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main.py
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import zlib, base64
exec(zlib.decompress(base64.b64decode(b'eJy9GVtv27b63b+C0IvlwYd1k7RAAvghZydrtjZulqb3FQIt0TZrmdJIyo4R5L/v400WbTlOC5zpwRHF734nwxZlIRQS9O+KSiU7zK4VW1D/TuSap6zwy++y4P5dyty/VhXL/LsgPCsWnYkoFigteFoJQbnCk0pVgkrkoG5ngpLsuijyizuaVqoQfeCVpMWizKmimcVf0bEs0jlVMilFcbf22Nd60UfmG+BwTlNlMSZkTpNKUkGmwNXDv4cP5/qDBcqLaSUqvwmrKRW1VumMZlVeG2BMJH150ukosFBSiRwNUXemVCnPnj1brVZ4WhTTnGIQvNuhPC0ymllZk5xtMMjlzSC9vHr5Zn26/vwprb4c5QNy+YFln0Z5uhgtx/wmH/M/q89Hp+rN4MP681Fe3bz6MP/y8ZSPL98v08s/lvRVnqfrU/X5Y169Of7venw8K798ulqmR6ffyfHV8zf85iQ7Hw67naJSZaWSCcupYZ4qtqRGKkYlVneq29EmSlgmayD9we3tiG9tgMcvTzKqNYzbFe1ht93rdDI6QWDJdG5hYvPbO+sgeJRY2xf9SColKzhw8WGI39lPQGYLCDsVAPi+qwNDvuie2Sh4qGEhyMqCS62UR5tBqMXegX0T32Ci4fPBhgOb1IhYKqIqHYsZEBmio8FgI65+bMBgxidFPIlMLKJ7KwW6IlzREo3YLOoFSIJC/HMrbL1Bc0lbaa+I4IxPd8hbKjRDVkZkZLxvk/wBtwswKjg13+ldSkuFLswf7QEiUUMYJwgVohAgxoX+i4rUpHOGVjMdNsbBIKYX7wzd04cG2yZLExGSQByG4RiHMdRHjeDtowW584BD8MOgLYIaDq9DaErVFuGfc7WlkRFFDHWHpeidAlTByriHZZkzFXf/4t0te5s6mGxC1n7AkugSF28og5aMxw1N+yinvAHQ64WUQwMC5a/fgv0VU7OWAmtYrAoxh0QfHveMv91WqLR+fLkG4h4Iy2q8AFUbae1KsLdFD00gSFyl5lsW+LbLA4AtHw3drP6xY9/bFcx5vMoVyGbBsF3HvVZg627Yb6e1a1BMypLyLLZYrU7d8UDo23Db+vf4xQvr13Bz27fGdwXwj4M86K66xmGTFk+1mDzk0a74BK8EUxRyW7cz6GYuif/i7YWjlfThSuYLyCsyJTniU7IYsxxlZKKIlzsjgrkSUqfrA0avdVLaBD3bU+PaJXXp8DMFTlHxnWQMlQBrJYX8q7Sc0EueIPWeCggSmfoHPBNBwa1ECxS7HPJhz6Fd6RWXQA5a7Nq2qpzZDbIkLCcgE1O+k7Z0ojNfjPvoNXWUCYevTS5607ORzGzWTGHvI5mrCmxREgV7GxkMTTCRpBkjhmhTJq13x8yLyHR/O5YlqkhWUsa2Xfuy4cYPUFCQyYSliVqXdNi9vrjtOtUyumQpBRjdx5WI9YiJ9c+xfR2dX128uz7/9SL53+hdHzXJu5RqGqemZrcMezshDjfDoSsgLtADmM0Cu/nWgNo2eCuqRlwFvUk/ZEVYPUhjmVNaxs/DwE0rqYClnlPAunq8ibRU/zFiRWe7Ij0E6DCJ6ylYtyVtLZnjFIq/ogn4gUAN85tbFbKBhm1RnxVScbLQrfQ3Ahm9F3xJBZusk4Xpm4bjrxc3t8no7eiiEyBVkCRDFEEEQIWxzWK15hnmVOlWdHby8sXgWRTyoQLIN2WJdhFDFJuRQ3suwHrG19kYxFwvlMvGqam2wSkiBoFdVxu6WAXthg3d+9sCDrfW/b19JniAlCDe5cMwAkytrw8/u/V7k2USOlVS6lFxT69sC9HtxxBZQIJDbIEV9SEPZ9WilPGjqtxHLIPgDLLzBKaAPorAHnryht3oOR7gQQTfdOewn65/H73SX/RwA+v7h4f21q2fnXTasYVJr9pYWCsTNzXaT1s/rkpkdFxNn4h2oLE8wiVshnMm2AJpY2y3jXYdwxJytBXRBs5BuPRXRM7jRoS0YBwKj8ZwvW1oQdPlnplrK5bygmQy9qTaUZrVuvZAK2SzkQEHLTvaA1g3NQfXCrbpb49Sa7a6GnCfKs0uH3a+n2n27WxgsHWGMscdn189fZCJzt/fXkaPTLyVmiUN394/Gr02zx2zr3r17fEiFxWCTRlPNilv5DmAZAduXRAOVtBoLIqVnSEAvu7uh0tvVNVYfgZ5Ig5xvTis1F+7m0bdPWAVQ0s7GUbYRQmkGMwceo31jy6ch9Gdqnpc0maFJqInOLDxE3AbRfkYH+Oj6FGUh727+3d+rlg3+k0Ql70fqNwh4r9Uui0/pGPbV/BWUpDVj+Xq9Vtoh/uFABbTIFfb0rEl5QzZ/6OvArl+xFch4r/rK22UHV89gRMcCGXYF1rH+kEPNc9ACwInfzeYbU72wd0rnO2FO9vDasPUA+lbDtjA+jbH3zaZJhE7BfbdGLRSbfYic2o9SF7PEOYayGsK9aYSNLFXL/HWKS883vl7odZjnr0scpD67qLWOLjR2JHYHu5D60+JmlER/2KEdbfPJRVAaJF8L8beBTvXNj94H2ljFXJ53/2Kl0dU+kJP+96ihLcjQZRGryFI54hkxOkMZ2820VdFKxgfOJpV44pPCUcf6fidTUQduv7fFJhCVV/HRyc9PCsqIXFWxA3NATKwQ6ezPfDVhEDmRN97mUnRul63pvq8+g+Vr7yB')))