00000000000000000000000000000011*2 => 00000000000000000000000000001001 => 000000000000000000000000000010 + 01 (3**2 => 9 => 2 + 1)
00000000000000000000000000000110*2 => 00000000000000000000000000100100 => 0000000000000000000000000010 + 0100 (6**2 => 36 => 2 + 4)
00000000000000000000000000000111*2 => 00000000000000000000000000110001 => 00000000000000000000000000110 + 001 (7**2 => 49 => 6 + 1)
00000000000000000000000000001010*2 => 00000000000000000000000001100100 => 0000000000000000000000000110 + 0100 (10**2 => 100 => 6 + 4)
00000000000000000000000000001111*2 => 00000000000000000000000011100001 => 0000000000000000000000001110 + 0001 (15**2 => 225 => 14 + 1)
00000000000000000000000000011100*2 => 00000000000000000000001100010000 => 00000000000000000000001100 + 010000 (28**2 => 784 => 12 + 16)
00000000000000000000000000011111*2 => 00000000000000000000001111000001 => 000000000000000000000011110 + 00001 (31**2 => 961 => 30 + 1)
00000000000000000000000000100100*2 => 00000000000000000000010100010000 => 00000000000000000000010100 + 010000 (36**2 => 1296 => 20 + 16)
00000000000000000000000000110011*2 => 00000000000000000000101000101001 => 000000000000000000001010 + 00101001 (51**2 => 2601 => 10 + 41)
00000000000000000000000000111111*2 => 00000000000000000000111110000001 => 00000000000000000000111110 + 000001 (63**2 => 3969 => 62 + 1)
00000000000000000000000001010101*2 => 00000000000000000001110000111001 => 000000000000000000011100 + 00111001 (85**2 => 7225 => 28 + 57)
00000000000000000000000001011011*2 => 00000000000000000010000001011001 => 00000000000000000010 + 000001011001 (91**2 => 8281 => 2 + 89)
00000000000000000000000001111000*2 => 00000000000000000011100001000000 => 000000000000000000111000 + 01000000 (120**2 => 14400 => 56 + 64)
00000000000000000000000001111111*2 => 00000000000000000011111100000001 => 0000000000000000001111110 + 0000001 (127**2 => 16129 => 126 + 1)
00000000000000000000000010001000*2 => 00000000000000000100100001000000 => 000000000000000001001000 + 01000000 (136**2 => 18496 => 72 + 64)
00000000000000000000000010010011*2 => 00000000000000000101010001101001 => 00000000000000000101010 + 001101001 (147**2 => 21609 => 42 + 105)
00000000000000000000000010101011*2 => 00000000000000000111001000111001 => 000000000000000001110010 + 00111001 (171**2 => 29241 => 114 + 57)
00000000000000000000000010111011*2 => 00000000000000001000100010011001 => 0000000000000000100010 + 0010011001 (187**2 => 34969 => 34 + 153)
00000000000000000000000011001101*2 => 00000000000000001010010000101001 => 000000000000000010100100 + 00101001 (205**2 => 42025 => 164 + 41)
00000000000000000000000011111111*2 => 00000000000000001111111000000001 => 000000000000000011111110 + 00000001 (255**2 => 65025 => 254 + 1)
00000000000000000000000101010110*2 => 00000000000000011100100011100100 => 0000000000000001110010 + 0011100100 (342**2 => 116964 => 114 + 228)
00000000000000000000000101011111*2 => 00000000000000011110000101000001 => 00000000000000011110 + 000101000001 (351**2 => 123201 => 30 + 321)
00000000000000000000000101101101*2 => 00000000000000100000100001101001 => 00000000000000100000100 + 001101001 (365**2 => 133225 => 260 + 105)
00000000000000000000000111110000*2 => 00000000000000111100000100000000 => 0000000000000011110000 + 0100000000 (496**2 => 246016 => 240 + 256)
00000000000000000000000111111111*2 => 00000000000000111111110000000001 => 00000000000000111111110 + 000000001 (511**2 => 261121 => 510 + 1)
00000000000000000000001000010000*2 => 00000000000001000100000100000000 => 0000000000000100010000 + 0100000000 (528**2 => 278784 => 272 + 256)
00000000000000000000001010101010*2 => 00000000000001110001100011100100 => 0000000000000111000110 + 0011100100 (682**2 => 465124 => 454 + 228)
00000000000000000000001011001001*2 => 00000000000001111100000111010001 => 000000000000011111000 + 00111010001 (713**2 => 508369 => 248 + 465)
00000000000000000000001100110100*2 => 00000000000010100100001010010000 => 00000000000010100100 + 001010010000 (820**2 => 672400 => 164 + 656)
00000000000000000000001101000101*2 => 00000000000010101011000010011001 => 0000000000001010101100 + 0010011001 (837**2 => 700569 => 684 + 153)
00000000000000000000001110001110*2 => 00000000000011001010001011000100 => 00000000000011001010 + 001011000100 (910**2 => 828100 => 202 + 708)
00000000000000000000001111111111*2 => 00000000000011111111100000000001 => 0000000000001111111110 + 0000000001 (1023**2 => 1046529 => 1022 + 1)
00000000000000000000010010010010*2 => 00000000000101001110001101000100 => 00000000000101001110 + 001101000100 (1170**2 => 1368900 => 334 + 836)
00000000000000000000010011101101*2 => 00000000000110000100001101101001 => 00000000000110000100 + 001101101001 (1261**2 => 1590121 => 388 + 873)
00000000000000000000010100110111*2 => 00000000000110110011000111010001 => 000000000001101100110 + 00111010001 (1335**2 => 1782225 => 870 + 465)
00000000000000000000011111100000*2 => 00000000001111100000010000000000 => 00000000001111100000 + 010000000000 (2016**2 => 4064256 => 992 + 1024)
00000000000000000000011111111111*2 => 00000000001111111111000000000001 => 000000000011111111110 + 00000000001 (2047**2 => 4190209 => 2046 + 1)
00000000000000000000100000100000*2 => 00000000010000100000010000000000 => 00000000010000100000 + 010000000000 (2080**2 => 4326400 => 1056 + 1024)
00000000000000000000101001101011*2 => 00000000011011001000100010111001 => 000000000110110010 + 00100010111001 (2667**2 => 7112889 => 434 + 2233)
00000000000000000000101100010011*2 => 00000000011110101010001101101001 => 00000000011110101010 + 001101101001 (2835**2 => 8037225 => 1962 + 873)
00000000000000000000101101101110*2 => 00000000100000101010001101000100 => 00000000100000101010 + 001101000100 (2926**2 => 8561476 => 2090 + 836)
00000000000000000000110001110010*2 => 00000000100110101110001011000100 => 00000000100110101110 + 001011000100 (3186**2 => 10150596 => 2478 + 708)
00000000000000000000110011001100*2 => 00000000101000111100001010010000 => 00000000101000111100 + 001010010000 (3276**2 => 10732176 => 2620 + 656)
00000000000000000000110110010001*2 => 00000000101110000000110000100001 => 00000000101110000 + 000110000100001 (3473**2 => 12061729 => 368 + 3105)
00000000000000000000111010100001*2 => 00000000110101100000000101000001 => 00000000110101100000 + 000101000001 (3745**2 => 14025025 => 3424 + 321)
00000000000000000000111110100101*2 => 00000000111101001100000001011001 => 00000000111101001100 + 000001011001 (4005**2 => 16040025 => 3916 + 89)
00000000000000000000111111111111*2 => 00000000111111111110000000000001 => 00000000111111111110 + 000000000001 (4095**2 => 16769025 => 4094 + 1)
00000000000000000001010101010101*2 => 00000001110001110000111000111001 => 000000011100011100 + 00111000111001 (5461**2 => 29822521 => 1820 + 3641)
00000000000000000001100100011010*2 => 00000010011101100001011010100100 => 0000001001110110 + 0001011010100100 (6426**2 => 41293476 => 630 + 5796)
00000000000000000001111111000000*2 => 00000011111100000001000000000000 => 000000111111000000 + 01000000000000 (8128**2 => 66064384 => 4032 + 4096)
00000000000000000001111111111111*2 => 00000011111111111100000000000001 => 0000001111111111110 + 0000000000001 (8191**2 => 67092481 => 8190 + 1)
00000000000000000010000001000000*2 => 00000100000100000001000000000000 => 000001000001000000 + 01000000000000 (8256**2 => 68161536 => 4160 + 4096)
00000000000000000010100101001011*2 => 00000110101010010001101111111001 => 00000110101010010 + 001101111111001 (10571**2 => 111746041 => 3410 + 7161)
00000000000000000010101000101011*2 => 00000110111100100010001100111001 => 0000011011110010 + 0010001100111001 (10795**2 => 116532025 => 1778 + 9017)
00000000000000000010101010101011*2 => 00000111000111001000111000111001 => 000001110001110010 + 00111000111001 (10923**2 => 119311929 => 7282 + 3641)
00000000000000000011010110010101*2 => 00001011001101110000100010111001 => 000010110011011100 + 00100010111001 (13717**2 => 188156089 => 11484 + 2233)
00000000000000000011011011011011*2 => 00001011110000010001111101011001 => 00001011110000010 + 001111101011001 (14043**2 => 197205849 => 6018 + 8025)
00000000000000000011110000111100*2 => 00001110001011000010111000010000 => 0000111000101100 + 0010111000010000 (15420**2 => 237776400 => 3628 + 11792)
00000000000000000011111111111111*2 => 00001111111111111000000000000001 => 000011111111111110 + 00000000000001 (16383**2 => 268402689 => 16382 + 1)
00000000000000000100010001000100*2 => 00010010001101000011001000010000 => 0001001000110100 + 0011001000010000 (17476**2 => 305410576 => 4660 + 12816)
00000000000000000100100100100101*2 => 00010100111001100001111101011001 => 00010100111001100 + 001111101011001 (18725**2 => 350625625 => 10700 + 8025)
00000000000000000101010101010110*2 => 00011100011100100011100011100100 => 0001110001110010 + 0011100011100100 (21846**2 => 477247716 => 7282 + 14564)
00000000000000000101011010110101*2 => 00011101010111100001101111111001 => 00011101010111100 + 001101111111001 (22197**2 => 492706809 => 15036 + 7161)
00000000000000000110011001100111*2 => 00101000111101100011110101110001 => 0010100011110110 + 0011110101110001 (26215**2 => 687226225 => 10486 + 15729)
00000000000000000111001001101111*2 => 00110011001001110000110000100001 => 00110011001001110 + 000110000100001 (29295**2 => 858197025 => 26190 + 3105)
00000000000000000111111110000000*2 => 00111111100000000100000000000000 => 0011111110000000 + 0100000000000000 (32640**2 => 1065369600 => 16256 + 16384)
00000000000000000111111111111111*2 => 00111111111111110000000000000001 => 00111111111111110 + 000000000000001 (32767**2 => 1073676289 => 32766 + 1)
00000000000000001000000010000000*2 => 01000000100000000100000000000000 => 0100000010000000 + 0100000000000000 (32896**2 => 1082146816 => 16512 + 16384)
00000000000000001001001001001010*2 => 01010011100110000111110101100100 => 01010011100110 + 000111110101100100 (37450**2 => 1402502500 => 5350 + 32100)
00000000000000001001100110011001*2 => 01011100001010000011110101110001 => 0101110000101000 + 0011110101110001 (39321**2 => 1546141041 => 23592 + 15729)
00000000000000001010101010101010*2 => 01110001110001100011100011100100 => 0111000111000110 + 0011100011100100 (43690**2 => 1908816100 => 29126 + 14564)
00000000000000001011101110111100*2 => 10001001101011000011001000010000 => 1000100110101100 + 0011001000010000 (48060**2 => 2309763600 => 35244 + 12816)
00000000000000001011110110100010*2 => 10001100011110001001101010000100 => 10001100011110 + 001001101010000100 (48546**2 => 2356714116 => 8990 + 39556)
00000000000000001100001111000100*2 => 10010101101101000010111000010000 => 1001010110110100 + 0010111000010000 (50116**2 => 2511613456 => 38324 + 11792)
00000000000000001101010111010101*2 => 10110010100111000010001100111001 => 1011001010011100 + 0010001100111001 (54741**2 => 2996577081 => 45724 + 9017)
00000000000000001110011011100110*2 => 11010000010000100001011010100100 => 1101000001000010 + 0001011010100100 (59110**2 => 3493992100 => 53314 + 5796)
00000000000000001111111111111111*2 => 11111111111111100000000000000001 => 1111111111111110 + 0000000000000001 (65535**2 => 4294836225 => 65534 + 1)
00000000000000010000000000000001*2 => 00000000000000100000000000000001 => 0000000000000010000000000000000 + 1 (65537**2 => 4295098369 => 65536 + 1)
00000000000000010000000100000000*2 => 00000010000000010000000000000000 => 000000100000000 + 10000000000000000 (65792**2 => 4328587264 => 256 + 65536)
00000000000000011000100111100000*2 => 01011110000000011000010000000000 => 010111100000 + 00011000010000000000 (100832**2 => 10167092224 => 1504 + 99328)
00000000000000011011010010110010*2 => 11101000111011101100101111000100 => 1110100011101110 + 1100101111000100 (111794**2 => 12497898436 => 59630 + 52164)
00000000000000011111111111111001*2 => 11111111111001000000000000110001 => 11111111111001000 + 000000000110001 (131065**2 => 17178034225 => 131016 + 49)
00000000000000100000000000000001*2 => 00000000000001000000000000000001 => 0000000000000100000000000000000 + 1 (131073**2 => 17180131329 => 131072 + 1)
00000000000000100000111111000000*2 => 00111111111110000001000000000000 => 0011111111111000000 + 1000000000000 (135104**2 => 18253090816 => 131008 + 4096)
00000000000000100001000000100000*2 => 01000001100001000000010000000000 => 0100000110000100000 + 0010000000000 (135200**2 => 18279040000 => 134176 + 1024)
00000000000000100011111110000100*2 => 00001101110100100011110000010000 => 00001101110100 + 100011110000010000 (147332**2 => 21706718224 => 884 + 146448)
00000000000000100100010001100100*2 => 00100011110101010100011100010000 => 00100011110101010100 + 011100010000 (148580**2 => 22076016400 => 146772 + 1808)
00000000000000100100010001111001*2 => 00100100001101001000000100110001 => 00100100001101001000 + 000100110001 (148601**2 => 22082257201 => 148296 + 305)
00000000000000100101010101010110*2 => 01110001110010100011100011100100 => 01110001110010 + 100011100011100100 (152918**2 => 23383914724 => 7282 + 145636)
00000000000000100101110101110101*2 => 10010111111100100011011101111001 => 10010111111100 + 100011011101111001 (154997**2 => 24024070009 => 9724 + 145273)
00000000000000100111000001000111*2 => 11110010010110100011001110110001 => 11110010010110 + 100011001110110001 (159815**2 => 25540834225 => 15510 + 144305)
00000000000000110000000000000001*2 => 00000000000001100000000000000001 => 0000000000000110000000000000000 + 1 (196609**2 => 38655098881 => 196608 + 1)
00000000000000110111100101000010*2 => 00010000111110110111010100000100 => 00010000111110 + 110111010100000100 (227650**2 => 51824522500 => 1086 + 226564)
00000000000000110111101101000011*2 => 00011110111010110111001110001001 => 00011110111010 + 110111001110001001 (228163**2 => 52058354569 => 1978 + 226185)
00000000000000111111111111100001*2 => 11111111000010000000001111000001 => 111111110000100000 + 00001111000001 (262113**2 => 68703224769 => 261152 + 961)
00000000000001000000000000000001*2 => 00000000000010000000000000000001 => 0000000000001000000000000000000 + 1 (262145**2 => 68720001025 => 262144 + 1)
00000000000001000000001000000000*2 => 00010000000001000000000000000000 => 0001000000000 + 1000000000000000000 (262656**2 => 68988174336 => 512 + 262144)
00000000000001010000000000000001*2 => 00000000000010100000000000000001 => 0000000000001010000000000000000 + 1 (327681**2 => 107374837761 => 327680 + 1)
00000000000001100000000000000001*2 => 00000000000011000000000000000001 => 0000000000001100000000000000000 + 1 (393217**2 => 154619609089 => 393216 + 1)
00000000000001100000110001101001*2 => 10010101100001100000001100010001 => 100101011000 + 01100000001100010001 (396393**2 => 157127410449 => 2392 + 394001)
00000000000001101000101000100000*2 => 11000100000001101000010000000000 => 11000100000 + 001101000010000000000 (428576**2 => 183677387776 => 1568 + 427008)
00000000000001110000000000000001*2 => 00000000000011100000000000000001 => 0000000000001110000000000000000 + 1 (458753**2 => 210454315009 => 458752 + 1)
00000000000001110001000000010000*2 => 11100001111000100000000100000000 => 1110000111100010000 + 0000100000000 (462864**2 => 214243082496 => 462608 + 256)
00000000000001110110001111111010*2 => 10011110101101110101000000100100 => 1001111010110 + 1110101000000100100 (484346**2 => 234591047716 => 5078 + 479268)
00000000000010000000000000000001*2 => 00000000000100000000000000000001 => 0000000000010000000000000000000 + 1 (524289**2 => 274878955521 => 524288 + 1)
00000000000010010000000000000001*2 => 00000000000100100000000000000001 => 0000000000010010000000000000000 + 1 (589825**2 => 347893530625 => 589824 + 1)
00000000000010100000000000000001*2 => 00000000000101000000000000000001 => 0000000000010100000000000000000 + 1 (655361**2 => 429498040321 => 655360 + 1)
00000000000010110000000000000001*2 => 00000000000101100000000000000001 => 0000000000010110000000000000000 + 1 (720897**2 => 519692484609 => 720896 + 1)
00000000000011000000000000000001*2 => 00000000000110000000000000000001 => 0000000000011000000000000000000 + 1 (786433**2 => 618476863489 => 786432 + 1)