LowerImageLimit = {
10950, 11078, 11099, 11047, 10964, 10910, 10976, 11012, 10956, 10998, 11037, 11067, 11075, 11058, 11027, 11129, 11132, 11177, 11259, 11304, 11202, 11261, 11345, 11453, 11386, 11554, 11427,
10835, 10955, 10988, 10905, 10789, 10717, 10758, 10776, 10724, 10757, 10802, 10895, 10863, 10822, 10796, 10890, 10865, 10874, 10944, 10997, 10910, 10988, 11042, 11137, 11042, 11194, 11023,
10739, 10845, 10883, 10784, 10705, 10595, 10644, 10637, 10597, 10633, 10679, 10787, 10747, 10721, 10701, 10796, 10769, 10764, 10840, 10919, 10785, 10859, 10931, 11012, 10927, 11068, 10904,
10684, 10807, 10837, 10714, 10678, 10556, 10591, 10620, 10561, 10597, 10652, 10748, 10710, 10697, 10701, 10762, 10754, 10769, 10902, 10967, 10790, 10835, 10921, 11008, 10927, 11065, 10937,
10595, 10716, 10733, 10628, 10573, 10485, 10515, 10535, 10500, 10506, 10637, 10662, 10658, 10676, 10637, 10702, 10681, 10723, 10877, 10971, 10745, 10786, 10893, 11000, 10890, 11020, 10883,
10619, 10721, 10727, 10649, 10585, 10492, 10539, 10570, 10515, 10517, 10712, 10674, 10694, 10706, 10670, 10718, 10700, 10724, 10899, 10964, 10749, 10815, 10916, 11022, 10949, 11068, 10937,
10400, 10503, 10523, 10442, 10398, 10313, 10351, 10379, 10331, 10368, 10514, 10490, 10517, 10553, 10484, 10572, 10535, 10563, 10769, 10802, 10638, 10692, 10787, 10900, 10819, 10981, 10819,
10324, 10430, 10419, 10359, 10324, 10229, 10301, 10320, 10249, 10325, 10424, 10405, 10454, 10472, 10400, 10497, 10467, 10559, 10735, 10756, 10620, 10686, 10812, 10878, 10787, 10958, 10809,
10512, 10603, 10583, 10537, 10500, 10391, 10492, 10519, 10445, 10511, 10555, 10604, 10656, 10661, 10596, 10673, 10646, 10727, 10850, 10922, 10802, 10889, 11018, 11094, 10975, 11196, 11033,
10442, 10501, 10515, 10454, 10421, 10326, 10446, 10459, 10387, 10470, 10546, 10528, 10577, 10589, 10517, 10612, 10581, 10679, 10778, 10872, 10751, 10837, 10954, 11038, 10921, 11170, 10972,
10265, 10338, 10367, 10318, 10277, 10182, 10308, 10322, 10244, 10364, 10398, 10391, 10479, 10448, 10382, 10490, 10497, 10561, 10632, 10763, 10617, 10717, 10845, 10902, 10847, 11051, 10887,
10209, 10309, 10332, 10308, 10231, 10160, 10255, 10290, 10203, 10327, 10378, 10372, 10443, 10432, 10378, 10482, 10470, 10529, 10634, 10769, 10623, 10731, 10859, 10935, 10883, 11086, 10915,
10137, 10223, 10253, 10231, 10157, 10088, 10171, 10211, 10139, 10253, 10304, 10295, 10364, 10321, 10288, 10400, 10388, 10466, 10547, 10689, 10562, 10650, 10778, 10865, 10810, 10985, 10827,
10114, 10211, 10217, 10210, 10149, 10106, 10196, 10223, 10126, 10231, 10282, 10298, 10337, 10320, 10280, 10408, 10397, 10469, 10562, 10679, 10560, 10667, 10783, 10858, 10839, 11012, 10848,
10104, 10207, 10230, 10209, 10150, 10088, 10194, 10223, 10122, 10221, 10245, 10259, 10282, 10284, 10295, 10386, 10392, 10468, 10598, 10680, 10564, 10673, 10776, 10877, 10844, 11009, 10858,
10082, 10176, 10187, 10175, 10123, 10068, 10166, 10186, 10092, 10185, 10211, 10217, 10262, 10263, 10256, 10347, 10367, 10450, 10575, 10661, 10545, 10690, 10761, 10874, 10827, 11014, 10851,
10073, 10198, 10197, 10169, 10131, 10078, 10160, 10185, 10111, 10188, 10210, 10220, 10249, 10271, 10223, 10359, 10394, 10473, 10582, 10670, 10559, 10716, 10801, 10922, 10865, 11075, 10886,
10062, 10182, 10192, 10170, 10129, 10050, 10133, 10174, 10113, 10165, 10198, 10223, 10233, 10265, 10225, 10369, 10384, 10455, 10580, 10676, 10570, 10722, 10823, 10941, 10868, 11107, 10921,
10111, 10233, 10244, 10226, 10176, 10094, 10157, 10215, 10152, 10217, 10249, 10260, 10275, 10275, 10265, 10395, 10412, 10487, 10600, 10712, 10622, 10725, 10847, 10985, 10916, 11124, 10962,
10099, 10215, 10228, 10187, 10149, 10084, 10121, 10197, 10120, 10195, 10204, 10235, 10266, 10239, 10260, 10375, 10388, 10449, 10585, 10689, 10577, 10696, 10826, 10980, 10919, 11090, 10949,
10138, 10256, 10246, 10205, 10164, 10100, 10139, 10217, 10121, 10189, 10211, 10244, 10276, 10277, 10273, 10383, 10388, 10470, 10588, 10691, 10598, 10721, 10844, 10979, 10945, 11092, 10949,
10115, 10241, 10223, 10196, 10137, 10092, 10120, 10189, 10112, 10139, 10205, 10222, 10250, 10244, 10229, 10345, 10385, 10448, 10540, 10673, 10581, 10687, 10819, 10946, 10940, 11078, 10931,
10190, 10310, 10303, 10281, 10222, 10163, 10182, 10219, 10181, 10194, 10277, 10292, 10322, 10323, 10289, 10397, 10413, 10482, 10582, 10725, 10611, 10721, 10871, 10986, 10954, 11119, 10982,
10220, 10293, 10310, 10262, 10220, 10145, 10181, 10219, 10166, 10202, 10277, 10289, 10333, 10308, 10290, 10413, 10410, 10476, 10571, 10691, 10597, 10692, 10858, 10967, 10931, 11081, 10955,
10216, 10316, 10313, 10279, 10222, 10138, 10193, 10229, 10195, 10230, 10288, 10294, 10329, 10314, 10294, 10432, 10421, 10486, 10593, 10715, 10579, 10693, 10874, 10964, 10930, 11058, 10940,
10170, 10283, 10269, 10247, 10198, 10133, 10166, 10200, 10162, 10208, 10244, 10256, 10283, 10289, 10256, 10382, 10367, 10444, 10530, 10679, 10535, 10626, 10814, 10910, 10865, 10979, 10841,
10233, 10357, 10353, 10319, 10279, 10202, 10244, 10285, 10238, 10274, 10300, 10330, 10361, 10367, 10338, 10465, 10442, 10509, 10607, 10745, 10613, 10695, 10886, 10935, 10895, 11013, 10862,
10309, 10394, 10420, 10388, 10328, 10252, 10300, 10326, 10279, 10301, 10313, 10367, 10374, 10396, 10371, 10493, 10476, 10519, 10655, 10772, 10635, 10738, 10874, 10950, 10929, 11078, 10914,
10277, 10335, 10381, 10343, 10283, 10199, 10270, 10294, 10247, 10284, 10303, 10316, 10332, 10343, 10343, 10453, 10421, 10439, 10585, 10732, 10644, 10755, 10877, 10944, 10886, 11037, 10856,
10270, 10347, 10399, 10361, 10304, 10235, 10302, 10304, 10272, 10299, 10330, 10341, 10363, 10360, 10308, 10416, 10474, 10490, 10613, 10759, 10638, 10771, 10874, 10952, 10889, 11042, 10829,
10377, 10438, 10490, 10442, 10367, 10291, 10343, 10367, 10310, 10352, 10364, 10385, 10420, 10415, 10412, 10535, 10536, 10574, 10697, 10807, 10685, 10838, 10924, 11003, 10942, 11084, 10856,
10433, 10474, 10532, 10481, 10475, 10385, 10423, 10467, 10395, 10451, 10508, 10472, 10512, 10490, 10465, 10577, 10575, 10619, 10725, 10832, 10721, 10883, 10949, 11023, 10964, 11112, 10902,
10514, 10583, 10614, 10573, 10531, 10449, 10489, 10518, 10456, 10495, 10568, 10524, 10525, 10527, 10518, 10631, 10626, 10652, 10742, 10858, 10752, 10914, 10967, 11021, 10994, 11123, 10915,
10562, 10640, 10671, 10630, 10588, 10547, 10550, 10575, 10518, 10566, 10620, 10581, 10598, 10597, 10576, 10688, 10679, 10694, 10799, 10892, 10796, 10948, 11005, 11043, 11003, 11156, 10920,
10767, 10856, 10874, 10836, 10788, 10751, 10743, 10766, 10721, 10743, 10814, 10766, 10791, 10798, 10763, 10904, 10877, 10893, 10986, 11072, 10964, 11105, 11176, 11219, 11157, 11299, 11081,
10591, 10676, 10711, 10657, 10601, 10562, 10560, 10593, 10545, 10586, 10623, 10616, 10632, 10622, 10599, 10729, 10703, 10733, 10793, 10880, 10806, 10925, 10996, 11019, 10976, 11086, 10870,
10750, 10820, 10867, 10812, 10769, 10706, 10724, 10758, 10718, 10759, 10772, 10780, 10782, 10766, 10745, 10874, 10832, 10848, 10935, 10995, 10965, 11063, 11125, 11154, 11077, 11201, 10983,
10916, 10984, 11006, 10985, 10933, 10871, 10882, 10916, 10843, 10904, 10908, 10906, 10922, 10904, 10889, 10990, 11001, 10991, 11075, 11147, 11097, 11196, 11280, 11280, 11208, 11326, 11115,
10896, 10944, 10974, 10961, 10919, 10849, 10835, 10873, 10809, 10843, 10862, 10868, 10867, 10862, 10850, 10940, 10937, 10947, 11005, 11130, 11036, 11145, 11209, 11251, 11172, 11271, 11077,
11074, 11123, 11162, 11130, 11084, 11018, 11009, 11072, 10973, 11006, 11036, 11011, 11042, 11025, 10990, 11120, 11086, 11082, 11157, 11293, 11200, 11295, 11357, 11406, 11294, 11388, 11185,
11115, 11185, 11223, 11180, 11165, 11084, 11111, 11147, 11074, 11099, 11098, 11081, 11114, 11094, 11060, 11171, 11133, 11135, 11237, 11354, 11253, 11342, 11413, 11439, 11336, 11429, 11238,
11228, 11149, 11155, 11135, 11093, 11035, 11060, 11077, 10997, 11002, 10992, 10949, 10935, 10900, 10874, 10963, 10901, 10907, 10993, 11081, 11047, 11114, 11193, 11226, 11121, 11256, 11147,
}

UpperImageLimit = {
18250, 18464, 18499, 18411, 18273, 18184, 18293, 18353, 18260, 18330, 18395, 18445, 18459, 18430, 18379, 18548, 18553, 18628, 18765, 18840, 18670, 18769, 18909, 19089, 18976, 19256, 19045,
18058, 18259, 18313, 18175, 17981, 17861, 17930, 17960, 17873, 17929, 18003, 18158, 18105, 18036, 17993, 18150, 18109, 18123, 18240, 18328, 18184, 18313, 18404, 18561, 18403, 18656, 18371,
17898, 18075, 18138, 17974, 17841, 17658, 17740, 17728, 17661, 17721, 17799, 17978, 17911, 17868, 17835, 17994, 17948, 17940, 18066, 18199, 17975, 18098, 18218, 18354, 18211, 18446, 18174,
17806, 18011, 18061, 17856, 17796, 17593, 17651, 17700, 17601, 17661, 17754, 17913, 17850, 17829, 17835, 17936, 17923, 17948, 18170, 18279, 17983, 18058, 18201, 18346, 18211, 18441, 18228,
17659, 17860, 17888, 17714, 17621, 17475, 17525, 17558, 17500, 17510, 17729, 17770, 17763, 17794, 17728, 17836, 17801, 17871, 18129, 18285, 17908, 17976, 18155, 18333, 18150, 18366, 18138,
17698, 17869, 17879, 17749, 17641, 17486, 17565, 17616, 17525, 17528, 17854, 17790, 17823, 17844, 17783, 17864, 17833, 17873, 18165, 18273, 17915, 18025, 18194, 18370, 18248, 18446, 18228,
17333, 17505, 17539, 17403, 17330, 17189, 17251, 17298, 17219, 17280, 17523, 17483, 17529, 17588, 17474, 17620, 17558, 17605, 17949, 18004, 17730, 17820, 17979, 18166, 18031, 18301, 18031,
17206, 17383, 17365, 17265, 17206, 17049, 17169, 17200, 17081, 17208, 17373, 17341, 17424, 17454, 17333, 17495, 17445, 17599, 17891, 17926, 17700, 17810, 18020, 18130, 17979, 18264, 18015,
17520, 17671, 17639, 17561, 17500, 17318, 17486, 17531, 17409, 17519, 17591, 17673, 17760, 17768, 17660, 17789, 17743, 17878, 18084, 18203, 18003, 18149, 18364, 18490, 18291, 18660, 18389,
17404, 17501, 17525, 17423, 17369, 17210, 17410, 17431, 17311, 17450, 17576, 17546, 17628, 17649, 17529, 17686, 17635, 17799, 17963, 18120, 17918, 18061, 18256, 18396, 18201, 18616, 18286,
17108, 17230, 17278, 17196, 17128, 16970, 17180, 17203, 17074, 17273, 17330, 17318, 17465, 17413, 17304, 17484, 17495, 17601, 17720, 17938, 17695, 17861, 18075, 18170, 18079, 18418, 18145,
17015, 17181, 17220, 17180, 17051, 16933, 17091, 17150, 17005, 17211, 17296, 17286, 17405, 17386, 17296, 17470, 17450, 17548, 17723, 17948, 17705, 17885, 18099, 18225, 18138, 18476, 18191,
16895, 17038, 17089, 17051, 16929, 16814, 16951, 17018, 16898, 17088, 17174, 17158, 17273, 17201, 17146, 17334, 17314, 17444, 17578, 17815, 17603, 17750, 17964, 18108, 18016, 18308, 18045,
16856, 17018, 17029, 17016, 16915, 16844, 16994, 17039, 16876, 17051, 17136, 17163, 17229, 17200, 17134, 17346, 17328, 17448, 17604, 17798, 17600, 17779, 17971, 18096, 18065, 18354, 18080,
16840, 17011, 17050, 17015, 16916, 16813, 16990, 17039, 16870, 17035, 17075, 17099, 17136, 17140, 17159, 17310, 17320, 17446, 17663, 17800, 17606, 17789, 17960, 18129, 18074, 18348, 18096,
16803, 16960, 16979, 16959, 16871, 16780, 16944, 16976, 16820, 16975, 17018, 17029, 17104, 17105, 17094, 17245, 17279, 17416, 17625, 17768, 17575, 17816, 17935, 18124, 18045, 18356, 18085,
16788, 16996, 16995, 16949, 16885, 16796, 16934, 16975, 16851, 16980, 17016, 17034, 17081, 17118, 17038, 17265, 17323, 17455, 17636, 17783, 17598, 17860, 18001, 18204, 18109, 18459, 18143,
16770, 16970, 16986, 16950, 16881, 16750, 16889, 16956, 16855, 16941, 16996, 17039, 17055, 17108, 17041, 17281, 17306, 17425, 17634, 17793, 17616, 17870, 18038, 18235, 18114, 18511, 18201,
16851, 17055, 17073, 17044, 16960, 16823, 16929, 17025, 16920, 17028, 17081, 17100, 17125, 17125, 17109, 17325, 17353, 17478, 17666, 17853, 17703, 17875, 18078, 18309, 18194, 18540, 18270,
16831, 17025, 17046, 16978, 16915, 16806, 16869, 16995, 16866, 16991, 17006, 17058, 17110, 17065, 17100, 17291, 17314, 17415, 17641, 17815, 17629, 17826, 18044, 18300, 18198, 18483, 18249,
16896, 17093, 17076, 17008, 16940, 16833, 16899, 17029, 16869, 16981, 17019, 17073, 17126, 17129, 17121, 17305, 17313, 17450, 17646, 17819, 17663, 17868, 18074, 18299, 18241, 18486, 18249,
16859, 17069, 17038, 16993, 16895, 16820, 16866, 16981, 16854, 16898, 17008, 17036, 17084, 17074, 17048, 17241, 17308, 17414, 17566, 17788, 17635, 17811, 18031, 18243, 18233, 18464, 18219,
16984, 17184, 17171, 17135, 17036, 16938, 16970, 17031, 16968, 16990, 17129, 17154, 17203, 17205, 17148, 17329, 17355, 17470, 17636, 17875, 17685, 17869, 18118, 18310, 18256, 18531, 18304,
17033, 17155, 17184, 17104, 17033, 16908, 16968, 17031, 16943, 17003, 17128, 17148, 17221, 17180, 17150, 17355, 17350, 17460, 17618, 17818, 17661, 17820, 18096, 18278, 18219, 18469, 18259,
17026, 17193, 17188, 17131, 17036, 16896, 16988, 17048, 16991, 17050, 17146, 17156, 17215, 17190, 17156, 17386, 17369, 17476, 17655, 17858, 17631, 17821, 18124, 18274, 18216, 18430, 18234,
16950, 17138, 17115, 17079, 16996, 16888, 16944, 17000, 16936, 17014, 17074, 17094, 17139, 17148, 17094, 17304, 17279, 17406, 17550, 17798, 17559, 17710, 18024, 18184, 18109, 18299, 18068,
17055, 17261, 17255, 17198, 17131, 17003, 17073, 17141, 17064, 17123, 17166, 17216, 17268, 17279, 17230, 17441, 17404, 17515, 17678, 17908, 17689, 17825, 18144, 18225, 18159, 18355, 18104,
17181, 17323, 17366, 17314, 17214, 17086, 17166, 17210, 17131, 17169, 17189, 17278, 17290, 17326, 17285, 17489, 17460, 17531, 17758, 17953, 17725, 17896, 18124, 18250, 18215, 18463, 18190,
17128, 17225, 17301, 17238, 17138, 16999, 17116, 17156, 17078, 17140, 17171, 17194, 17220, 17239, 17239, 17421, 17368, 17398, 17641, 17886, 17740, 17925, 18129, 18240, 18143, 18395, 18094,
17116, 17245, 17331, 17268, 17173, 17058, 17170, 17174, 17120, 17165, 17216, 17235, 17271, 17266, 17180, 17360, 17456, 17483, 17688, 17931, 17730, 17951, 18123, 18254, 18148, 18404, 18049,
17295, 17396, 17484, 17404, 17278, 17151, 17238, 17278, 17184, 17254, 17273, 17309, 17366, 17358, 17354, 17559, 17560, 17624, 17828, 18011, 17809, 18063, 18206, 18339, 18236, 18473, 18094,
17389, 17456, 17553, 17468, 17458, 17308, 17371, 17445, 17325, 17418, 17513, 17453, 17520, 17483, 17441, 17629, 17625, 17698, 17875, 18053, 17869, 18139, 18248, 18371, 18274, 18520, 18170,
17524, 17639, 17690, 17621, 17551, 17415, 17481, 17530, 17426, 17491, 17614, 17540, 17541, 17545, 17530, 17719, 17710, 17753, 17904, 18096, 17920, 18190, 18278, 18369, 18323, 18539, 18191,
17603, 17733, 17785, 17716, 17646, 17579, 17584, 17625, 17530, 17610, 17700, 17635, 17663, 17661, 17626, 17814, 17798, 17824, 17998, 18153, 17993, 18246, 18341, 18405, 18338, 18593, 18200,
17945, 18093, 18124, 18060, 17980, 17918, 17905, 17943, 17868, 17905, 18023, 17943, 17985, 17996, 17939, 18173, 18128, 18155, 18310, 18454, 18273, 18508, 18626, 18699, 18595, 18831, 18468,
17651, 17793, 17851, 17761, 17668, 17603, 17600, 17655, 17575, 17644, 17705, 17694, 17720, 17704, 17665, 17881, 17839, 17888, 17989, 18134, 18010, 18209, 18326, 18365, 18294, 18476, 18116,
17916, 18034, 18111, 18020, 17949, 17844, 17873, 17930, 17864, 17931, 17953, 17966, 17970, 17944, 17908, 18123, 18054, 18080, 18225, 18325, 18275, 18439, 18541, 18590, 18461, 18669, 18305,
18193, 18306, 18343, 18308, 18221, 18119, 18136, 18194, 18071, 18174, 18180, 18176, 18204, 18173, 18148, 18316, 18335, 18319, 18459, 18578, 18495, 18660, 18800, 18800, 18680, 18876, 18525,
18160, 18240, 18290, 18269, 18199, 18081, 18059, 18121, 18015, 18071, 18104, 18113, 18111, 18103, 18083, 18233, 18229, 18245, 18341, 18550, 18394, 18575, 18681, 18751, 18620, 18785, 18461,
18456, 18538, 18604, 18550, 18473, 18364, 18348, 18453, 18288, 18344, 18393, 18351, 18403, 18375, 18316, 18533, 18476, 18470, 18595, 18821, 18666, 18825, 18928, 19010, 18823, 18980, 18641,
18525, 18641, 18705, 18633, 18609, 18474, 18518, 18578, 18456, 18498, 18496, 18469, 18524, 18490, 18433, 18619, 18555, 18558, 18729, 18924, 18755, 18903, 19021, 19065, 18893, 19048, 18730,
18714, 18581, 18591, 18559, 18488, 18391, 18433, 18461, 18328, 18336, 18320, 18248, 18225, 18166, 18124, 18271, 18169, 18179, 18321, 18469, 18411, 18524, 18655, 18710, 18535, 18760, 18579,
}
