Sparse Approximation of Gram Matrices for GMMN-based Speech Synthesis（INTERSPEECH2019 読み会）

Transcript

1. Sparse Approximation of Gram Matrices for GMMN-based Speech Synthesis ਢా
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    ํ޲ y <latexit sha1_base64="YzhhfzJFrE0hBOIrIALy2w1Rk5I=">AAAB4XicZZDLTsJAFIZP8YZ4Q126MbJh0TQUqOCO6MYlJnJJaENmhqGMzLRNZ0ogDQ/gSmPc6ZO4xZfwQdxbLhvk35wv/8n5c87BAWdSFQo/Wmpre2d3L72fOTg8Oj7Jnp41pR+FhDaIz/2wjZGknHm0oZjitB2EFAnMaQsP7+b91oiGkvneo5oE1BHI9VifEaQSq5s17EVGJ3SxExeMglUuFS09gUq5WKzO4dq6qVSnGRuLeDLtZnOJtdDlJpgryMFK9W720+75JBLUU4QjKTtRwJGiYyd+kihUjHCaZEeSBogMkUs7kepXnZh5QaSoR9Z7vRELpIcElbocuUsYm+YCnHi8uGRtIkZCCqQGelLlRGAdC11w2lchcwdqmknOMf8vvwnNomGWDOuhnKvd4hc7/zuDNFzAFeTBhArU4B7q0AAC7/AFM/jWiPasvWpvyx+ktNUzzmFN2scfbBuKuQ==</latexit>
    ํ޲ x <latexit sha1_base64="eiKd+scTQbKqG+w6WfzXTHcZlrU=">AAAB4XicZZDLTsJAFIZP8YZ4Q126MbJh0RAKVHBHdOMSE7kktCEzw1BGZtqmMyUlDQ/gSmPc6ZO4xZfwQdxbLhvk35wv/8n5c87BPmdSFYs/Wmpre2d3L72fOTg8Oj7Jnp61pBcGhDaJx72gg5GknLm0qZjitOMHFAnMaRuP7ub99pgGknnuo5r41BbIcdmAEaQSq5ctWIuMbuBgOy4WimalXDL1BKqVUqk2h2vzplqbZiws4mjay+YSa6HLTTBWkIOVGr3sp9X3SCioqwhHUnZDnyNFIzt+kihQjHCaZIeS+oiMkEO7oRrU7Ji5fqioS9Z7/THzpYsElbocO0uIDGMBdhwtLlmbiJGQAqmhnlQ5EVjHQhecDlTAnKGaZpJzjP/Lb0KrVDDKBfOhkqvf4hcr/zuDNFzAFeTBgCrU4R4a0AQC7/AFM/jWiPasvWpvyx+ktNUzzmFN2scfasyKuA==</latexit> ʹ CY |X = ( > + I) 1 > <latexit sha1_base64="qVtQkNmkmlJO3KbaXbhM2S4833I=">AAACJHicZZC7TsMwFIZt7pRbgZEloksRoWpKS8uAVMECW5EoFDWhsl03NdhJiJ2qVcgz8ALMvAgrG0KIhbdgRCINHSj8y/nkc/P5sceZVPn8O5yYnJqemZ2bTy0sLi2vpFfXzqUb+ITWictdv4GRpJw5tK6Y4rTh+RQJzOkFvjka5i961JfMdc7UwKOWQLbDOowgFT+10rdmMqPp29gK87l8qbhbKOkxlIuFQmUIe6X9ciVKHbXCy7tGpB1oJhZmrcuySZTsylSuN2JtWzN5vLyNhlXhSbR1Fe4Ykfa7tJXOxFMTaf/BGEEGjFRrpR/MtksCQR1FOJKyGXgcKdq3wmuJfMUIp1HKDCT1ELlBNm0GqlOxQuZ4gaIOGc+1e8yTDhJU6rJn/0DfMBKwwn5ixlhHiIQUSHX1OMqBwDoWuuC0o3xmd1WUis8x/n7+P5wXcsZurnRazFQP8b2Z/XwCc2ADbIIsMEAZVMExqIE6IOANfMEZOAsf4TN8ga8/HkzAkRnrYEzw4xu7E6K1</latexit> ਖ਼ଇԽ (x) <latexit sha1_base64="hPujv+po4C40Zfiq8yGB+QTdmqs=">AAAB8nicZZC7TgJBFIbP4g3xhlraGGkw2RCWi2Al0cYSE7kk7IbMDMMyMrO72ZklkA3PYG9sjLHzLSxttfBB7F0WGuRvzpf5Z86c/2CPM6ny+R8tsba+sbmV3E7t7O7tH6QPj5rSDXxCG8Tlrt/GSFLOHNpQTHHa9nyKBOa0hYc3M781or5krnOvJh61BLId1mcEqeiom74y4x4d38ZWmM/ly6VioaxHUCkVCtUZXJQvK9VpyvQkMzntq6yJRTiemj6zB+q8m85Ed2KdroKxgAwsVO+mn82eSwJBHUU4krITeBwpOrbCB4l8xQin0WeBpB4iQ2TTTqD6VStkjhco6pBlrzdinnSQoFKXI3sOY8OIwQrHcbSlFyESUiA10KMqJwLrWOhilipOM01FcYz/w69Cs5AzirnyXSlTu8aPZvb3A5JwAmeQBQMqUINbqEMDCLzBJ3zBt6a0J+1Fe53vIKEtlnEMS9Le/wBpu5Hc</latexit> µY |x <latexit sha1_base64="WlGwAfIpj6zuHZUJ2knL104dFO8=">AAAB6XicZZDLTsJAFIZPvSLeUJdujGxYNIQCBdwR3bjERC6GNmRmGMrITNt0pgRSeQbjzhh2voku9QV8EPeWywb5N+fL+XOu2OdMqlzuR9vY3Nre2U3sJfcPDo+OUyenDemFAaF14nEvaGEkKWcurSumOG35AUUCc9rEg5uZ3xzSQDLPvVdjn9oCOS7rMYJUnOqkSta8RztwsB3lsjmzWMibegzlYj5fmUHJvCpXJkkLi8gS4aQTPTyNJp1UOrbmulgHYwlpWKrWSU2trkdCQV1FOJKyHfocKTqyo0eJAsUIp/GMUFIfkQFyaDtUvYodMdcPFXXJqtcdMl+6SFCpy6GzgJFhzMGORvOLVioiJKRAqq/HUY4F1rHQBac9FTCnrybJ+Bzj//Lr0MhnjULWvCumq9f42cr8fkICzuESMmBAGapwCzWoA4EpfMAXfGsD7UV71d4WP9jQls84gxVp7399GY5y</latexit> CY |X <latexit sha1_base64="cGkVPvNagYfXSM5ms7MtZS9I0Ig=">AAAB8HicZZA7T8JQFMdP8YX4Qh1djCwMDaFABQcTIosjJvIwtGluL5dy5d626b1FSOUzuDqYGOPm13By1ckP4m55LOh/Ob+cxz/nHNtnVMh8/ltJrKyurW8kN1Nb2zu7e+n9g6bwwgCTBvaYF7RtJAijLmlIKhlp+wFB3GakZQ9q03prSAJBPfdajn1icuS4tEcxknHKSp8bM49O4NhmlM/l9VKxoKsxlEuFQmUKp/pZuTJJzfuiuz6VZJKqWdHNfXtipTNxx0zH/0FbQAYWqlvpJ6Pr4ZATV2KGhOiEPkOSjMzoVqBAUsxicyMUxEd4gBzSCWWvYkbU9UNJXLxc6w6pL1zEiVDF0JnDSNNmYEaj2cJLExHigiPZV+MoxtxWba5yRnoyoE5fTlLxOdrf5f9Ds5DTijn9qpSpXtgPRvbnHZJwBCeQBQ3KUIVLqEMDMLzCB3zClxIoj8qz8jL/QUJZPOMQlqS8/QIUsJEY</latexit>
13. $..%
    ͷܭࢉ w
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    w ͨͩ͠ X = ˜ X <latexit sha1_base64="UnxfbK3vF3Y5YBPp9+HtSZ0ec3I=">AAAB6HicZZDPTsJAEMan/hf/oR69ELl4aAhFKngwMXrxiIlIE9qQ7TLUld226W4JpOEZ9GaMnnwT402fwAfxbqlckO8yv8yXmcw3bsiZVOXyt7awuLS8srq2ntvY3Nreye/u3cogjig2acCDyHKJRM58bCqmOFphhES4HFtu/3LitwYYSRb4N2oUoiOI57Meo0SlrU7etLMd7chznaRcKpvV44qpp1CrVir1CZyYp7X6OGcVzgq2YryLiTXu5Iupk6kwD8YUijBVo5N/tbsBjQX6inIiZTsOOVE4dJJ7SSLFKMdxzo4lhoT2iYftWPXqTsL8MFbo01mvO2Ch9IlAqcuB9wdDw8jASYZZoJmJhAgpiLrT0ypHwtVdoQuOPRUx706Nc2kc4//x83BbKRnHJfO6Wjy/cB/so58PWIMDOIQjMKAG53AFDWgChRd4h0/40u61R+1Je/77wYI2fcY+zEh7+wVcYIz2</latexit> 13 CMMD2 = CY |X C˜ Y | ˜ X 2 F⌦G = ( > + I) 1 > ˜ ( ˜ > ˜ + I) 1 ˜ > 2 F⌦G <latexit sha1_base64="+ETlIaAdS/ReuWr9EwNFZpa9Oug=">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</latexit> ͨͩ͠
    A? = (A + I) 1 <latexit sha1_base64="5Jsek6xTi7MPQyCduNqSUWyNUtA=">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</latexit> = Tr (KXX K? XX KY Y K? XX ) + Tr K ˜ X ˜ X K? ˜ X ˜ X K˜ Y ˜ Y K? ˜ X ˜ X 2Tr K ˜ XX K? XX K Y ˜ Y K? ˜ X ˜ X <latexit sha1_base64="/Pl9fdBu0nurhKdMkOMinQNvVAw=">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</latexit> ৚݅෇͚ʹΑΔ߲
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    ͱͳ͍ͬͯΔɻ ⌥ = <latexit sha1_base64="QxIEmfoNiFVKGqwgcg1uW9B14B0=">AAAB8HicZZBLT8JAEMenPhFfVY9eiFw8NIQCFTyQkHjx4AETCyS0IdtlKSu7bdPdEkjD9/BgYow3v4mJXvTkt7EULsj/Mr/Zee2MEzAqZLH4q2xsbm3v7Gb2svsHh0fH6slpS/hRiImJfeaHHQcJwqhHTEklI50gJIg7jLSd0c083h6TUFDfe5DTgNgcuR4dUIxk8tRT61baoxu6jh0XC0WjUi4ZWgLVSqlUm8OVcV2tzbKWwy0zEJT5Xq6em3tNQXtqPslIlVsHfQl5WKrZU5+tvo8jTjyJGRKiGwUMSTKx40eBQkkxI8moSJAA4RFySTeSg5odUy+IJPHwaqw/poHwECdCE2N3ARNdT8GOJ+liKxUx4oIjOdQSK6bc0RyucUYGMqTuUM6yyTr6/8+vQ6tU0MsF476Sb+h3n4m+IAPncAGXoEMVGnALTTABwxt8wDf8KKHypLwor4sbbCjLY5zBipT3P1n2kV8=</latexit> ·? = ¯ · <latexit sha1_base64="10P1B9X1e4xBuxvOib4zm+WnPSA=">AAAB9HicZZDLTsJAFIZP8YZ4Q126IbJx0RDKRXBhgnHjwgUmckloJdNhKCMzbTMzJZCGN2FnjDufRLYa38ZS2CD/5nw593Nsn1Gp8vlfLbG1vbO7l9xPHRweHZ+kT8+a0gsEJg3sMU+0bSQJoy5pKKoYafuCIG4z0rKH94t4a0SEpJ77rCY+sThyXNqnGKnI1U3fmXGPjnBsK8zn8uVSsVDWI6iUCoXqAq7LN5XqNGXinqdeTKmQyNxmTBuJMHZNu+lslBUrswnGCrKwUr2bnpk9DwecuAozJGUn8BlSZGyFrxIJRTEj0bhAEh/hIXJIJ1D9qhVS1w8UcfF6rDeivnQRJ1KXI2cJY8OIwQrH8XFrFSHikiM10CMrJ9zWba5zRvpKUGegpqnoHOP/8pvQLOSMYq78VMrWjMevSHNIwgVcwhUYUIEaPEAdGoDhA+bwDT/aSJtpb9r78gcJbfWMc1iT9vkHtOCTbA==</latexit> L = K ? XX KXX K ? XX = H ? HH ? <latexit sha1_base64="0tRT7RlhJcSI0e8jw9vK+3RLRg8=">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</latexit> = Tr [(KY Y + K˜ Y ˜ Y 2K Y ˜ Y ) L] = Tr [GL] <latexit sha1_base64="Towx5L9Yi4+tAXFA0SO5CiHy6zk=">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</latexit>
14. $..%
    ͷܭࢉ w
    ͱ͢Δ X = ˜ X <latexit sha1_base64="UnxfbK3vF3Y5YBPp9+HtSZ0ec3I=">AAAB6HicZZDPTsJAEMan/hf/oR69ELl4aAhFKngwMXrxiIlIE9qQ7TLUld226W4JpOEZ9GaMnnwT402fwAfxbqlckO8yv8yXmcw3bsiZVOXyt7awuLS8srq2ntvY3Nreye/u3cogjig2acCDyHKJRM58bCqmOFphhES4HFtu/3LitwYYSRb4N2oUoiOI57Meo0SlrU7etLMd7chznaRcKpvV44qpp1CrVir1CZyYp7X6OGcVzgq2YryLiTXu5Iupk6kwD8YUijBVo5N/tbsBjQX6inIiZTsOOVE4dJJ7SSLFKMdxzo4lhoT2iYftWPXqTsL8MFbo01mvO2Ch9IlAqcuB9wdDw8jASYZZoJmJhAgpiLrT0ypHwtVdoQuOPRUx706Nc2kc4//x83BbKRnHJfO6Wjy/cB/so58PWIMDOIQjMKAG53AFDWgChRd4h0/40u61R+1Je/77wYI2fcY+zEh7+wVcYIz2</latexit> 14 CMMD2 = CY |X C˜ Y | ˜ X 2 F⌦G = ( > + I) 1 > ˜ ( ˜ > ˜ + I) 1 ˜ > 2 F⌦G <latexit sha1_base64="+ETlIaAdS/ReuWr9EwNFZpa9Oug=">AAADH3icjVLLjtMwFHXCayivDizZRFRCRbRVk2lpWSCNKOKxGKlIdKajOq2c1E1N7SSKnaoj19/AD7DhW1iwQ4jdfAgSS5w0qigDEndzz73H9+g+7MWUcNFsnhvmpctXrl7bu166cfPW7Tvl/bvHPEoTHw/8iEbJ0EMcUxLigSCC4mGcYMQ8ik+8RS/jT5Y44SQK34mzGLsMBSGZER8JnZrsGwuYi4ySwHNls9Fstw6cdk2DTstxuhl40n7a6aoSZEjMEyZ7R0cv1NixHj6DFM8EXPcm8nQ9VHXtoSB0iuWpWhdoqBRMSDDXz8aO5jMNH1H5UsFIEIb5NvNKKQvCUTsWbmkrDT0mYX9OVHWDOFFjKKJYR1lgPbYg1bNOkZXxb9Sjsazbyiro/KlVt4pe8myu9Vu8VdzN/VP5b6X/PeCkXNH7zM26COwCVEBh/Un5I5xGfspwKHyKOB+lMUUCr1z5nqNEEJ9ifZiU4xj5CxTgUSpmXVeSME4FDv1dbrokMQ+R7qnGl8EGrGw7B65c5d9gp0IixrPua9rzM+bVPFZj2WHygVVJj2P/2fxFcOw07ING+22rcvjc+wCrPz6DPXAfPABVYIMOOASvQR8MgG98N36ahmman8wv5lfz22YHplEs4x7YMfP8F8krA4s=</latexit> = Tr (KXX K? XX KY Y K? XX ) + Tr K ˜ X ˜ X K? ˜ X ˜ X K˜ Y ˜ Y K? ˜ X ˜ X 2Tr K ˜ XX K? XX K Y ˜ Y K? ˜ X ˜ X <latexit sha1_base64="/Pl9fdBu0nurhKdMkOMinQNvVAw=">AAADQXicnZJNb9MwGMdd8zbCWwc3uESUQxGharKWlgPSNC5IXIa0bqnqUDmpm5nZSWQ7VSfLHwHtC+zb7FPsI3BDCE5cSLNQUQYV4rn4p+ev5+0vhxmjUrXb5zV45eq16zc2blq3bt+5e6++eX9fprmIyCBKWSr8EEvCaEIGiipG/EwQzENGDsKj1wv9YEaEpGmyp44zEnAcJ3RKI6yK1Hiz9hGVTUYiDgPdbrW7nS2v6xTQ63hefwEvui97fWO9shHH6lBwvScMYmSqmjYKuX5rxtr3za/8HkmFxc/EcPgnUdD4UD21n9nW39siRdmEaN8swazTVsdW+aFZwr8UV2s9ty1vzb3LsrV3/8fgcb1ROF6GfRncChqgit1x/RRN0ijnJFERw1KO8oxhReaB/iCxUDRixFgolyTD0RGOyShX036gaZLliiTRqjaZ0UwmmBPpyFl8AXPXLSHQ8/KjrFRozOXCJKd45TEPnZA7fGFVeY2xinPc35e/DPtey91qdd91Gts74QlqfjsDG+AReAyawAU9sA3egF0wAFHtK3wIG/AJPIOf4Gf45cIDWKvMeABWAn7/AVSTFRU=</latexit> ৚݅෇͚ʹΑΔ߲
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    ߦྻʣ = Tr [(KY Y + K˜ Y ˜ Y 2K Y ˜ Y ) L] = Tr [GL] <latexit sha1_base64="Towx5L9Yi4+tAXFA0SO5CiHy6zk=">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</latexit> $..%
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    ͱͳ͍ͬͯΔɻ ⌥ = <latexit sha1_base64="QxIEmfoNiFVKGqwgcg1uW9B14B0=">AAAB8HicZZBLT8JAEMenPhFfVY9eiFw8NIQCFTyQkHjx4AETCyS0IdtlKSu7bdPdEkjD9/BgYow3v4mJXvTkt7EULsj/Mr/Zee2MEzAqZLH4q2xsbm3v7Gb2svsHh0fH6slpS/hRiImJfeaHHQcJwqhHTEklI50gJIg7jLSd0c083h6TUFDfe5DTgNgcuR4dUIxk8tRT61baoxu6jh0XC0WjUi4ZWgLVSqlUm8OVcV2tzbKWwy0zEJT5Xq6em3tNQXtqPslIlVsHfQl5WKrZU5+tvo8jTjyJGRKiGwUMSTKx40eBQkkxI8moSJAA4RFySTeSg5odUy+IJPHwaqw/poHwECdCE2N3ARNdT8GOJ+liKxUx4oIjOdQSK6bc0RyucUYGMqTuUM6yyTr6/8+vQ6tU0MsF476Sb+h3n4m+IAPncAGXoEMVGnALTTABwxt8wDf8KKHypLwor4sbbCjLY5zBipT3P1n2kV8=</latexit> ·? = ¯ · <latexit sha1_base64="10P1B9X1e4xBuxvOib4zm+WnPSA=">AAAB9HicZZDLTsJAFIZP8YZ4Q126IbJx0RDKRXBhgnHjwgUmckloJdNhKCMzbTMzJZCGN2FnjDufRLYa38ZS2CD/5nw593Nsn1Gp8vlfLbG1vbO7l9xPHRweHZ+kT8+a0gsEJg3sMU+0bSQJoy5pKKoYafuCIG4z0rKH94t4a0SEpJ77rCY+sThyXNqnGKnI1U3fmXGPjnBsK8zn8uVSsVDWI6iUCoXqAq7LN5XqNGXinqdeTKmQyNxmTBuJMHZNu+lslBUrswnGCrKwUr2bnpk9DwecuAozJGUn8BlSZGyFrxIJRTEj0bhAEh/hIXJIJ1D9qhVS1w8UcfF6rDeivnQRJ1KXI2cJY8OIwQrH8XFrFSHikiM10CMrJ9zWba5zRvpKUGegpqnoHOP/8pvQLOSMYq78VMrWjMevSHNIwgVcwhUYUIEaPEAdGoDhA+bwDT/aSJtpb9r78gcJbfWMc1iT9vkHtOCTbA==</latexit> ͨͩ͠
    A? = (A + I) 1 <latexit sha1_base64="5Jsek6xTi7MPQyCduNqSUWyNUtA=">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</latexit>
15. $..%
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    w ຊ౰͸ܥྻશମʹରͯ͠ܭࢉ͠ͳ͍ͱ͍͚ͳ͍ 15 CMMD2 = Tr ⇥ (KY Y + K˜ Y ˜ Y 2KY ˜ Y ) · (H + I) 1 H (H + I) 1 ⇤ <latexit sha1_base64="IJCU9ZquIJ7dV6SCdl/sCwCaLEQ=">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</latexit>
16. $..%
    ͷܭࢉͷۙࣅ w ϛχόον୯ҐͰܭࢉ͍ͨ͠ 16 (a) Block-diagonal approximation (b) RFF approximation
17. ཚ୒ԽϑʔϦΤಛ௃ w 3BOEPN
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    ཚ୒ԽϑʔϦΤಛ௃ʹΑͬͯۙࣅͰ͖Δ 17 k(y, ˜ y) ⇡ z(y)>z(˜ y) z(y) = r 2 M 2 6 4 cos(y>!1 + b1) . . . cos(y>!M + bM ) 3 7 5 <latexit sha1_base64="TzhliHgQu9dxtnAku+ma+1cXmoc=">AAAC8HicjZBNj9MwEIad8LWEry4cuURUWrUiqppsQ4sE0gouXCotEt1dqQ6RnbhZ0zgxtlOlWPkNXDkgIcSNv8GJK5z4IdxJ07JSdyXEXPx4xu/M68E8pVL1+78M89LlK1ev7Vy3bty8dftOa/fukcwLEZFJlKe5OMFIkpRmZKKoSskJFwQxnJJjPH++qh8viJA0z16pJScBQ0lGZzRCqk6Fu8YT2DSZigQHut/r+4N9z3dqGA48b7SCR/7j4aiy5h0bYqaXlWNDRdOY6PW16lp7EHEu8rJ58K7qrAvd11Dl/G/qnATCqc9VYP3v9O3O9t5TG8q3Qmk4EyjSXqXHVQUxSWimMUNK0LJa9ZYbxZkVmDOSoCp07Yc4dLs2hDZcxLmSDf1DMF4JxrVxksVnI8JWu7bYhH0R3A20wSYOw9ZHGOdRwUimohRJOS14ihQpA/1GIqFolJLadyEJR9EcJWRaqNko0DTjhSJZtF2LF5TLDDEiHblI1lC6bgOBLpvNbik0YrJ2furUp1wy7GDmsJTM6r8kp6qy6u+4581fhCOv5+73/JeD9sEz/B52fn8DO+A+eAA6wAVDcABegEMwAZHxxfhu/DB+msL8YH4yP693YBqbZdwDW2F+/QO4Nuuo</latexit> k = e k k2 2 $ p(!) = 1 (2⇡)M/2 e k!k2 2 <latexit sha1_base64="4Rp47YwAMUch06B0M5jGoqrexJY=">AAACWHicZZDNbhMxFIU9U6BtCjQtSzYjskmlIWSmCQkgpApYsEEqEmkrxZPIdm+mJvbMyPaEVO48Ay/AlifhKeA92OP8qFLo2fjTvTpH14cWgmvTbv/2/K179x9s7+zW9h4+erxfPzg803mpGAxYLnJ1QYkGwTMYGG4EXBQKiKQCzun0/WJ/PgOleZ59MdcFJJKkGZ9wRowbjes/8TJjqFKa2Har3e0cx93QQa8Tx/0FvOy+6vWr2jR4G8DIBs/xRBFmA3yDP4AwBN+M4srGVRXgMMACJkbx9MoQpfJvblI0MZU4l5CSI5ewMkeVbca44Ecj++nFwuqC17kulkq7MlS32eN6w12yVHAXojU00Fqn4/oPfJmzUkJmmCBaD8tCEAPzxH7VRBnOBFQ1XGooCJuSFIalmfQTy7OiNJCxzd3ljBc6IxJ0qGfpCuZRtITEzpcFbjgskVoScxW6V19LGlIZyttqqpr7TvT/8XfhLG5Fx63u507j5B39jpt/f6Ed9BQ9Q00UoR46QR/RKRog5u15kffae+P98ZG/7e+uOvC9dRlP0Ib8w3+a/7HI</latexit> "MJ
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18. ཚ୒ԽϑʔϦΤಛ௃ͷҙຯ w
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19. $..%
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