Giải giùm mình nhanh ạ , cần gấp , có thể ko cần vẽ hình cũng đc Bài 1: Cho ABC có AB = 5cm; AC = 12cm; BC = 13cmChứng minh ABC vuông tại A và tính độ dài đường cao AH;Kẻ HEAB tại E, HF AC tại F. Chứng minh: AE.AB = AF.AC;Chứng minh: AEF và ABC đồng dạng.Bài 2: Cho (ABC vuông tại A, đường cao AH. Biết HB = 3,6cm ; HC = 6,4cmTính độ dài các đoạn thẳng: AB, AC, AH.Kẻ HEAB ; HFAC. Chứng minh rằng: AB.AE =...
Đọc tiếp
Giải giùm mình nhanh ạ , cần gấp , có thể ko cần vẽ hình cũng đc
Bài 1: Cho ABC có AB = 5cm; AC = 12cm; BC = 13cm
Chứng minh ABC vuông tại A và tính độ dài đường cao AH;
Kẻ HEAB tại E, HF AC tại F. Chứng minh: AE.AB = AF.AC;
Chứng minh: AEF và ABC đồng dạng.
Bài 2: Cho (ABC vuông tại A, đường cao AH. Biết HB = 3,6cm ; HC = 6,4cm
Tính độ dài các đoạn thẳng: AB, AC, AH.
Kẻ HEAB ; HFAC. Chứng minh rằng: AB.AE = AC.AF.
Bài 3: Cho hình chữ nhật ABCD. Từ D hạ đường vuông góc với AC, cắt AC ở H. Biết rằng AB = 13cm; DH = 5cm. Tính độ dài BD.
Bài 4: Cho ABC vuông ở A có AB = 3cm, AC = 4cm, đường cao AH.
Tính BC, AH. b) Tính góc B, góc C.
Phân giác của góc A cắt BC tại E. Tính BE, CE.
Bài 5 Cho tam giác ABC vuông tại A, đường cao AH. Biết AH = 4, BH = 3. Tính tanB và số đo góc C (làm tròn đến phút ).
Bài 6: Cho tam giác ABC vuông tại A có B = 300, AB = 6cm
a) Giải tam giác vuông ABC.
b) Vẽ đường cao AH và trung tuyến AM của ABC. Tính diện tích AHM.
Bài 7: Cho tam giác ABC vuông tại A, đường cao AH = 6cm, HC = 8cm.
a/ Tính độ dài HB, BC, AB, AC
b/ Kẻ . Tính độ dài HD và diện tích tam giác AHD.
Bài 8: Cho tam giác ABC vuông tại A có AB = 10cm,
a) Tính độ dài BC?
b) Kẻ tia phân giác BD của góc ABC (D AC). Tính AD?
(Kết quả về cạnh làm tròn đến chữ số thập phân thứ hai)
Bài 9: Trong tam giác ABC có AB = 12cm, B = 400, C = 300, đường cao AH.
Hãy tính độ dài AH, HC?
Bài 10: Cho tam giác ABC vuông ở A ; AB = 3cm ; AC = 4cm.
a) Giải tam giác vuông ABC?
b) Phân giác của góc A cắt BC tại E. Tính BE, CE.
c) Từ E kẻ EM và EN lần lượt vuông góc với AB và AC. Hỏi tứ giác AMEN là hình gì ? Tính diện tích của tứ giác AMEN
Lời giải:
1. $CH=\sqrt{AC^2-AH^2}=\sqrt{5^2-3^2}=4$ (cm) theo định lý Pitago
Áp dụng hệ thức lượng trong tam giác vuông:
$BH=\frac{AH^2}{CH}=\frac{3^2}{4}=2,25$ (cm)
$BC=BH+CH=2,25+4=6,25$ (cm)
2.
Vì $AH$ là đường kính nên $\widehat{AEH}=\widehat{AFH}=90^0$ (góc nt chắn nửa đường tròn)
Tứ giác $AEHF$ có $\widehat{A}=\widehat{E}=\widehat{F}=90^0$ nên là hình chữ nhật.
3.
Vì $AEHF$ là hcn nên $\widehat{AEF}=\widehat{AHF}$
Mà $\widehat{AHF}=\widehat{C}$ (cùng phụ $\widehat{FHC}$)
$\Rightarrow \widehat{AEF}=\widehat{C}$ nên $BEFC$ là tứ giác nội tiếp.
3. Gọi $T$ là trung điểm $HB$
Tam giavs $BEH$ vuông tại $E$ nên $ET=\frac{1}{2}BH=TH$
$\Rightarrow ETH$ cân tại $T$
$\Rightarrow \widehat{TEH}=\widehat{THE}=\widehat{C}$ (hai góc đồng vị với $EF\parallel AC$)
$=\widehat{AEF}$
$\Rightarrow \widehat{TEF}=\widehat{TEH}+\widehat{HEF}=\widehat{AEF}+\widehat{HEF}=\widehat{AEH}=90^0$
$\Rightarrow TE\perp EF$ nên $EF$ là tiếp tuyến đường tròn đường kính $BH$
Tương tự $EF$ là tiếp tuyến đường tròn đường kính $CH$
Ta có đpcm.
Hình vẽ:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAeIAAAE6CAYAAADKhFHhAAAgAElEQVR4nO3dfXzT5bk/8E/5YgxWK4VSLFYzssywSoF1MpmIq/JwVLSzo7ZkxbpOjgqjtmvp6A/UMSceMBSKMHrggH2t2lNai0W2CgfEdSKsWuVhxbpqF40Lq5TUYCFdjIT+/shymz7R53zzTT7v12uvIWmbC1py5bru+77ukPb29nYQERGRLEbIHQAREVEwYyImIiKSERMxERGRjJiIiYiIZMRETEREJCMmYiIiIhkxERMREcmIiZiIiEhGTMREREQyYiImIiKSERMxERGRjJiIiYiIZMRETEREJCMmYiIiIhkxERMREcmIiZiIiEhGTMREREQyYiImIiKSERMxERGRjJiIiYiIZMRETEREJCMmYiIiIhkxERMREcmIiZiIiEhGTMREREQyYiImIiKSERMxERGRjJiIiYiIZMRETEREJCMmYiIiIhkxERMREcmIiZiIiEhGTMREREQyYiImIiKS0Ui5AwhECQldf0+lAqKigPh4YMEC38dERET+iYl4mOzd2/G/29sBiwV48UVgzBjgzjvliYuIiPwLW9M+EhIC3HADkJ0NVFTIHQ0REfkLJmIfkyTgq6/kjoKIiPwFW9M+4mlN//73wKOPyh0NERH5CybiYdLdhi0AeOABQK/3bSxEROS/mIiHSefNWgDQ0gK8+ipw7Bg3axERkRvXiH1o7FggPR2oqZE7EiIi8hdMxD42ciTw/vtyR0FERP6CidjHzGZAp5M7CiIi8hdMxD70t78B69cDSUlyR0JERP4ipL29vV3uIAJNTyMuJ00CfvITIC7O9zEREZF/YiImIiKSEVvTREREMmIiJiIikhETMRERkYw4WWuAqqur8d5778HhcGDGjBmIj4/HyJH86yQiov7hZq1+qqmpgcGQDrt9JK69dg4kSY22trcBfI7y8pcwY8YMuUMkIiIFYSLuh5qaGsyZcw+mTXsFY8bM6fBYS0s1PvjAgP37K5mMiYioz5iI+2HixO/i+us3d0nCHi0t1fjHP/4T9fXHcfXVV/s4OiIiUiJu1uqj6upq/Otf6h6TMACMHRsP4DpUV1f7LjAiIlI0JuI+qqmpwTXXxPf6cVdddTtOnDjhg4iIiCgQMBETERHJiIm4j2bMmIHz53tvOX/55Z8QExPjg4iIiCgQMBH3UXx8PEaNcuCLL97o8WNaWqpx/vzHOHDgABobG30YHRERKRV3TfdDTU0N7rvvQXznO0UYN67r8aW6ukWYOnUiwsPDIUkSFi5ciB//+MdQq9UyRUxERP6OibifampqkJz8EByOq3DNNT/CiBHugR6SdBYlJS/ik08+QWVlJVwuFwAgOjoay5cvh1arlTlyIiLyR0zEA+BwOPDSSy9h48aNaG9vxy9+8Qv87Gc/E2eHzWYzCgsLUV9fDwCQJAnJyclITk6GJElyhk5ERH5GWr169Wq5g1CakSNHQqVS4cSJExg7dix+/vOf44YbbhCPjx49GnPmzMGlS5fw8ccf4+LFizh16hTef/99fOc730F4eLiM0RMRkT/hZq1hlJqaivz8fOj1egBAY2MjcnJyUFpaKlrXREQU3JiIh5lGo4HRaERiYiIkSYLL5UJpaSlycnK4s5qIiJiIfSU9PR1GoxE6nQ4AYDKZkJ2djZKSEjidTpmjIyIiuTAR+5BOp4PRaERKSoo40lRWVoZf/epXrI6JiIIUb7L3MUmSkJqaittvvx2bNm1CY2MjTCYT8vLysGDBAixYsAAqlcrncc2dO7fXjzl48KAPIiEiCi5MxDLxrB2Xl5ejvLwcTqcTpaWlOHr0KDIzM0UL21c6J9m5c+cy8RIR+QBb0zKSJAkGgwEFBQXQaDQA3GeQc3NzuXZMRBQkmIj9gEajQUFBAVJSUqBSqeByuVBWVoacnByYzWa5wyMiomHEROwnPGvH3ueOzWYzsrKyUFZWxuqYiChAMRH7Gc/acWpqqjh3XFJSgry8PO6sJiIKQEzEfiolJaXDuePGxkbk5uairKwMDodD5uiIiGioMBH7Mc+5487V8VNPPcW1YyKiAMFE7OckSepSHTc0NCArKwsVFRWcWU1EpHBMxArhqY4NBoOojouLi5GRkYGGhga5wyMiogFiIlYQ73PHWq0WAGCxWJCXl4fi4mLurCYiUiAmYgXSaDTIz89HUlKSqI4rKiqwatUqWCwWucMjIqJ+YCJWKEmSkJaW1uHccUNDAzIyMoakOuZ4SyIi32AiVjitVguj0YikpCQAENVxTk4OTCaTzNEREVFvmIgDRFpaWoe1Y7PZjJycHFRUVHDtmIjIjzERBxCtVov8/Pwed1ZfuHABO3bswH333Yfbb78dTz75JD799FO5wyYiCmoh7e3t7XIHoUR1dXVYtWoVAGDNmjWIjY2VOaKOGhsbsXXrVjEW86uvvsKJEycgSRLCw8MxcuRInD9/HmfPnkVJSQkSEhJkjpiIKDixIg5QOp0OGzZsQGpqKgDg/fffx1VXXYWYmBhMmDABkZGR+Pa3v41JkybBYDDg888/lzliIqLgxEQc4FJSUpCRkYG2tjZotVqEhIR0eHz06NGIiIhAeXm5TBESEQU3JuIgcObMGYwfPx4jRnT/7R41ahRqamp8HBUREQFMxEHhuuuuw1dffdXj4xcvXsT48eN9GBEREXkwEQc4h8OBjz/+GC0tLWhra+vyeHt7O5qbm2EymXjumIhIBkzEAayurg5Lly7Fvn37cNNNN+HEiRNobW0Vj1+8eBH19fVQq9W4dOkScnJyUFpayhudiIh8aKTcAdDQczgc2LFjBw4dOiSSqsFgwMiRI2E0GtHe3o6RI0fCbrcjMTERs2fPxp49e+ByuVBaWora2lrk5uYiKipK5j8JEVHgYyIOMLW1tdi2bRuam5sBAKGhoXjssccQHx8PAPjVr36FU6dO4dy5c7jlllugVqsBALNmzcILL7wAk8mExsZGZGRkYMGCBUhOToYkSbL9eYiIAh0TcYCw2+0oLi7GgQMHRBU8a9YsLF68GOHh4R0+dvLkyV0+3zOVq7i4GHv37oXT6URpaSneeecdPPHEE2J0JhERDS2uEQeAY8eOITMzE/v27YPL5UJoaCgyMzORm5vbJQlfjiRJSE9PR35+vki8JpOJa8dERMOIFbGC2e12bNu2DYcPHxZJcubMmXjkkUcQEREx4K/buTrm2jER0fBhRaxQhw8fxtKlS1FdXQ2XywW1Wo0VK1ZgxYoVg0rCHp7quKCgADqdDgDE2nFlZSWrYyKiIcKKWGFsNht27NiBw4cPi9+bOXMm0tPTERkZOeTPp9FoYDQaO6wdFxUV4ejRo1i2bBk0Gs2QPycRUTBhRawgNTU1yMrKEklYrVYjOzsbK1asGJYk7OFdHXvWjhsaGsR9x6yOiYgGLugq4rlz5/b6MQcPHvRBJH3X2tqKHTt2oLq6Wvze7NmzkZ6ejrCwMJ/FodFosHbtWrz88suoqqqC0+lEcXEx3nnnHVmr47lz5172e9bb40REcgq6RAz4X6K9nJqaGmzfvh1WqxWA+1xweno65s2bJ0s8arUaixcvxl133YWNGzfCbDaL6njhwoVITEzkuWMion4IykSsBFarFdu3b+9wK1JsbCyWLVvmF7uWtVotjEYjdu/ejYqKCr+pjomIlIaJ2A8dO3YMW7duFdOx1Gq1mI7lT9WmWq1GamoqbrnlFmzYsAFNTU2sjomI+omJ2I94dkQfPXpUbICaOnUqMjMz+3QkyeFwoLW1FTabDVarFQ6HAzabDV9//bV4rDsqlQqjR48GAISFhUGtViMiIgKhoaGIjIzsdR1ar9dj69at2LVrV4fq+M9//jOWL1/O6piI6DKCMhFfbsOWXOvHx44dw4YNG0Sy9KwFz549u0tVabPZ0NTUBLPZjL///e84c+YMTp8+LdaRh5pKpcLEiRMRHR2N66+/HlqtFtHR0Rg7dqyITZIkpKam4tZbb8WWLVtgMplgNpuRlZWF5OTkYZ9Z3ZdNeERE/igoE7E/bdbq7lxwXFwcli1bJqrg5uZm1NfXo6GhAadOnYLFYun3kSHvqrezy1XLAOB0OtHQ0ICGhoYOvx8eHo6YmBjcdNNNiI2NxcSJE6HT6fD8889j9+7dKC8vF1O5jh49OqzVcW+7pomI/FVQJmJ/UVNTg8LCQthsNgDuKjgtLQ0zZ85EbW0tTp06hbq6OrFW3J2wsDBERkYiIiICGo0G48aNQ1hYGCIiIhAWFobRo0dDpVL1OSabzQa73Q6bzYZz587hzJkzaGlpQVNTEywWC1paWsSbAJvNhiNHjuDIkSMi/piYGEydOhXz589HXFwcCgsLfV4dExEpCROxDLo7Fzxp0iR8//vfx9tvv42dO3fC6XR2+bzw8HBER0dDp9Phu9/9LqKjoxEVFTWkSS08PFw8T0+xNzU1ob6+HqdOnUJ9fT3sdjsA9+zr2tpa1NbWYseOHdBqtZg1axa0Wi3+9Kc/+aw6JiJSEiZiH/M+F3zp0iU4HA5ERUXho48+wt/+9rcOHytJEuLi4jB58mTExcUhOjpa9koyLCwMYWFh0Ov1SExMBOCujD2J+eTJk7BYLADcNzeZTCYAwJgxY/DFF1/A5XKxOiYi8sJE7CN2ux1btmzBkSNH8NVXX+Hs2bP4+uuvER0djS+//FJ8XHh4OGbMmIEpU6YgNjbWp5OzBio8PBwzZ87EzJkzAQB1dXU4deoUamtr0djYCAD44osv0N7ejubmZjgcDowbN47VMRERgjQR97Z5Z6g3c3l2RH/++ef4/PPPce7cObEDOSQkBKGhobjjjjvwox/9CDqdrl9ruv4oNjYWsbGxMBgMaGpqQm1tLaqqqtDU1ISoqCjY7XZ8+umnCAkJgdVqRUZGBgwGA6tjIgpKIe3t7e1yB6FEdXV1WLVqFQBgzZo1iI2N7fIxnh3Rf/zjH/HPf/4T58+fx7XXXouJEydCpVJBp9Nh7ty5uOOOOxAaGurrP4LPmUwm/N///R/eeustXLhwAf/85z/xz3/+E1dccQXGjRuH6dOn4//9v//H6piIgkpQVsS+cOzYMTz99NP429/+hgsXLkCSJEycOBETJkzAnXfeiXvvvVfcZBQstFotlixZgrS0NOzbtw+vv/46xowZA5PJhNOnT+PMmTM4fvw4lixZgoceeojVMREFBVbEA9RTRWyz2fDrX/8a+/btw/nz5wG411AnTZqExMRE3H///QgPD5ctbn/idDrxzjvvoKysDH/5y1/w+eefw+VyYeTIkZg6dSrWrl3bbaeBiCiQMBEPQHV1NVavXi1GUU6bNg35+flobW3FqlWrcPbsWQDuXc8xMTFIS0vDT37yk6BoPw9UTU0NduzYgTfffBNtbW0A3LOsH374Yfz0pz/F+vXr8dprr+Hs2bOYMmUKlixZgscff1zmqImIBo+JuJ/27NmDhx56CBqNBmPGjMGIESNw9uxZNDY2IjQ0VGy0GjNmDB5//HE8+uijUKvVMketHIcPHxYt/fb2drhcLpw/fx7R0dGIjIzElVdeiQsXLsBisWDevHn4/e9/L3fIRESDwkTcDxcuXMD48eNx880349prr+3w2Pnz5/Hee+8hMjISDz74ILKzs7npaICcTideffVVPPvsszCZTIiOju7yd+lyuXDs2DHs2rULd999t0yREhENHjdr9cP+/fsRERHRJQkDwDXXXIMxY8ZAp9Ph6quvxvbt22WIMLDccccd+Oijj3DjjTd2eUySJERFReF///d/mYiJSNGYiPvh1KlTuOKKK3p8PDQ0FGfOnEFdXZ0PowpcLS0tUKvVCAkJ6fbxUaNGdbmIgohIaZiI+yEmJkZsJOqO0+nElClTMHnyZB9GFbjsdjvef/99tLe3d5uM//WvfyEqKkqGyIiIhg4TcR/Z7XacOHECVqsVFy5cwNVXX93l8dbWVuzcuVNcX0iDd+rUKTQ1NWHChAkdfv/SpUv47LPP8MUXX8BoNCIjI4Ob4ohIkbhZqw/q6+uxfv16WK1WnD59GqdOncK3v/1tjBs3ToxpbGxsxMMPP4xt27bJHW5AefvttzFnzhxERUVhwoQJuPLKK3H+/Hk0Njbi4sWLCA0NRUhICKZNm4bNmzdDp9PJHTIRUb+MkDsAf3fo0CGsXr0aVqsVALBkyRL84Q9/wLXXXou//OUvOHz4MM6ePYvvfe97sNlsaGpqkjniwOFyufDqq6/i9ttvR3t7O95//3386U9/QlNTE5555hmUlpZi3LhxaG9vx/Hjx/HAAw+gtLRU3JdMRKQErIh74HK5UFhYiAMHDgBwD5dYunQp4uPjAXScrPWLX/wCO3fuhMPhQExMDNauXStb3IGkrKwMJSUlAICkpCRUVFQAAAwGAwwGAwDAarXioYcewl//+le4XC5cddVVuOuuu5CdnY2YmBjZYici6itWxN1wOp147rnnRBKOiorChg0bRBLubMKECeJu3vr6euzdu9dnsQYqk8mEV155BYD77z85Obnbj4uIiEBlZSUWLVqEa665Bm1tbTh48CCysrJQVlYGp9Ppy7CJiPqNibgTm82GvLw81NbWAnBfVGA0GhEdHX3Zz0tOThbrk0VFRTCZTMMea6DydCOcTickSUJ2dvZlN2Kp1WqsW7cOmZmZuOGGG3Dx4kXU19ejsLAQOTk5POJERH6NidhLc3MzcnNzxWX2cXFxWLNmDcLCwnr9XEmSsHTpUqhUKrhcLmzfvp1rlQNUXl4ukuf8+fOh1+v79HnLli1DdnY2br75ZowaNQofffQRTpw4gdzcXFRWVvL7QUR+iYn430wmE3Jzc9Hc3AwAmD17Np566ql+XdSg0+mQkJAAwN2i9rS2qe8sFgsqKysBANHR0Vi0aFG/Pt9gMODXv/41pk6diuuvvx4mkwlWqxVFRUUd3mQREfkLJmIAZrMZTz/9NGw2GwBg3rx5WLZs2YDuw01NTRVzkYuLi0Vip945nU4UFhbC4XBAkiRkZmYO6GzwzJkzsXLlSmg0Gtx88804e/asuJgjNzcXZWVlcDgcw/AnICLqv6BPxM3NzfjNb36D1tZWAO5W6JIlSwZ8Kb0kSSKJ2+12GI3GoQw3oO3atUuMB01MTOxzS7o7cXFxeOqppzB69Gh897vfxaVLl9DW1gaXy4WSkhJWx0TkN4I6Ebe2tnY4I5yQkIDFixcPOAl76PV6JCUlAQAaGhqwb9++Qcca6Mxms2hJazQaLFy4cNBfc+rUqXjuueegVqsxfvx4XHnllRg7dqx4vtzcXJ47JiLZBW0i9hxRslgsANxrwunp6YNOwh4PPvggtFotAGDnzp1sUV+Gy+XC+vXr4XK5REvac6/zYOl0OuTl5QFwdyvOnz+Pu+66C5IkweVyobS0FFlZWTCbzUPyfERE/RWUidjzwl9fXw8AiI+PH/CacE9UKpX4mk6nE1u3bh2yrx1oKisrRSJMSkoa8jGVcXFxWLlypfheHD9+HE8//bRYyzebzTx3TESyCcpEvGPHDtTU1ABw36g01EnYQ6fTiUEUx44dQ1VV1ZA/h9KZzWbs3r0bgLsl/eCDDw7L88yYMQPLli0D4D4r/uKLL+KZZ56BwWAQ1XFJSQnPHRORzwVdIt63b59IiFqtFitXrhyyNmh3FixYIK7qKyoqEq1wcncmNm3aBLvdDgB49NFHh/V7MXv2bDEBzWw2Y926dViwYAEKCgo6VMe5ubkoKSnh2jER+URQJWKz2YyioiIAQHh4OJ588sk+DesYDJVKhezsbNEW3bZtG1/g/62yslLsXE5KSkJsbOywP2d6ejri4uIAuM96FxcXQ6PRoKCgQFTHgHvONXdWE5EvBE0ittvteO6558T50ZUrV/rs3mC9Xi8GfZw8eZItarjfFO3atQuAe5b0ggULfPbceXl5okuxd+9eHDlyBJIkwWAwdKiOPeeOWR0T0XAKmkS8ZcsWcUXhYM+oDkRqaqqYV/3yyy+LI1PBasuWLWJjVHZ2dr8mmA2WWq3GihUrxLCQnTt3inPknatjl8vF6piIhlVQJOKKigocOXIEgHsHbVpams9j8G5ROxwOrFu3LmirrKKiIrEhKiUlxedvigD3/oDMzExIkgSr1Qqj0Si+H5erjnnumIiGWsAnYpPJJFqg4eHhIhnKwXsWdUNDQ1C2qBsbG8U1kdHR0cO2S7ovZs6ciRkzZgDofsmgu+qY546JaKgFdCJ2uVzYuHGjaIFmZmYO++as3qSlpYlBHy+//LJolwcDl8uFrVu3isEd2dnZw7pLui8yMzPFenFxcXGXBNtddew5d1xRUcHqmIgGLaATcXl5uXhhTUxMFLtl5SRJkphl7XA4sGnTJrlD8pmqqiqxzpqQkDDkgzsGQq1Wixa10+nExo0bu02u3VXHxcXFyMjI4LljIhqUgE3EZrMZ5eXlAIDIyEgYDAaZI/qGXq/HvHnzALiP0HhatYHMZDKhuLgYgDupybFO35OYmBixZGAymXpcMvCujj1dDYvFgry8PBQXF3MqFxENSMAm4qKiIlHZZGdnD+g6veGUnp4udlEH+nWJLpcLhYWFcDqdYpa0XOv0PTEYDKL1XFRUdNklA41Gg/z8fCQlJYnquKKiAqtWreLAFiLqt4BMxAcOHMCxY8cAuO8WjomJkTmirtRqNR577DHREt2wYUPArjeWl5eL9m1iYqJftKQ7U6vVYsnA5XKJwS89kSQJaWlpyM/PF7u+GxoakJGRweqYiPol4BKx3W4XLdDQ0FC/aoF2NnXqVMyfPx+Au0V94MABmSMaehaLRVxvqNPphuR6w+ESExOD2bNnAwBqampw8uTJXj9Hq9XCaDSKay891XFOTg5MJtOwxktEgSHgEnFpaakYzpCWlib7LuneLFq0SLREA61F7XQ6UVhYCIfDIW6jknuXdG/S0tLEcJGtW7eKSWx9+TzvtWOz2YycnBxUVFSwOiaiywqoRNzU1CQ22mg0GrEhyp95t0TtdjuMRqPcIQ2ZXbt2oa6uDoD78gtPkvJnYWFhYmNfU1MT/vjHP/b5c7VaLfLz87mzmoj6JaAScVVVlVhnXbx4sd9tCOqJ967dhoYG7Nu3T+aIBs9sNouWtF6vF7ceKcH8+fPFRrrXX3+9z1Ux8M3OaqPRKNbCm5qaOJWLiHoUMIm4ublZrLHOmDEDU6dOlTmi/vGeRd3brl1/5xmk4hncsWTJEr/btX45kiSJSyisVmu/qmIPnU6HDRs2IDU1VfxeaWkp8vLyuHZMRB0ETCIuLS0VlYs/b9DqiUqlwmOPPQYAcDgc2LJli2Krp/3794tkk5ycrIiWdGfx8fFi7X737t1i30F/paSkwGg0ir+DhoYG5OTkoKioiGvHRAQgQBKx1WpFdXU1APf8YE9lqTTeu6jr6uoUOYvaZDKJoz+RkZGi5a40kiSJHd52u31Q3wu9Xo/8/HwsXrwYKpUKLpcLlZWVyMrK4o1ORBQYiXjPnj2iepTzEoGhsHjxYlE9FRUVKe5yge3bt4vBHbm5uT693nCozZgxQ8yhrqqqGlQFK0kSEhISsGbNGlFpWywWrh0TkfITsd1ux6FDhwC4rzhUYhvUmyRJePTRRwG411o3bdqkmBfpyspK1NfXA5Dnzueh5kmeANDa2orDhw8P+mvq9XoUFBQgNTW1y41OXDsmCk6KT8SHDh2C3W4HALHBRuliYmLELuPGxkax+9ifmc1mlJaWAnAnG38e3NEfc+fOFVW9d+dlMCRJQkpKCvLz87ucO2Z1TBR8FJ+IPRcmaLVaxMbGyhzN0ElLSxPHX0pKSvy6Re3ZJe29Wc7fB3f0lUqlwj333APAnSyHck3Xc+64c3Wcm5ur6F3zRNQ/ik7EtbW1YhLVXXfdJXM0Q0uSJKSnp4sXaH9uUe/du1e0VZOSkgLqDREA3HvvveJM+lBvoOuuOm5sbERGRgarY6IgoehEfPDgQQDu6VSeGcGBJDY2Vsww9tcWtclkEtdNajQaJCcnyxzR0IuIiMD06dMBuGdQe5ZChpKnOk5MTBQXgZSWlnJmNVEQUGwibm1tRW1tLQD37lYl7869nIULF4rjWCUlJX73olxYWAi73Q5JkvDLX/5SUYM7+mPu3LkA3Ge8jxw5MizP4emCeFfHJpOJa8dEAU6xibi6ulq8MHnO3gYiz2QqT4v6hRde8JtBEJWVlWKGclJSkuJ3rF/O9OnTERERAcA9sGQ4da6OuXZMFNgUm4g9R0k0Go1f3m87lGJjY0XL12Qy4ZVXXpE5IvfGJU9LOioqKmB2rF/ObbfdBsC9TGC1Wof1uTzVcUFBgfj59qwdV1ZWsjomCiCKTMRWq1XsXr3tttsUc7nDYBgMBlFxVlRUyNqi9uyS9qyVZmdnB2xL2tusWbPEr48ePeqT59RoNDAajR3WjouKipCXl+fXO+mJqO8UmYgPHz4sKgLvF8dA592iXr9+vWxVUVVVlXgjYDAYFD+4o6/0er1Yr/fsT/AF7+q488zqiooKVsdECqfIROypRqKiohQ7V3og9Hq9uNDCYrGI1rAvNTQ0oLi4GID7hqFA3CV9OZ5bvT788EPYbDafPrdGo8HatWuRkJAgquPi4mJWx0QKp7hEbLPZRFs60M6r9kViYmKHW4EsFovPntvlcqGwsFDMkvaccw4m8fHxAACn04mTJ0/6/PnVajUWL16M/Px88XPA6phI2RSXiOvr68WLzS233CJzNPLIzMyESqWC0+nE+vXrffa83mvTCQkJQflGSKfTiaNyciRiD61WC6PRiJSUFFbHRAqnuER86tQpAO7KIC4uTuZo5KHT6cQtUyaTCSUlJcP+nN67taOjoztceB9MJElCTEwMAODIkSOyHiVTq9VITU3F2rVrxS1RrI6JlEexiViv1wfMPOOBSElJEZukysrKxHne4eB9flmSJGRnZwf1371nndjhcPjFfcJ6vR5bt27tUh1nZWWxOnu+iS8AACAASURBVCZSAEUlYrvdLtZEg7Ua9rZs2TKxRutZux0O3i3p5OTkgD+33RtPIgYgrn2UmyRJSE1NhdFo7HCjU1ZWFqdyEfk5RSVi7/XhYFyf7Eyj0YhZ1MPVovZuSQfqLOn+0mg0CAsLAwB89tlnMkfTkU6nw/PPPw+DwdDlvmNWx0T+SVGJ2NOWBiDWxILdwoULxe5Z71uQhkLnlnRmZmbQ7ZLuieeN4CeffCJzJF2pVCoYDAasXbuW1TGRAigqEdfV1QFwVySBeslDf0mSJFrUnkEfQ9WiZku6Z9/97ncBuBPccNzGNBT0ej3y8/ORlJTE6pjIjykqEXvuHp44caLMkfgXvV4vWtQWiwV79+4d9Nf0bkkH4+CO3nh3ZPz5IgZJkpCWlgaj0Sg6J6yOifyLYhJxU1MTWltbATARd2fhwoWiDblr165Btag7t6SXLl3KlnQnniNMAPDxxx/LGEnf6HQ6FBQUsDom8kOKScTeE6QC+bq9gZIkCU888YQY9FFYWDjgaqe4uJgt6V6EhoaK5ZHTp0/LHE3feFfHXDsm8h+KScTe185FRkbKGIn/0mq1YtBHQ0PDgO7NNZvNqKqqEl+PLemeedrTSqsodTod8vPzubOayE8oJhF/+umnANzThMaOHStzNP4rKSlJXISxY8eOfrWoXS4XtmzZIlrS3ueUqSvPmmtLS4vMkfSfJEkwGAwd7jtmdUwkD8Uk4jNnzgAAxo8fH9RTnXrjmXzlqXReeOEFOByOPn1ucXGxmNDFlnTvPJ0ZzyZCJfLcd5ySkgK1Wt2hOvaXYSVEgU4xidiTTDyDFKhnOp0OiYmJANy7n3fv3t3r53i3pLlLum88idjpdIqNhErkPZXLe2d1Xl4eiouL+/xGjogGRjGJ2HP36+jRo2WORBkWLlwo1jArKioue8TG4XBg06ZNcDqdUKlUoqKmy4uIiBC/VnJV7KHRaFBQUCDWjgH3z052djarY6JhpJhE7HmhGz9+vMyRKIN3QnW5XFi3bl2P634vv/yyuLwgNTVVrDHT5anVavFr782ESuZZO968ebNYmrBYLKyOiYaRIhKxw+EQSeSqq66SORrl0Ov1HVrU3Q36MJlMoiWt1+uRkJDg0xiVLDw8XPxaya3p7kRHR2Pt2rUwGAxiTwarY6LhoYhE7P0i5/3iR71buHChqHBLSko6tKgdDgc2btwIl8sFlUrFXdL95L1M4lk6CSSemdX5+fniZ8hTHXNnNdHQUUQipoFTqVTisoa2tjY8/PDDmD9/Pm6//XYsXLgQH374IYCOl0dQ33jv3r906ZKMkQwvjUaDzZs3Y/HixeLPXFpaitzcXL+4j5lI6RSRiL2rDe6a7j+9Xo+77roLhw8fxrFjx/Dpp5/i/PnzOHnyJA4fPoyRI0eKFjb1jycxff311zJHMrwkSUJCQgKef/556PV6AEBjYyNyc3NRVlbGtWOiQVBEIva+Tch7gwz1XWlpKcaNG4dp06ZhwoQJiIyMhE6nw5QpU7B//36cPXtW7hAVydOeDsTWdHe0Wi2MRiPS0tLEueOSkhJWx0SDoIhETIPT2NiI+vp6TJw4ESEhIR0eGz16NMaNG4fy8nKZoiMlSkpKwoYNG8TlF55zxxUVFVw7JuonJuIgUFNTg/DwcIwY0f23e9SoUaipqfFxVKR0np3VnurY6XSiuLiYU7mI+omJOAhcd911uHjxYo+PX7x4Edddd50PI6JA0lN1XFZW1mFZiYi6x0QcBG6//Xa0traira2ty2Pt7e348ssvMW/ePBkio0DRuToG3MflcnJyxPxyIuoeE3EQUKvVyMzMxIkTJzqcyb548SI++OADjB8/HnPmzJExQgoU3VXHubm5qKys5NoxUQ8UkYi9h3icO3dOxkiUyeVyobW1FTqdDn/9619x7Ngx1NXV4S9/+QuuvPJKTJw4EZ999pncYSqS5+eRx+q+0V11XFRUxJ3VRD1QRCL2HpzANaf+KykpgclkgkajwYsvvog///nPqKiowLvvvovvfe97CAkJQWFhIc+CDoDn55HH6rrqXB3z3DFR9xSRiL13+zIR909jYyMqKysBuCckJScnY/Lkybj99tsxZcoUMcijoaEBr732mpyhKo732eHQ0FAZI/Ffnatjnjsm6koRidj7ujm2pvvO5XJh06ZNcLlckCQJy5cv7zJL2nsW9a5du/ji2A8tLS3i1567ial7Pa0dc2Y1kUISMfBN6y/QbrkZTpWVlTCbzQCA5OTkbmdJe8+i9k7c1Du73S5+zYq4d943Onl+3kpLS5GVlSV+TomCkWISsWfDFhNx3zQ2NmLXrl0AvmlJ90Sv14vHzWYzp2z1kfcdxLwVrO8MBgMKCgrEG0Oz2YysrCyeO6agpbhE3NzcLHMk/s/lcmHbtm1wOp09tqQ7866Yd+/eDZPJ5ItQFc37Z5Gt6f7RaDQoKCjoUB3z3DEFK8Uk4rFjxwLouC5H3SsvLxcvZj21pDvzTthOpxNbtmxhi7oXnp/F8PDwDjv7qW8kSeq2Os7NzUVJSQl//ihoKCYRezYUWa3WDmtz1JF3a7m3lnRn3h/f2NiIioqKYYkxUJw5cwbAN28SaWA6V8cAUFZWxp3VFDQUl4gBoKmpScZI/Fdfdkn3xruCfuWVV/hCeBme1nRUVJTMkShfd9Wx59wxq2MKdIpJxDfeeKP4Ndcvu+d9/KivLenOOreoN2zYwBfBbtjtdpGIvd8k0uB0t3bM6pgCnWIS8fjx40V198knn8gcjf8xm81iIEd/W9KdeX++xWLhLupunDlzRrxBmThxoszRBJbLVcc8d0yBSDGJWK1Wi3+UTMQduVwurF+/Hg6HY8At6c68K+ry8nKe8+zEezY3d0wPj+6qY547pkCkmEQMfLMWZzab+a7Yi3eiTExMHFBLujPvhM5BH1153gyGhoYOyd83da+nndVZWVmoqKjgzyQFBEUl4smTJwNwr8+xKnbzbh1HR0djwYIFQ/a1O++iZov6G3V1dQCAmJiYQXcfqHfdVcfFxcXIyMjguWNSPEUmYgCor6+XMRL/0Hkz1ZIlS4Z81GLnFjU3ynV8I+j9M0nDy7s61mq1ANxvRPPy8lBcXMypXKRYikrEGo1GJBoeYXJPwPLsJE1KSkJsbOyQP0fnFrVnLTqYeW/U8iQE8h2NRoP8/HwkJSWJn8uKigqsWrUKFotF7vCI+k1RiRiAuL2ltrY2qNeHzGYzdu/eDWDoW9KdcRd1R7W1teLX119/vYyRBC9JkpCWlob8/Hzo9XoA7qs8MzIyWB2T4iguEXtagc3NzUG7TuxyubBu3TrxYjMcLenOvFvUlZWVQX2m85133gEAxMbGdriik3xPq9XCaDQiKSkJAER1nJOTw2UUUgzFJWLv9uv7778vYyTy2b9/v2jBDVdLurPudlEHY4u6tbVVvAGcMmWKzNGQR1paWoe1Y7PZjJycHFRUVLA6Jr+nuEQ8ceJEUYWcOnVK5mh8r7m5Gb///e8BDH9LujPvFnWwXpdYV1cnlkR88QaI+k6r1SI/P587q0lxFJeIJUnCrbfeCgD48MMPYbPZZI7ItzZs2CAqUV+0pDvr3KIOthe4o0ePAnAPmNHpdDJHQ515dlYbjUbx/WlqauJULvJrikvEADB9+nQA7uM7x44dkzka36moqBDHtubPny9LRSZJEn75y19CpVLB5XIF1XWJdrtd/LzNnDmTVx/6MZ1Ohw0bNiA1NVX8XmlpKfLy8rh2TH5HkYl46tSpohI8fPiwzNH4hsViEbukdTod0tPTZYtFq9XiwQcfBBBcLeqamhpxBaenK0P+LSUlBUajUawdNzQ0ICcnB0VFRVw7Jr+hyEQsSRLuuOMOAO514mBoTxcWFsJut0OSJCxdulT2aiwpKUncOhQss6g9b/rUajXi4uJkjob6Sq/XIz8/H4sXLxadnMrKSmRlZQX17n/yH4pMxABw2223AXC3pz3rdoGqoqJCjFRMTk72i7VJSZKwYsUKqNVqMegjkFvUNptNbA5kW1p5JElCQkIC1qxZI/Y4WCwWrh2TX1BsIp46daq4BOLQoUMyRzN8vFvS0dHRSExMlDmibwTTLurq6mrRyoyPj5c5GhoovV6PgoICpKamdrnRiWvHJBfFJmIAuOuuuwC4LyQI1BaTpyWtUqmwZMkSqNVquUPqIDExUVTogdyi3r9/PwD3lYecL61skiQhJSUF+fn5Xc4dszomOSg6Ec+ePVu0CKuqqmSOZuh5t6QXLlzol+dWJUlCZmZmh1nUgfZCVltbK2abz507l7ctBQjPuePO1XFubi5n2ZNPKToRR0REiKNMhw8fFjtaA4F3S1qj0fhVS7oz7/gCsUW9Z88eAIBKpcLs2bNljoaGUnfVcWNjIzIyMlgdk88oOhEDwAMPPADAvWlr3759MkczdDwtaQB49NFH/b4KS01NFS9kgdSiNpvNoisxa9YszpYOUJ7qODExEZIkwel0orS0lDOryScUn4j1er04RvP6668HxPxj75Z0amqqX7akO/MM+vC0+LZs2SJ3SEPi4MGD4te+HCdKvidJEtLT0ztUxyaTiWvHNOwUn4gBiJ27VqsVb731lszRDI6SWtKdecfb0NCAiooKmSManNbWVrFJa/r06eINHwW2ztUx145puAVEIr7ttttEy7C8vFzRE3O8W9LLli1T3HnVhQsXioS1a9cuRV/UvmfPHvGzZDAYZI6GfMlTHRcUFIhTAZ6148rKSlbHNKQCIhGrVCoxU7a5uVmxAz68W9IpKSniwnMlUalUYhe10+nEpk2b5A5pQOx2u9hzEBsb6xdDVMj3NBoNjEZjh7XjoqIi5OXlBcw+CJJfQCRiwD1kITIyEgBQXFysuLXizrOkPbOclUiv1yMhIQGAclvU5eXlojORlpYmczQkJ+/quPPM6oqKClbHNGgBk4glSeqwVuxJakrhb7OkBystLU28aCmtRd3c3CzOpc+aNUuRnQkaehqNBmvXrkVCQoKojouLi1kd06AFTCIG3AM+vO/KtVqtMkfUN/44S3qwJEnCsmXLFNmi9tzMI0kSFi1aJHc45EfUajUWL16M/Px88VrD6pgGK6ASsaeFBECs5fg7Je+S7o1Op0NSUhIA5bSoa2pqcOTIEQBAQkKCmGdO5E2r1cJoNCIlJYXVMQ1aQCViAIiLi8OMGTMAuKdtnTx5UuaIeuZyubBu3TrRks7MzPS7WdKD9eCDDypmF7XL5UJxcTEAICwsTCx1EHVHrVYjNTUVa9euFW/YWB3TQARcIgbcx35CQ0MBANu2bfPbfxDeE6gCpSXdmUqlwmOPPaaIFvXevXvFG4XU1FTxM0R0OXq9Hlu3bu1SHWdlZbE6pj4JyEQcFhYmzn1aLBbs2rVL5oi68p7J7H2dYCCaOnWq+PP5a4vaZDJ1+H7MmzdP5ohISSRJQmpqKoxGY4cbnbKysjiVi3oVkIkYAObPny9aohUVFX41L7bzLUVKmCU9WMnJyX7dot6+fbtYIlixYkXAfz9oeOh0Ojz//PMwGAxd7jtmdUw9CWlvb2+XO4jh4nlH6nK5oNfrsXbt2iF7ga2rq8Mjyx6Bq92FlCUpuOHbN/T5c48eOIqjB9xDR2b+x0z8cO4Pu3zM/Nj5CBsVNiSx+ovGxkbk5uaK74fRaOzX53vOJhsMhiGddFVWVoaSkhIA7pZ0SkrKkH1tCl4NDQ0oLCwURYDniGVycjLf6FEHI+UOYDh5Wr6lpaVoaGhAcXGx2FU9WH8/+3d89sVnAICqv1bhGus1ffq8f33xL9S/Wo/2S+0YNWYUGkMbYXqnY7UeEhICADD8ILDGKup0OsyfPx979+4VLWrPrmq51NfX45VXXgEAxMTEBNSudZKXXq9Hfn4+SkpKxFjM0tJSHD16FMuXLxfHn/yF2Qzs3g288w7gdAJXXw3cdhtgMACjR8sdXWAL2Na0h/cmqMrKSnFed7AutV8S//+162s4Lzp7/d9Xzq/w8Rsfw+Vy4VL7JUy4bQIutl/s8nEB3KTAokWLxA5TuVvULpcLGzZsgNPphFqtRmZmpuIHqZB/kSQJaWlpMBqNIvH649pxdTXw298C3/seUFICVFYCRUXApElATg6gkJEMihXQFTHg/oeQm5uLzMxMOBwOrF+/Hvn5+UN6r+wjsx7BvXfc2+vH7anYg8qrK4GrgR//5Mf4SfJPunzMwy8+PGRx+SO1Wo3c3Fzk5uaKXdT9bVEPlcLCQjQ3NwMAHnvsMZ4ZpmGj0+lQUFDgl9WxxQK89BKQn9+x8h05ErjzTuCLL4CtW4Gnn5YtxIAX8BUxAERFRSE7OxsAYLPZ8Oyzz/r8hibLPyzYW7kXADBROxE/XvBjnz6/P9HpdB2uS/RcruBLFRUVOHDgAAD3RLbZs2f7PAYKLt7VsT/trH7tNeCBB3puP993n7tFTcMnKBIxAMyYMUO8+JtMJp9O3XK5XCjcXAiXywVJkvCzxT8L+s0aCxcuFJd07Ny5U1SmvlBTUyM2Z0VGRoqbu4h8QafTIT8/3292Vh87Bkyf3vPjV14JzJnju3iCUdAkYsB9EYFngH9VVZUY7D/c/lD5B1g+c6+F3nP/PfiW9ls+eV5/plKpkJ2d7fNBH2azGZs2bRJvivLy8oZ0mYKoLyRJgsFg6HDfsVzVcUsLcN11Pns66kZQJWJJkrBy5Urxwrtt2zZUV1cP63N6t6Sjb4xGwgMJw/p8ShITEyMGZ9TV1Q17i9pms+G3v/2tuN5w2bJlATnNjJTDc99xSkoK1Gp1h+q4vr7eJzH8+5AGySioEjEAhIeH48knnxQznTdt2jRsP/CdW9L/+fh/4kr1lcPyXEqVlpYmNqoMZ4vaM0TFe3MW14XJH3hP5fLeWZ2Xl+eTu9UnTAB8uDJE3Qi6RAy4b07Jy8uDSqUSFy8MRwLwbkknJCawJd2N0NDQYb8u0eVy4bnnnhNH1+655x7Mnz9/yJ+HaDA0Gg0KCgrE2jHg3lSYnZ09rNXxtGlAbe3lP+ZPfxq2pycEaSIG3Lc0LVu2DIC7ZZmXlzekybhzS/r+xPuH7GsHGr1eP6wt6i1btqD23680cXFxeOSRR4b06xMNFc/a8ebNm8WyicViGdbq+J573OeGv/yy+8draoCmpiF/WvIStIkYAOLj48WOWavVipUrVw5JMna5XNj+u+2iJf3o0sCfJT1Y6enp4hxvUVERmoboX/6WLVtw6NAhAO4kvHLlSg7tIL8XHR2NtWvXwmAwiJ/X4aqOo6OBhARgxQr3YA/PPjGrFaioAPbsARYsGNKnpE6COhEDQEpKimhTNjc3D0llfGDfAZg/dR9DuHPOndB8y79G2fkjz6APSZLgcDhgNBoHvXN03bp14qywTqdDbm4ukzAphkqlgsFgQH5+vrgwxVMdD/XO6oQE4JFHgDfeAFJS3OeKn3zSPeryN79xH2Gi4RP0iRhwb9zxtEatVityc3MHfFvTmc/PYE/FHgCA5lsaLExdOGRxBjqdTicudmhsbBSVbH85nU4YjUYcOXIEgHtPwOrVq3m/MCmSRqPB5s2bsXjxYvFGsrS0FDk5OUN67nj6dODZZ7+pgv/7v4Gf/pRJ2BeYiP9t2bJlYuCHzWbDqlWr0NjY2K+v4XK58LuC34l1nEU/W4QrVFcMeayBzGAwiONlO3bs6PcLjd1ux6pVq3D48GEA7iNSzzzzDMLCAusmKwoukiQhISEBzz//vJiFYDKZkJGR4Zf3e1P/MBF7SU9PR1paGiRJgt1ux8qVK3Hy5Mk+f753S/re++/FTZNuGq5QA5Zarcby5cuhUqngcDiwcePGPm9QsVqtWLVqFRoaGgC414SZhCmQaLVaGI1GLFmyRBzBLC4uRlZWlt/d8U19x0TcSVJSErKzs0UiWL16dZ8mcJk/NePV8lcBuHdJP7DggeEONWDFxMTg7rvvBuB+119aWtrr59TX1yMnJ0csKcyfP58bsyhg3XPPPdiwYQNiY2MBfFMd9+XfCvkfJuJuzJo1C0899ZSYdLNt2zYUFhZ2uCjig5MfoM3ahrazbag/WY+d/70TTqdT7JLm4I7B8b4usaqq6rLv9qurq7F69WrYbDYA7vb2Y489xiRMAS06Ohpr1qwRa8eeqVzd7XGprq7G+vXr8eyzz+KNN97AxYsXZYqauhPSHsiX3w6S2WzGunXrRBLQaDS49957sXRpNr5sBUZfOxeSpMa5L99Em/0TTJ6ig+EhA1JSUwb8nA+/+DBUI1VIvTUVhh8YhuqPokj19fVYtWoVXC4XIiMjUVtbC4fDgcTERKxevRpqtRrFxcXiWjlJkrBkyRKx8Y4oWJjNZmzcuFEkYEmSkJSUhIkTJyI19RHY7SNx7bVzIElqtLW9DeBzlJe/hBkzZsgbOAFgIu6Vw+HAhg0bUFNTA5vNhnfeOYbp0/dg7Ni5HT6upaUax479BC+/8j+4bdbA7wxjIu6ouLgYzz77LMxmM0aPHg21Wo2vvvoK7e3t+I//+A+cO3cOABAREYHly5cjJiZG5oiJ5OFyubBr1y5UVlbC6XTCZrPh3XePY/r0PRgzpuP1SS0t1fjgAwP2769kMvYDbE33Qq1WY+XKlUhLS8OJE3/D979f2SUJA8DYsfGIi3sVTzyeKy4VoME7f/48mpubMX36dEyZMgU33XQTYmNjcd1116GsrAxfffUVYmNjkZ+fzyRMQc0zs3rz5s3Q6/U4ceJviIt7tUsSBtyvVzffXIrk5Idw4cIFGaIlbyPlDkApIiIiMGrUBIwb13Pbc+zYePzdNA6b/3szpkyfMqDnudB0AVdIV+Aff/8H6kbVDTTcgOByubBq1SrExMRg1KhRHR6LjIyE1WrFpUuXkJycDIvFwl2jRP82adIkqFTje329+sc/rkN1dTXuu+8+H0ZHnTER91FNTQ2uvfauXj/umqt/hJ3btuKqV68a8HONCBmBC0cu4O3Rbw/4awSC1tZWXLx4scdBHBERETh58iSeeuopH0dG5N8aGxsxenTXSrizq666HSdOnGAilllQtabffdc9yu3dd4f3eUJCQjAiZMSA/wdA/D8REQW2oKqIjx4FfvQj4O23gR/8oH+fO2PGDBQU/LLXj7OdexOLH1uMWXfOGmCUbt8a+y1cIQX3VK6DBw+ipqYGdru926q4paUFCxYswNKlS2WIjsh/1dbWIi+v9ytF29rexrRpK3wQEV1O0CTi9nZ3JVxUBDz8sPu/Q0L6/vnx8fEYNcqBL754o9vND4B7J6LjX5/gk1PR+MHNP8CCBQt4lnUATp48iaKiIphMJkyaNAkffPABpk6diiu9ht42NzfDbrfj17/+Na677joZoyXyP7Gxsfjtb429vl4BnyM+Pt63wVEX0urVq1fLHYQvvPcecP48cOedQEMDMGoUcP31/fsaM2bcghdeSIVaPQWhodoOj7mPAzyE731PjyuvvBKnTp3CwYMHAQA33XQTRoxgq7k3DQ0NKCwsxMsvvyyGc3z/+9/HjTfeiDfeeANff/01zp07h88//xxtbW0oLy/H5MmTZY6ayD/19nr197//J3bvfglarbaHr0C+EjTniDdtAqZMcSfiN98E6uqAzMz+f52amhokJz8Ep/NqXHNNfJcD8qNGjcKmTZtgtVrF50RGRuLuu+/GPffcwxuAunHy5ElUVVWhpqZG/F54eDhSU1Mxe/ZsSJIEi8WC/fv3w2Kx4JZbbsGcOXPErF0i6l5vr1c8Q+wfgiIRt7cDqanA9u3A1VcDbW3Az38OlJb2rz3t4XA48Pbbb+O9997DxYsXMW3aNMTHx+Pqq68G4L6G75133sHLL7/c4YL70NBQJCQkYPbs2YiMjByqP54iOZ1OHD58GFVVVR1uuVKr1ViwYAF+/OMfM9ESDYHeXq9IfkGRiI8fB3bvdt+16fHUU0BiIhAXN3zP63K5UFVVhd27d4tWK+A+eD9r1izcfffd0Ov1kCRp+ILwM1arFQcPHsTevXs7DD4JDQ3FvHnzcP/994trEImIgkFQJOIXXgDeeKPr78+bByxbNvzP73Q6UV1djddff73LMHaNRoO5c+fitttuC9gE5HQ6cfLkSRw8eBC1tbVwuVzisfDwcMyePRsLFixg256IglLAJ2JPW3rrVmD06G9+/8svgV/8AnjppYG1pwfKsx7aOSFJkoTJkycjPj4e06dPV/wduk6nEw0NDXjzzTdx7NixDh0BwH1zzP33348777yTLWgiCmoBn4iPHweqqoAnn+z62LPPAvffD0yd6vu4bDYbDh06hDfffLPb0YwxMTG49dZbERsbi4kTJyqifW2z2VBfX4/33ntPnP/1plKpcOutt2LevHmYKsdfOhGRHwr4RPy73wHTp3c/wKOmBnj/fXdlLKf6+nocPHgQJ0+e7LDb2iM0NBRxcXGIiYnBjTfeCK1WK3sb1+VywWw24/Tp06ivr8epU6dgsVg6VPmAu9KPi4vDrbfeipkzZ8oeNxGRvwnoRNzeDmRkAJs3d99+bm93rxH/7ne+j607LpcL9fX1OH78ON566y00Nzd3+3GSJEGj0eD666+HXq9HVFQUoqOjERkZOSyVc2trK5qammCxWPDJJ5/AYrGgoaGhx1umQkNDRUU/Y8aMYW2zz53b9SYsb56z3ErjdDo7DDDxFsD/ZImCUkAnYqVrbm7GW2+9hePHj6OhoQFOp7PXz4mIiEBkZCQiIyMRERGBa665RiTC8PBwXHFF17GZDocDra2tcDgcaGlpgc1mg81mQ3NzM5qbm3t93tDQUIwfPx7Tp0/Hrbfe6tNW+ty5cxWbbC9n//792LFjByoqKuQOhYiGWdCMuFSiyMhIJCUlISkpCS6XC5988gmamppQX18vqtPW1tYOn2O1WmG1WlFfXz8sMalUKowdOxZarRaTJ0/G5MmTER0drYg1bCU5e/YsYmNj5Q6D9Gj6pwAAA2VJREFUiHyAiVghJEmCTqeDTqfDrFnfXChhtVrx2WefoampCc3NzbBarWhpaUFzczNsNluXNdu+CA8PR3h4OMaOHYvIyEiMHTsW48ePx8SJExEZGcn52T7w9ttv4/777+/3523ZsgXr1q3DmTNnMHPmTPzP//wPdDodAPetYK+99hry8vLQ2NgIrVaLLVu2wGazYdWqVTCZTBgxYgT27t2Lu+++e6j/SETUAyZihYuIiLjs+WO73S7Wcm02W7dtZpVKhfDwcIwYMQLh4eGsbv3A6dOnUVpaivT0dJw/fx6TJ0/G2rVrMWdOz3fM7tmzB1u3bsWf//xnfOtb38JLL72EpKQknDhxQnzMmjVrsGfPHuh0OvzXf/0XDAYDYmJicOjQIdxwww3Yv38/EhIS+rQMQkRDg2vEpGiBukY8evRorFixAitWrMCIESNgs9mwfPlyLFq0CHfeeWe3n3PvvffiiSee6LGaDQkJwbvvvovp06cDAC5evIgrrrgCH374ISZNmtTh4/iyQOQ7TMSkaJfbNR1oCfof//gHFi5ciCNHjnT7eFhYGM6dO9fjTV8hISFwuVwdHu8u6TIRE/kWW9OkeIGWcHtyww03oLa2tsfH29raer1uk9dxEvkf/qskUohLly5h5Mie3zurVCpcunTJhxER0VBgIibyQ9dff32HKzQB4KOPPrrsZq0f/vCHeKO7202IyK8xERP5oRUrVmDlypVoa2sDALS0tOA3v/kNnnnmmR4/5/HHH0deXh5Onz6NS5cuoaSkBNOmTfNVyEQ0QFwjJvJDTzzxBIqKijBt2jSYTCZMmTIF+fn5l02sDz74IJqamnDLLbfAZrMhPj4ef/jDH3wYNRENBHdNExERyYitaSIiIhkxERMREcmIiZiIiEhGTMREREQyYiImIiKSERMxERGRjJiIiYiIZMRETEREJCMmYiIiIhkxERMREcmIiZiIiEhGTMREREQyYiImIiKSERMxERGRjJiIiYiIZMRETEREJCMmYiIiIhkxERMREcmIiZiIiEhGTMREREQyYiImIiKSERMxERGRjJiIiYiIZMRETEREJCMmYiIiIhkxERMREcmIiZiIiEhGTMREREQyYiImIiKSERMxERGRjJiIiYiIZMRETEREJCMmYiIiIhn9fwKokrZnrz6SAAAAAElFTkSuQmCC)