiaTys3NtaaJRqOK\nRqNuugV8hkwANjIB2NLNBHlA0JEJ+Flag+OvfOUr2rBhg3Xf5Zdfrn79+umnP/3pEW94gKAjE4CN\nTAA2MgHYyAT8LK3BcWFhoQYNGmTd16VLFx111FFH3A+EAZkAbGQCsJEJwEYm4GcZX+cYAAAAAICg\nSPts1Z+1ZMkSB20AwUEmABuZAGxkArCRCfgFe44BAAAAAKHH4BgAAAAAEHqeD6vOVExxSUVt9fTu\nGeNh2nr/LyiU9nvuRqqtdVDEEa+9JBJScbGTVvzMRSaMIm6acSAiD5lQlaSCQ//1USbML37poBGv\ny0aHMvHrXzvpxc/iinneSnhe1pLMP9zk6oMPMp92f0Q6se4HP2XC0WtOhO1Es5xsI170/vdykSlJ\nktfVr/70LjIRpPdNUigy8Ze/eK+xqNj7NZOr8733IUlVC5/zViDnH5LOP/R/MnGkFmaCPccAAAAA\ngNBjcAwAAAAACD0GxwAAAACA0EtrcDxjxgxFIhHrduyxx2arN8D3yARgIxOAjUwANjIBP0v7hFwD\nBw7U4sWLUz/n5uY6bQhob8gEYCMTgI1MADYyAb9Ke3Ccl5fHpztAPWQCsJEJwEYmABuZgF+l/Z3j\nd955Rz169FCfPn10ySWXaPPmzdnoC2g3yARgIxOAjUwANjIBv0prz/Epp5yihx56SH379tWuXbt0\n++23a/To0Xrttdd01FFHNThNMplUMplM/ZxIJLx1DPgImQBsZAKwpZsJ8oCgIxPws7T2HE+cOFEX\nXnihBg8erPHjx+upp56SJP3hD39odJqysjLFYrHUrbS01FvHgI+QCcBGJgBbupkgDwg6MgE/83Qp\npy5dumjw4MF65513Gn3MtGnTFI/HU7eKigovTwn4GpkAbGQCsDWXCfKAsCET8JO0T8hVXzKZ1Btv\nvKEzzjij0cdEo1FFo1EvTwO0G2QCsJEJwNZcJsgDwoZMwE/S2nN80003aenSpdqyZYtefvllfeMb\n31AikdDkyZOz1R/ga2QCsJEJwEYmABuZgJ+lted4+/bt+ta3vqXdu3frmGOO0amnnqoVK1aod+/e\n2eoP8DUyAdjIBGAjE4CNTMDP0hocP/roo9nqA2iXyARgIxOAjUwANjIBP/N0Qi4AAAAAAIKAwTEA\nAAAAIPQ8na3ai65dpUjEW42PP/beh5HHJv4pIuNh6ipJBYf+u2+vpC7eG8px8LlHba33GmixeG43\nFXkNxUHvfXhblw8zeR0ynrYqz9QlQmbfPhkHmYjkeM96xFEmvL7uuHrd8ruY4pKK2roNjR3jJhNL\ne2T+d6vK16FNhchENqZvD+KKeU5Dbo6DddnRWwOvf7N675zcvHfifVO74yITenOn5z4ix3b3XEOS\nIhO+6q1AflVqO0EmMseeYwAAAABA6DE4BgAAAACEHoNjAAAAAEDoMTgGAAAAAIRe2oPj999/X9/5\nznd01FFHKT8/X8OGDdPq1auz0RvQLpAJwEYmABuZAGxkAn6V1tmq9+zZo9NOO03jxo3TM888o5KS\nEr377rsqLi7OUnuAv5EJwEYmABuZAGxkAn6W1uD417/+tUpLS1VeXp667/jjj3fdE9BukAnARiYA\nG5kAbGQCfpbWYdVPPPGERowYoYsuukglJSU6+eSTdf/99zc5TTKZVCKRsG5AUJAJwEYmAFu6mSAP\nCDoyAT9La3C8efNmzZ49W1/4whf07LPP6uqrr9Z1112nhx56qNFpysrKFIvFUrfS0lLPTQN+QSYA\nG5kAbOlmgjwg6MgE/CxijDEtfXDHjh01YsQIvfjii6n7rrvuOq1cuVIvvfRSg9Mkk0klk8nUz4lE\nQqWlperaNa5IpMhD69LHH3uaXJJkFPFeRFJELV6MR8qvkqoKJEn7zF51URfvDeU4OBF5ba33Gg4k\nEgnFiosVj8dVVORtnXHNZSbiubkqinhcHw8e9Da9PK7L9Zi8DhlPW5VvVBCvkSTtNfucZCKS4yDr\njjLh9XUnkUiouDgW+ExIcUltP39jxrips3RZ5n/3qnypoOrQ/8nEkYKUiUa3EfKehtwc76/vrt4a\neP2b18+Ek/dOAXrfJAXrvVM2M6GdO71WUOTY7p5rOOF6PBHSTKQ118cdd5wGDBhg3de/f39t27at\n0Wmi0aiKioqsGxAUZAKwkQnAlm4myAOCjkzAz9IaHJ922ml66623rPvefvtt9e7d22lTQHtBJgAb\nmQBsZAKwkQn4WVqD4xtuuEErVqzQnXfeqU2bNmnevHmaM2eOpkyZkq3+AF8jE4CNTAA2MgHYyAT8\nLK3B8ciRI7VgwQI98sgjGjRokG677TbNnDlTl156abb6A3yNTAA2MgHYyARgIxPws7SucyxJ55xz\njs4555xs9AK0S2QCsJEJwEYmABuZgF85OA0ZAAAAAADtG4NjAAAAAEDopX1YtSvv7Yn54OqVUoc8\nN9d07eRhSZpOUrL5h6XHxXXFXFzfTPLVNc58rabGcwkX1yh2de1vebnkcr1pIzJurr3sYj28/Xbv\nNSRFPF6POpJ0/ooRWC7W5+gKN9sJb+txlaQCJ32k+Gg7EfHYi6vrs/tZzMFVXV38tVxtI7z/zRxn\nwkd54H1TC/Xu7XmZD53g/RrFzt43eeR8KxHSTLDnGAAAAAAQegyOAQAAAAChx+AYAAAAABB6DI4B\nAAAAAKGX1uD4+OOPVyQSOeI2ZcqUbPUH+BqZAGxkArCRCcBGJuBnaZ1jeeXKlaqpd0bdjRs36qtf\n/aouuugi540B7QGZAGxkArCRCcBGJuBnaQ2OjznmGOvnu+66SyeccILGjh3rtCmgvSATgI1MADYy\nAdjIBPws46vzVldX6+GHH9bUqVMViTR+fa9kMqlkvWtyJhKJTJ8S8DUyAdjIBGBrSSbIA8KETMBv\nMj4h18KFC/XJJ5/osssua/JxZWVlisViqVtpaWmmTwn4GpkAbGQCsLUkE+QBYUIm4DcRY4zJZMKv\nfe1r6tixo5588skmH9fQpz2lpaWKSyrK5Ikd65CX0ewfIS/jffCSya9SsrJAkrTP7FUXdXHSk2c5\njk5mXlvrafJEIqFYcbHi8biKivyw1jTMD5mIyPv6bNT4Hr7WUpUvFVQd+r+vMnH77W7qHDzoafJE\nMqnYr38d+EzIQSpcrM/Rjm62E9XVHibOr5KqDm0n9pp9TjLh4vWC7UR6WpKJbObBxZ+rptbNNsLz\n+lcvE77ZTvgkD1I4MhHv3VtFHpf50MLNnqaXpPWvtv37Jsmn753aYSYyGtJt3bpVixcv1l//+tdm\nHxuNRhWNRjN5GqDdIBOAjUwAtpZmgjwgLMgE/Cij4Xx5eblKSkp09tlnu+4HaJfIBGAjE4CNTAA2\nMgE/SntwXFtbq/Lyck2ePFl5Xo4lBgKCTAA2MgHYyARgIxPwq7QHx4sXL9a2bdt0xRVXZKMfoN0h\nE4CNTAA2MgHYyAT8Ku2PaiZMmKAMz+EFBBKZAGxkArCRCcBGJuBXjk4hBgAAAABA+9XqB/nXfUrk\nl8t3G+OmEy8ffhlTlVogCZNQjWqc9OQbHi/WXnex96B+wug2E96r+CGbVUb+zMSBA27q1Hibn8Q/\nL2kR9Ez4ZX12tZ3w1oT77YSTSzm5wnaiUS7z4GLxuEuDx0pBfu/kMQ+HSgQ/EwkHl/epqfHHdsYF\n3753cqEVM9Hqg+O9e/dKknxz+e6amJsyXta/pKR/ttFDn3PRjr8UFzsps3fvXsVibv5efuI2E96X\njy+W8D8U7Ew4EvRMuEiFk6XzqQ+Wcb1MfE492rSVrGA70SiXeXAxTnK3dD1WCvJ2wlEepGBnorSi\nwkG1gLxvkshECzWXiYhp5Y+Uamtr9cEHH6iwsFCRyJEXza67sHdFRYWni5b7qY6fenFVpzV7McZo\n79696tGjh3JcXUzcR8gE85RuHTLhn7+7qzp+6sVVHTLhRnN5kPz1d3dVx0+9uKpDJtwgE23fi6s6\nfsxEq+85zsnJUc+ePZt9XFFRkaeF5Mc6furFVZ3W6iVon3rWRyb80YurOmTCOzLhj15c1SET3rQ0\nD5K//u6u6vipF1d1yIQ3ZMI/vbiq46dMBOujJAAAAAAAMsDgGAAAAAAQer4bHEejUU2fPl3RaDQw\ndfzUi6s6fuol6Py2rIO4/gRxnoLMb8s6iOtPEOcpyPy2rIO4/gRxnoLMb8s6iOtPEOdJaoMTcgEA\nAAAA4De+23MMAAAAAEBrY3AMAAAAAAg9BscAAAAAgNBjcAwAAAAACD0GxwAAAACA0GNwDAAAAAAI\nPQbHAAAAAIDQY3AMAAAAAAg9BscAAAAAgNBjcAwAAAAACD0GxwAAAACA0GNwDAAAAAAIPQbHAAAA\nAIDQY3AMAAAAAAi9Nh8c33jjjTr33HMDVcdVLwgnP63LruqQCXjhp3XZVR0yAS/8tC67qkMm4IWf\n1mVXdchE22jzwfG6des0dOjQQNVx1cuYMWMUiUQUiUTUoUMHnXTSSZo3b167ruOqlyDz07rsqg6Z\nyH4vQeanddlVHTKR/V6CzE/rsqs6ZCL7vQSZn9ZlV3XIRHb7aJRpY0cddZT585//HKg6LmrU1taa\nwsJCU1ZWZnbs2GE2b95srrjiCpOXl2c2b97cLuu46iXo/LQuu6pDJrLbS9D5aV12VYdMZLeXoPPT\nuuyqDpnIbi9B56d12VUdMpG9PprSpoPjbdu2GUnm8ccfN+PHjzedO3c2ffv2NStWrGi3dVz18tZb\nbxlJZvny5an7Nm3aZCSZhQsXtss6rnoJMj+ty67qkIns9xJkflqXXdUhE9nvJcj8tC67qkMmst9L\nkPlpXXZVh0xkt4+mtOlh1evWrZMk3XPPPZo2bZrWr1+vXr166eabb263dVz1snr1akUiEQ0ZMiR1\n3/bt2yVJ3bt3b5d1XPUSZH5al13VIRPZ7yXI/LQuu6pDJrLfS5D5aV12VYdMZL+XIPPTuuyqDpnI\nbh9NcjLEztCtt95qunbtanbt2pW6b9asWWbgwIHGGGMuuOACU1xcbC688MKM62zbts2MHTvW9O/f\n3wwePLjJwxOaqpNIJMyIESPM0KFDzaBBg8ycOXMymidjjKmqqjK9evUyN954Y6O93HTTTebzn/98\n6uc333zTjBgxwgwbNszU1NQ0uTzSqfPkk0+aa665xnMdF70YY0x5ebkZPny4GThwoOnfv7/505/+\n1NJZDQQyQSbIhI1MkAkyYSMTZIJM2MhEeDLRGnlo8z3H559/vkpKSlL3bd68WSeeeKIk6brrrtND\nDz3kqU5eXp5mzpyp119/XYsXL9YNN9ygqqqqtOvk5+dr6dKlWrdunV5++WWVlZWpsrIy7XmSpDvu\nuEOnnHJKk/O0evVqvffeeyooKFCnTp00bNgwDRw4UIsWLVJOTsv/bM3VefXVV3XyySd7ruOilwce\neEDl5eVatGiRNm7cqKVLl6qmpqbF8xoEZKJxZIJM1CETh5AJMlGHTBxCJshEHTJxSNAy0Rp5aPPB\n8ahRo6z71q5dq2HDhkmSxo0bp8LCQk91jjvuuFS9kpISdevWTR9//HHadXJzc5Wfny9JOnDggGpq\namSMSXue3nnnHb355ps666yzmpyntWvX6sc//rHWrVunzZs3a//+/Zo7d27qkIE//vGPOuWUUzR4\n8GCdd955qq6uzqjOq6++qjfeeEPDhw/XwIED9fbbb2dUZ+vWrTrnnHNSK+n777+fVo19+/bp9ttv\n1/z583X00UdLko455hhNmjSpyeUUNGSicWSCTNQhE4enIRNkQiIT9achE2RCIhP1pwlSJlolD2nt\nZ3YokUiYSCRiXnnlFev+rl27mgULFqR+fv7555s8DKKldYwxZuXKldbhCOnW2bNnjxkyZIjp3Lmz\nmTVrVkY1zjvvPPPWW2+Z8vLyRg+DePfdd40ks3jx4sZm2+zevTv1/8svv7zBx7akTv/+/c3dd99t\njDFm9uzZ5qqrrkq7TjKZNAMHDjRLly41xhhTWVlpPv3007RqPPjgg+biiy9utM8wIBNkoj4yQSbI\nhI1MkAkyYSMTZCJMmWitPLTZnuN169YpJydHgwcPTt23detW7dmzJ/WpiMs6lZWV+u53v6s5c+Zk\nXKe4uFjr16/Xli1bNG/ePO3atSutGn/729/Ut29f9e3bt8l5qvuy+fDhwxv8vTFGc+bM0ciRIzV0\n6FAtWLBAnTp1SrtOMplUdXW1pkyZIkkaMmSIdu/enXadBQsW6NRTT9WYMWMkSd26dVNeXl5aNTZu\n3Gh9uT6MyETjyEQ4kYnGkYlwIhONIxPhRCYaF7RMtFYe8pp/SHasX79e/fr1s/4Ia9euVXFxsY4/\n/nindZLJpL7+9a9r2rRpGj16tOd+unfvriFDhmjZsmW66KKLWlzjvvvu06OPPqrHHntM+/bt06ef\nfqqioiLdcsstVv01a9boxBNPVHFxcYO9zp07V5s2bdKyZcvUuXNn9e7dWwMGDDjicc3Vee211zRg\nwIDUMf5r165tcKVqrs6GDRs0cuTIBn/X0hpdunRRbW1tkzWCjkyQifrIBJkgEzYyQSbIhI1MkIkw\nZaLV8uB533OWNXcYRHNqa2vNJZdcYqZPn+6pj507d5p4PG6MMSYej5sBAwaY9evXZ1yvqcMgmnPj\njTeaBx54wBhjzMyZM03Pnj0z7mHAgAGmurra7Nq1y4wYMcJ89NFHade5++67U2eoO3jwoKmsrEy7\nxgsvvGD69++fOrzjk08+MQ8//HDadcKATByJTIQbmTgSmQg3MnEkMhFuZOJIQcuEqzy06Qm5mvO1\nr31NF110kZ5++mn17NlTK1euTLvGCy+8oPnz52vhwoUaNmyYhg0bpg0bNqRdZ/v27RozZoyGDh2q\n008/Xddcc02bHcoyadIk3XbbbRo7dqwqKyutwy7SsWHDBl144YUaOXKkxo8fr7vuuiv1BfZ0XHbZ\nZXr33Xc1aNAgjRgxQps2bUq7xujRozV16lSNGzdOgwcP1pgxY0J3tsWWIBMNIxPhRSYaRibCi0w0\njEyEF5loWNAy4SoPEWMaOEUaAAAAAAAh4us9xwAAAAAAtAYGxwAAAACA0GNwDAAAAAAIPQbHAAAA\nAIDQY3AMAAAAAAg9BscAAAAAgNBjcAwAAAAACD3fDY6TyaRmzJihZDIZmDp+6sVVHT/1EnR+W9ZB\nXH+COE9B5rdlHcT1J4jzFGR+W9ZBXH+COE9B5rdlHcT1J4jzJEkRY4zxXMWhRCKhWCymeDyuoqKi\nQNTxUy+u6vipl6Dz27IO4voTxHkKMr8t6yCuP0GcpyDz27IO4voTxHkKMr8t6yCuP0GcJ8mHe44B\nAAAAAGhtDI4BAAAAAKGX19pPWFtbqw8++ECFhYWKRCJH/D6RSFj/ZspPdfzUi6s6rdmLMUZ79+5V\njx49lJMTvM9zyETb9uKqDplwh0y0bS+u6pAJN5rLg+Svv7urOn7qxVUdMuEGmWj7XlzV8WMmWv07\nx9u3b1dpaWlrPiUCoqKiQj179mzrNpwjE8gUmQBsQcwEeYAXZAKwNZeJVt9zXFhYKEmquPlmFXXq\n5KlWbMYNnvvJzfVcQpLk5UM5k1+lg9t6SJI+MO+ri7p4b6i42HuNTz7xXsOBRCKh0l69UutO0NTN\n1+LFFerSxdtJBAaMinlv6KWXvNeQpPHjM560qrNRj3f3SyITDQlLJnJyKhSJeMvEx/1Ge29o+3bv\nNSTpwIGMJ63KN+rxXrUk6X3zgZNMRIodvF6QiaxLvW/6xS88v29SWZnnfvpEP/BcQ5K2fOxt/avK\nl3rsOPR/J9uJAG0jpJBk4tvfVlHHjt6KPfaY536+0MVNJryq7Vyl3a86HE+ENBOtPjiuO/yhqFMn\n7y/y8n6GvkaOxmjdOpHc1KwUmSI3AwEXfHYGxMYOnWnv6uarS5ciFRR4W+ZFLpZRQYH3GpKnUOTm\niEy0QNAzEYkUeR4cF7n4BNQHG4rciJxnwslckYmsc/q+ycHyyclx8zf3ur3KjRj/bSd8lgcp4Jno\n2NH74NhHmfAsx4fjiXaYiWB9CQEAAAAAgAxkNDi+99571adPH3Xq1EnDhw/X8uXLXfcFtCtkArCR\nCcBGJgAbmYAfpT04nj9/vq6//nr9/Oc/19q1a3XGGWdo4sSJ2rZtWzb6A3yPTAA2MgHYyARgIxPw\nq7QHx7/73e905ZVX6nvf+5769++vmTNnqrS0VLNnz85Gf4DvkQnARiYAG5kAbGQCfpXW4Li6ulqr\nV6/WhAkTrPsnTJigF1980WljQHtAJgAbmQBsZAKwkQn4WVpnq969e7dqamrUvXt36/7u3btr586d\nDU6TTCaVTCZTP3u9yDPgJ2QCsJEJwJZuJsgDgo5MwM8yOiHXZ0+BbYxp9LTYZWVlisViqRsX7UYQ\nkQnARiYAW0szQR4QFmQCfpTW4Pjoo49Wbm7uEZ/qfPjhh0d8+lNn2rRpisfjqVtFRUXm3QI+QyYA\nG5kAbOlmgjwg6MgE/CytwXHHjh01fPhwPffcc9b9zz33nEaPHt3gNNFoVEVFRdYNCAoyAdjIBGBL\nNxPkAUFHJuBnaX3nWJKmTp2qSZMmacSIERo1apTmzJmjbdu26eqrr85Gf4DvkQnARiYAG5kAbGQC\nfpX24Pjiiy9WZWWlbr31Vu3YsUODBg3S008/rd69e2ejP8D3yARgIxOAjUwANjIBv0p7cCxJP/zh\nD/XDH/7QdS9Au0UmABuZAGxkArCRCfhRRmerBgAAAAAgSBgcAwAAAABCL6PDqp2YMcNzCaObPdeI\nHDSea0jSl76U+bQ1naTVTrqop7bWe42OHb3XkKT9+71Nf/Cgmz58bsComDyff7F/f++NDB7svYak\niDxkq7ZKUoGTPg7XdJCJHEefJ7roJQRqahwU2bDBc4mI8cHfK8d9Jkyt9+1fZMZ0B53Ie7YOHHDT\nh491m36tIhFvW4lPD97kuY+POnTzXENykCvjOBMuXpdvucV7DcnN+68QZEJz53ou0bmT99fBf+w8\n8trMGcnzNiyryjdutxIhfd/EnmMAAAAAQOgxOAYAAAAAhB6DYwAAAABA6DE4BgAAAACEXtqD42XL\nluncc89Vjx49FIlEtHDhwiy0BbQfZAI4jDwANjIB2MgE/CztwXFVVZWGDh2qWbNmZaMfoN0hE8Bh\n5AGwkQnARibgZ2mfM3zixImaOHFiNnoB2iUyARxGHgAbmQBsZAJ+lvXrHCeTSSWTydTPiUQi208J\n+BqZAGxkAjiMPAA2MoHWlPUTcpWVlSkWi6VupaWl2X5KwNfIBGAjE8Bh5AGwkQm0pqwPjqdNm6Z4\nPJ66VVRUZPspAV8jE4CNTACHkQfARibQmrJ+WHU0GlU0Gs320wDtBpkAbGQCOIw8ADYygdbEdY4B\nAAAAAKGX9p7jffv2adOmTamft2zZonXr1qlbt27q1auX0+aA9oBMAIeRB8BGJgAbmYCfpT04XrVq\nlcaNG5f6eerUqZKkyZMna+7cuc4aA9oLMgEcRh4AG5kAbGQCfpb24PjMM8+UMSYbvQDtEpkADiMP\ngI1MADYyAT/jO8cAAAAAgNDL+tmqsyk3x/unTqY24qATSa9kPmlVvlRQ90NBobTfQT+1td5rVFd7\nr+FCXrteTVvs2M5xRSJFnmpUveF9fY52dPNpbs7BzKc1OVKqCz9lwkUNtFhcMXlLhBTx0d4Jo8zz\nWaXD24lIQYEiDjJhah1sQ2f8ynsjDphEQrrrrrZuI6tqarzXiMjB3/wPT3pvRJI5z9v2qn4mnGwn\nXLy+33qr9xquJBLSnXe2dRdZFVNc8rqVOOC9Dxe5kqT8jt6mNx3rpcIvmWiH75vYcwwAAAAACD0G\nxwAAAACA0GNwDAAAAAAIPQbHAAAAAIDQY3AMAAAAAAi9tAbHZWVlGjlypAoLC1VSUqILLrhAb731\nVrZ6A3yPTAA2MgHYyARgIxPws7QGx0uXLtWUKVO0YsUKPffcczp48KAmTJigqqqqbPUH+BqZAGxk\nArCRCcBGJuBnaV1AdtGiRdbP5eXlKikp0erVqzVmzBinjQHtAZkAbGQCsJEJwEYm4GdpDY4/Kx6P\nS5K6devW6GOSyaSSyWTq50Qi4eUpAV8jE4CNTAC25jJBHhA2ZAJ+kvEJuYwxmjp1qk4//XQNGjSo\n0ceVlZUpFoulbqWlpZk+JeBrZAKwkQnA1pJMkAeECZmA32Q8OL7mmmv06quv6pFHHmnycdOmTVM8\nHk/dKioqMn1KwNfIBGAjE4CtJZkgDwgTMgG/yeiw6muvvVZPPPGEli1bpp49ezb52Gg0qmg0mlFz\nQHtBJgAbmQBsLc0EeUBYkAn4UVqDY2OMrr32Wi1YsEBLlixRnz59stUX0C6QCcBGJgAbmQBsZAJ+\nltbgeMqUKZo3b57+9re/qbCwUDt37pQkxWIxde7cOSsNAn5GJgAbmQBsZAKwkQn4WVrfOZ49e7bi\n8bjOPPNMHXfccanb/Pnzs9Uf4GtkArCRCcBGJgAbmYCfpX1YNYDDyARgIxOAjUwANjIBP8v4bNUA\nAAAAAARFRmerdiGmuKQib0VqvfcRkR8+vaqSVHDov/v2SurivWSOg889ah0sYLTYjh1SkcdIuPi4\nK1kd8V7Eo6raVCLIRIi52E7s3++9j875bZ+J+sy+fTIOMhHJ8T5fptYP29BwiCvm9V2TE5Hz3PzN\nna45LrYTbCPaHb9kQt/6lpMyufPneZre1F+FyUTG2HMMAAAAAAg9BscAAAAAgNBjcAwAAAAACD0G\nxwAAAACA0Ev7OsdDhgxRUVGRioqKNGrUKD3zzDPZ6g3wPTIB2MgEYCMTgI1MwM/SGhz37NlTd911\nl1atWqVVq1bpy1/+ss4//3y99tpr2eoP8DUyAdjIBGAjE4CNTMDPIsbjlbi7deum3/zmN7ryyitb\n9PhEIqFYLCa5uJRTUORXSVWHLlyzz+xVFy5bY0kkEooVFysej6vI87WOsi/TTHzyiff5c3FpFj+o\nypcKqg79n0wcKSyZcLGdCMqlnOpnYq/Z5yQTQbqUUyKRUHFxLJCZqMuDX941uboEppG39c/5diJA\n2wgp2NsJv2XCN5dyyq+S2etwPBHSTGR8neOamho99thjqqqq0qhRozItAwQGmQBsZAKwkQnARibg\nN2kPjjds2KBRo0bpwIEDKigo0IIFCzRgwIBGH59MJpVMJlM/JxKJzDoFfIpMADYyAdjSyQR5QBiQ\nCfhV2vvLTzrpJK1bt04rVqzQD37wA02ePFmvv/56o48vKytTLBZL3UpLSz01DPgNmQBsZAKwpZMJ\n8oAwIBPwK8/fOR4/frxOOOEE3XfffQ3+vqFPew6t1L75pkDb4zvHTWpv35vJNBN85/gwvnPctLBk\ngu8cH8Z3jpvW3r5z3FQmGsuDX9418Z3jJvhkGyEFazvh90zwneMmtMNMZPyd4zrGGGuF/axoNKpo\nNOr1aYB2g0wANjIB2JrKBHlAGJEJ+EVag+Of/exnmjhxokpLS7V37149+uijWrJkiRYtWpSt/gBf\nIxOAjUwANjIB2MgE/CytwfGuXbs0adIk7dixQ7FYTEOGDNGiRYv01a9+NVv9Ab5GJgAbmQBsZAKw\nkQn4WVqD4wcffDBbfQDtEpkAbGQCsJEJwEYm4GcOvmkNAAAAAED7xuAYAAAAABB6ns9Wnam4Yr44\n/bqzSxKcfkbG01Z1qlGBky7qcXHq9Ftv9V5D8t5LE2e5DZJIcczjhS2kz/Xwvj6//4Gby9Z4y1aV\n5DoVPrqcgJPLI6BFXFyGydV2whv3mXBxGabIrb9y0Il3kQMH2rqFrIs5uHCN18snSZKJuHn9ini7\nkqicZyJI75ukULx36pYbVyTiLRMHD3rvwzzi5n1TjR7xNH1VreOtREjfN/EODQAAAAAQegyOAQAA\nAAChx+AYAAAAABB6DI4BAAAAAKHnaXBcVlamSCSi66+/3lE7QPtGJgAbmQBsZAKwkQn4ScaD45Ur\nV2rOnDkaMmSIy36AdotMADYyAdjIBGAjE/CbjAbH+/bt06WXXqr7779fXbt2dd0T0O6QCcBGJgAb\nmQBsZAJ+lNHgeMqUKTr77LM1fvz4Zh+bTCaVSCSsGxA0ZAKwkQnA1tJMkAeEBZmAH+WlO8Gjjz6q\nNWvWaOXKlS16fFlZmX71q1+l3RjQXpAJwEYmAFs6mSAPCAMyAb9Ka89xRUWFfvSjH+nhhx9Wp06d\nWjTNtGnTFI/HU7eKioqMGgX8iEwANjIB2NLNBHlA0JEJ+Flae45Xr16tDz/8UMOHD0/dV1NTo2XL\nlmnWrFlKJpPKzc21polGo4pGo266BXyGTAA2MgHY0s0EeUDQkQn4WVqD46985SvasGGDdd/ll1+u\nfv366ac//ekRb3iAoCMTgI1MADYyAdjIBPwsrcFxYWGhBg0aZN3XpUsXHXXUUUfcD4QBmQBsZAKw\nkQnARibgZxlf5xgAAAAAgKBI+2zVn7VkyRIHbQDBQSYAG5kAbGQCsJEJ+AV7jgEAAAAAocfgGAAA\nAAAQehFjjGnNJ0wkEorFYopLKvJYKyLvrRtFPNeQJEUyr1OVb1Sw79D/93WRuux30E9trYMi/pBI\nJBQrLlY8HldRkde1xn/qMiEnqfCPESMyn7amU5XWLi+QRCYaEpZM+GU74YqX7U1VvlRQdej/rjJh\nav2zbLxKJBIqLo4FMhN+20aYJUvdFDrzTE+TO89EgLYRUrC3Ey4zYd7b6rmfyPG9PdeQvI9JyETT\nWpoJ9hwDAAAAAEKPwTEAAAAAIPQYHAMAAAAAQo/BMQAAAAAg9NIaHM+YMUORSMS6HXvssdnqDfA9\nMgHYyARgIxOAjUzAz/LSnWDgwIFavHhx6ufc3FynDQHtDZkAbGQCsJEJwEYm4FdpD47z8vL4dAeo\nh0wANjIB2MgEYCMT8Ku0v3P8zjvvqEePHurTp48uueQSbd68ucnHJ5NJJRIJ6wYECZkAbGQCsKWT\nCfKAMCAT8Ku0BsennHKKHnroIT377LO6//77tXPnTo0ePVqVlZWNTlNWVqZYLJa6lZaWem4a8Asy\nAdjIBGBLNxPkAUFHJuBnEWOMyXTiqqoqnXDCCfrJT36iqVOnNviYZDKpZDKZ+jmRSKi0tFRxSUWZ\nPvE/RZRx6ylGEc81JEmRzOtU5RsV7Dv0/31dpC77HfRTW+ugiD8kEgnFiosVj8dVVOR1rckuL5mQ\nk1T4x4gRmU9b06lKa5cXSCITDQlLJvyynXDFy/amKl8qqDr0f1eZMLX+WTZeJRIJFRfHApEJv28j\nzJKlbgqdeaanyZ1nIkDbCClY24lsZsK8t9XT9JIUOb635xqS9zEJmWhaSzOR9neO6+vSpYsGDx6s\nd955p9HHRKNRRaNRL08DtBtkArCRCcDWXCbIA8KGTMBPPF3nOJlM6o033tBxxx3nqh+gXSMTgI1M\nADYyAdjIBPwkrcHxTTfdpKVLl2rLli16+eWX9Y1vfEOJREKTJ0/OVn+Ar5EJwEYmABuZAGxkAn6W\n1mHV27dv17e+9S3t3r1bxxxzjE499VStWLFCvXu7OdYeaG/IBGAjE4CNTAA2MgE/S2tw/Oijj2ar\nD6BdIhOAjUwANjIB2MgE/MzTd44BAAAAAAgCT2er9iLmk0sSOLvMh5cypkrSocvWaN9eSV2895Pj\n4HOPgJ3CPQxcXJrs78vdZOL0MzxetqbuBzIRWi62E3v3eu+joNDRJf8cMfv2yTjIRCTH+3wF6XJQ\nfhdXzAfvmqTImW7+5k7XHBfbCbYR7Y6TTBzvoBFHa3OHPG91TJ7j8URIM8GeYwAAAABA6DE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d9zljV3GERzamtrzSWXXGKmT5/uqY+dO3eaeDxujDEmHo+bAQMGmPXr12dcr6nDIJpz4403mgce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\n7/8HnAPh6iY4v1EAAAAASUVORK5CYII=\n"
}
}
],
"source": [
"x = torch.tensor(df_train.x.map({'a':0,'b':1,'c':2,'C':3}))\n",
"y = torch.tensor(df_train.y.map({'a':0,'b':1,'c':2,'C':3}))\n",
"X = torch.nn.functional.one_hot(x).float().to(\"cuda:0\")\n",
"y = torch.nn.functional.one_hot(y).float().to(\"cuda:0\")\n",
"fig,ax = plt.subplots(5,5,figsize=(10,10))\n",
"for i in range(5):\n",
" for j in range(5):\n",
" rnn = torch.nn.RNN(4,4).to(\"cuda:0\")\n",
" cook = torch.nn.Linear(4,4).to(\"cuda:0\")\n",
" loss_fn = torch.nn.CrossEntropyLoss()\n",
" optimizr = torch.optim.Adam(list(rnn.parameters()) + list(cook.parameters()), lr=0.1)\n",
" for epoc in range(500):\n",
" ## 1\n",
" h,_ = rnn(X)\n",
" netout = cook(h)\n",
" ## 2 \n",
" loss = loss_fn(netout,y)\n",
" ## 3 \n",
" loss.backward()\n",
" ## 4 \n",
" optimizr.step()\n",
" optimizr.zero_grad()\n",
" h = rnn(X)[0].data.to(\"cpu\")\n",
" yhat = soft(cook(rnn(X)[0])).data.to(\"cpu\")\n",
" mat = torch.concat([h,yhat],axis=1)[:8]\n",
" ax[i][j].matshow(mat,cmap=\"bwr\")\n",
" ax[i][j].axvline(x=3.5,color=\"lime\")\n",
" ax[i][j].set_xticks(range(8),[r'$h_1$',r'$h_2$',r'$h_3$',r'$h_4$',r'$P_a$',r'$P_b$',r'$P_c$',r'$P_C$'])\n",
"fig.suptitle(\"RNN -- # of hidden nodes = 4\",size=20)\n",
"fig.tight_layout()"
],
"id": "ff0986d3-b0d9-4873-836c-e8da16c2f474"
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## C. LSTM"
],
"id": "5067cb65-a05a-44b0-90eb-172e7a914425"
},
{
"cell_type": "code",
"execution_count": 157,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"image/png": 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pXXarDplIfS9+5qV12a06ZCL1vfiZl9Zlt+qQidT2UZ9m3a26tLRUkvSnP/1J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sLCpnxI+ERZWZm6dOnS3G24jkwgWWQCsPkxE+QBTpAJwNZQJpp8y3FOTo4kqezdd5X71c/JOvdy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\n5Z3jqALZYpfo/vvv9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o/NMQAAAAAg8tgcAwAAAAAij80xAAAAACDyfG2Om5qaNHr0aNXV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\n/3uR1fFeF0l3BjLKfhFtgkeOAQAAAACRx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}
}
],
"source": [
"x = torch.tensor(df_train.x.map({'a':0,'b':1,'c':2,'C':3}))\n",
"y = torch.tensor(df_train.y.map({'a':0,'b':1,'c':2,'C':3}))\n",
"X = torch.nn.functional.one_hot(x).float().to(\"cuda:0\")\n",
"y = torch.nn.functional.one_hot(y).float().to(\"cuda:0\")\n",
"fig,ax = plt.subplots(5,5,figsize=(10,10))\n",
"for i in range(5):\n",
" for j in range(5):\n",
" lstm = torch.nn.LSTM(4,4).to(\"cuda:0\")\n",
" cook = torch.nn.Linear(4,4).to(\"cuda:0\")\n",
" loss_fn = torch.nn.CrossEntropyLoss()\n",
" optimizr = torch.optim.Adam(list(lstm.parameters()) + list(cook.parameters()), lr=0.1)\n",
" for epoc in range(500):\n",
" ## 1\n",
" h,_ = lstm(X)\n",
" netout = cook(h)\n",
" ## 2 \n",
" loss = loss_fn(netout,y)\n",
" ## 3 \n",
" loss.backward()\n",
" ## 4 \n",
" optimizr.step()\n",
" optimizr.zero_grad()\n",
" h = lstm(X)[0].data.to(\"cpu\")\n",
" yhat = soft(cook(lstm(X)[0])).data.to(\"cpu\")\n",
" mat = torch.concat([h,yhat],axis=1)[:8]\n",
" ax[i][j].matshow(mat,cmap=\"bwr\",vmin=-1,vmax=1)\n",
" ax[i][j].axvline(x=3.5,color=\"lime\")\n",
" ax[i][j].set_xticks(range(8),[r'$h_1$',r'$h_2$',r'$h_3$',r'$h_4$',r'$P_a$',r'$P_b$',r'$P_c$',r'$P_C$'])\n",
"fig.suptitle(\"LSTM -- # of hidden nodes = 4\",size=20)\n",
"fig.tight_layout()"
],
"id": "904dc979-14b3-4d10-8896-1a2ae1c2370d"
}
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