static final int[] NUMBER_OF_ADDITIONAL_DIGITS_AFTER_LEFT_SHIFT = {

0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817,

0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067,

0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF,

0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0,

0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA,

0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC,

0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C,

0x051C, 0x051C

};

static final byte[] POWER_OF_FIVE_DIGITS = {

5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5,

3, 9, 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8,

2, 8, 1, 2, 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2,

5, 6, 1, 0, 3, 5, 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1,

5, 2, 5, 8, 7, 8, 9, 0, 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5,

3, 8, 1, 4, 6, 9, 7, 2, 6, 5, 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2,

8, 1, 2, 5, 9, 5, 3, 6, 7, 4, 3, 1, 6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3,

7, 1, 5, 8, 2, 0, 3, 1, 2, 5, 2, 3, 8, 4, 1, 8, 5, 7, 9, 1, 0, 1, 5,

6, 2, 5, 1, 1, 9, 2, 0, 9, 2, 8, 9, 5, 5, 0, 7, 8, 1, 2, 5, 5, 9, 6,

0, 4, 6, 4, 4, 7, 7, 5, 3, 9, 0, 6, 2, 5, 2, 9, 8, 0, 2, 3, 2, 2, 3,

8, 7, 6, 9, 5, 3, 1, 2, 5, 1, 4, 9, 0, 1, 1, 6, 1, 1, 9, 3, 8, 4, 7,

6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8, 0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1, 2,

5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4, 6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8,

6, 2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5, 7, 0, 3, 1, 2, 5, 9, 3, 1, 3,

2, 2, 5, 7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5, 6, 2, 5, 4, 6, 5, 6, 6, 1,

2, 8, 7, 3, 0, 7, 7, 3, 9, 2, 5, 7, 8, 1, 2, 5, 2, 3, 2, 8, 3, 0, 6,

4, 3, 6, 5, 3, 8, 6, 9, 6, 2, 8, 9, 0, 6, 2, 5, 1, 1, 6, 4, 1, 5, 3,

2, 1, 8, 2, 6, 9, 3, 4, 8, 1, 4, 4, 5, 3, 1, 2, 5, 5, 8, 2, 0, 7, 6,

6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7, 2, 2, 6, 5, 6, 2, 5, 2, 9, 1, 0, 3,

8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6, 1, 3, 2, 8, 1, 2, 5, 1, 4, 5,

5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8, 0, 6, 6, 4, 0, 6, 2, 5,

7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9, 0, 3, 3, 2, 0, 3,

1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2, 9, 5, 1, 6,

6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8, 5, 6,

4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7,

2, 9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7,

3, 5, 0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5,

2, 2, 7, 3, 7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5,

9, 7, 6, 5, 6, 2, 5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0,

2, 9, 7, 3, 9, 3, 7, 9, 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8,

8, 6, 0, 8, 0, 8, 0, 1, 4, 8, 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5,

2, 8, 4, 2, 1, 7, 0, 9, 4, 3, 0, 4, 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4,

9, 7, 0, 7, 0, 3, 1, 2, 5, 1, 4, 2, 1, 0, 8, 5, 4, 7, 1, 5, 2, 0, 2,

0, 0, 3, 7, 1, 7, 4, 2, 2, 4, 8, 5, 3, 5, 1, 5, 6, 2, 5, 7, 1, 0, 5,

4, 2, 7, 3, 5, 7, 6, 0, 1, 0, 0, 1, 8, 5, 8, 7, 1, 1, 2, 4, 2, 6, 7,

5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7, 1, 3, 6, 7, 8, 8, 0, 0, 5, 0, 0, 9,

2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8, 9, 0, 6, 2, 5, 1, 7, 7, 6, 3, 5,

6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4, 6, 7, 7, 8, 1, 0, 6, 6, 8, 9,

4, 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1, 9, 7, 0, 0, 1, 2, 5, 2, 3,

2, 3, 3, 8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5, 6, 2, 5, 4, 4, 4, 0, 8,

9, 2, 0, 9, 8, 5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9, 4, 5, 2, 6, 6, 7, 2,

3, 6, 3, 2, 8, 1, 2, 5, 2, 2, 2, 0, 4, 4, 6, 0, 4, 9, 2, 5, 0, 3, 1,

3, 0, 8, 0, 8, 4, 7, 2, 6, 3, 3, 3, 6, 1, 8, 1, 6, 4, 0, 6, 2, 5, 1,

1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2, 5, 1, 5, 6, 5, 4, 0, 4, 2, 3, 6, 3,

1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2, 5, 5, 5, 5, 1, 1, 1, 5, 1, 2,

3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5, 8, 3, 4, 0, 4, 5, 4, 1,

0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5, 6, 2, 8, 9, 1, 3,

5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8, 1, 2, 5, 1,

3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9, 5, 3,

9, 5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3,

9, 0, 3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6,

7, 6, 2, 6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3,

6, 1, 4, 1, 8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7,

6, 5, 6, 2, 5, 1, 7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9,

4, 4, 1, 1, 9, 2, 4, 4, 8, 1, 3, 9, 1, 9, 0, 6, 7, 3, 8, 2, 8, 1, 2,

5, 8, 6, 7, 3, 6, 1, 7, 3, 7, 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9,

6, 2, 2, 4, 0, 6, 9, 5, 9, 5, 3, 3, 6, 9, 1, 4, 0, 6, 2, 5

};

static final int MIN_POWER_OF_FIVE = -342;

static final long[] POWERS_OF_FIVE = {

0xeef453d6923bd65aL, 0x113faa2906a13b3fL,

0x9558b4661b6565f8L, 0x4ac7ca59a424c507L,

0xbaaee17fa23ebf76L, 0x5d79bcf00d2df649L,

0xe95a99df8ace6f53L, 0xf4d82c2c107973dcL,

0x91d8a02bb6c10594L, 0x79071b9b8a4be869L,

0xb64ec836a47146f9L, 0x9748e2826cdee284L,

0xe3e27a444d8d98b7L, 0xfd1b1b2308169b25L,

0x8e6d8c6ab0787f72L, 0xfe30f0f5e50e20f7L,

0xb208ef855c969f4fL, 0xbdbd2d335e51a935L,

0xde8b2b66b3bc4723L, 0xad2c788035e61382L,

0x8b16fb203055ac76L, 0x4c3bcb5021afcc31L,

0xaddcb9e83c6b1793L, 0xdf4abe242a1bbf3dL,

0xd953e8624b85dd78L, 0xd71d6dad34a2af0dL,

0x87d4713d6f33aa6bL, 0x8672648c40e5ad68L,

0xa9c98d8ccb009506L, 0x680efdaf511f18c2L,

0xd43bf0effdc0ba48L, 0x212bd1b2566def2L,

0x84a57695fe98746dL, 0x14bb630f7604b57L,

0xa5ced43b7e3e9188L, 0x419ea3bd35385e2dL,

0xcf42894a5dce35eaL, 0x52064cac828675b9L,

0x818995ce7aa0e1b2L, 0x7343efebd1940993L,

0xa1ebfb4219491a1fL, 0x1014ebe6c5f90bf8L,

0xca66fa129f9b60a6L, 0xd41a26e077774ef6L,

0xfd00b897478238d0L, 0x8920b098955522b4L,

0x9e20735e8cb16382L, 0x55b46e5f5d5535b0L,

0xc5a890362fddbc62L, 0xeb2189f734aa831dL,

0xf712b443bbd52b7bL, 0xa5e9ec7501d523e4L,

0x9a6bb0aa55653b2dL, 0x47b233c92125366eL,

0xc1069cd4eabe89f8L, 0x999ec0bb696e840aL,

0xf148440a256e2c76L, 0xc00670ea43ca250dL,

0x96cd2a865764dbcaL, 0x380406926a5e5728L,

0xbc807527ed3e12bcL, 0xc605083704f5ecf2L,

0xeba09271e88d976bL, 0xf7864a44c633682eL,

0x93445b8731587ea3L, 0x7ab3ee6afbe0211dL,

0xb8157268fdae9e4cL, 0x5960ea05bad82964L,

0xe61acf033d1a45dfL, 0x6fb92487298e33bdL,

0x8fd0c16206306babL, 0xa5d3b6d479f8e056L,

0xb3c4f1ba87bc8696L, 0x8f48a4899877186cL,

0xe0b62e2929aba83cL, 0x331acdabfe94de87L,

0x8c71dcd9ba0b4925L, 0x9ff0c08b7f1d0b14L,

0xaf8e5410288e1b6fL, 0x7ecf0ae5ee44dd9L,

0xdb71e91432b1a24aL, 0xc9e82cd9f69d6150L,

0x892731ac9faf056eL, 0xbe311c083a225cd2L,

0xab70fe17c79ac6caL, 0x6dbd630a48aaf406L,

0xd64d3d9db981787dL, 0x92cbbccdad5b108L,

0x85f0468293f0eb4eL, 0x25bbf56008c58ea5L,

0xa76c582338ed2621L, 0xaf2af2b80af6f24eL,

0xd1476e2c07286faaL, 0x1af5af660db4aee1L,

0x82cca4db847945caL, 0x50d98d9fc890ed4dL,

0xa37fce126597973cL, 0xe50ff107bab528a0L,

0xcc5fc196fefd7d0cL, 0x1e53ed49a96272c8L,

0xff77b1fcbebcdc4fL, 0x25e8e89c13bb0f7aL,

0x9faacf3df73609b1L, 0x77b191618c54e9acL,

0xc795830d75038c1dL, 0xd59df5b9ef6a2417L,

0xf97ae3d0d2446f25L, 0x4b0573286b44ad1dL,

0x9becce62836ac577L, 0x4ee367f9430aec32L,

0xc2e801fb244576d5L, 0x229c41f793cda73fL,

0xf3a20279ed56d48aL, 0x6b43527578c1110fL,

0x9845418c345644d6L, 0x830a13896b78aaa9L,

0xbe5691ef416bd60cL, 0x23cc986bc656d553L,

0xedec366b11c6cb8fL, 0x2cbfbe86b7ec8aa8L,

0x94b3a202eb1c3f39L, 0x7bf7d71432f3d6a9L,

0xb9e08a83a5e34f07L, 0xdaf5ccd93fb0cc53L,

0xe858ad248f5c22c9L, 0xd1b3400f8f9cff68L,

0x91376c36d99995beL, 0x23100809b9c21fa1L,

0xb58547448ffffb2dL, 0xabd40a0c2832a78aL,

0xe2e69915b3fff9f9L, 0x16c90c8f323f516cL,

0x8dd01fad907ffc3bL, 0xae3da7d97f6792e3L,

0xb1442798f49ffb4aL, 0x99cd11cfdf41779cL,

0xdd95317f31c7fa1dL, 0x40405643d711d583L,

0x8a7d3eef7f1cfc52L, 0x482835ea666b2572L,

0xad1c8eab5ee43b66L, 0xda3243650005eecfL,

0xd863b256369d4a40L, 0x90bed43e40076a82L,

0x873e4f75e2224e68L, 0x5a7744a6e804a291L,

0xa90de3535aaae202L, 0x711515d0a205cb36L,

0xd3515c2831559a83L, 0xd5a5b44ca873e03L,

0x8412d9991ed58091L, 0xe858790afe9486c2L,

0xa5178fff668ae0b6L, 0x626e974dbe39a872L,

0xce5d73ff402d98e3L, 0xfb0a3d212dc8128fL,

0x80fa687f881c7f8eL, 0x7ce66634bc9d0b99L,

0xa139029f6a239f72L, 0x1c1fffc1ebc44e80L,

0xc987434744ac874eL, 0xa327ffb266b56220L,

0xfbe9141915d7a922L, 0x4bf1ff9f0062baa8L,

0x9d71ac8fada6c9b5L, 0x6f773fc3603db4a9L,

0xc4ce17b399107c22L, 0xcb550fb4384d21d3L,

0xf6019da07f549b2bL, 0x7e2a53a146606a48L,

0x99c102844f94e0fbL, 0x2eda7444cbfc426dL,

0xc0314325637a1939L, 0xfa911155fefb5308L,

0xf03d93eebc589f88L, 0x793555ab7eba27caL,

0x96267c7535b763b5L, 0x4bc1558b2f3458deL,

0xbbb01b9283253ca2L, 0x9eb1aaedfb016f16L,

0xea9c227723ee8bcbL, 0x465e15a979c1cadcL,

0x92a1958a7675175fL, 0xbfacd89ec191ec9L,

0xb749faed14125d36L, 0xcef980ec671f667bL,

0xe51c79a85916f484L, 0x82b7e12780e7401aL,

0x8f31cc0937ae58d2L, 0xd1b2ecb8b0908810L,

0xb2fe3f0b8599ef07L, 0x861fa7e6dcb4aa15L,

0xdfbdcece67006ac9L, 0x67a791e093e1d49aL,

0x8bd6a141006042bdL, 0xe0c8bb2c5c6d24e0L,

0xaecc49914078536dL, 0x58fae9f773886e18L,

0xda7f5bf590966848L, 0xaf39a475506a899eL,

0x888f99797a5e012dL, 0x6d8406c952429603L,

0xaab37fd7d8f58178L, 0xc8e5087ba6d33b83L,

0xd5605fcdcf32e1d6L, 0xfb1e4a9a90880a64L,

0x855c3be0a17fcd26L, 0x5cf2eea09a55067fL,

0xa6b34ad8c9dfc06fL, 0xf42faa48c0ea481eL,

0xd0601d8efc57b08bL, 0xf13b94daf124da26L,

0x823c12795db6ce57L, 0x76c53d08d6b70858L,

0xa2cb1717b52481edL, 0x54768c4b0c64ca6eL,

0xcb7ddcdda26da268L, 0xa9942f5dcf7dfd09L,

0xfe5d54150b090b02L, 0xd3f93b35435d7c4cL,

0x9efa548d26e5a6e1L, 0xc47bc5014a1a6dafL,

0xc6b8e9b0709f109aL, 0x359ab6419ca1091bL,

0xf867241c8cc6d4c0L, 0xc30163d203c94b62L,

0x9b407691d7fc44f8L, 0x79e0de63425dcf1dL,

0xc21094364dfb5636L, 0x985915fc12f542e4L,

0xf294b943e17a2bc4L, 0x3e6f5b7b17b2939dL,

0x979cf3ca6cec5b5aL, 0xa705992ceecf9c42L,

0xbd8430bd08277231L, 0x50c6ff782a838353L,

0xece53cec4a314ebdL, 0xa4f8bf5635246428L,

0x940f4613ae5ed136L, 0x871b7795e136be99L,

0xb913179899f68584L, 0x28e2557b59846e3fL,

0xe757dd7ec07426e5L, 0x331aeada2fe589cfL,

0x9096ea6f3848984fL, 0x3ff0d2c85def7621L,

0xb4bca50b065abe63L, 0xfed077a756b53a9L,

0xe1ebce4dc7f16dfbL, 0xd3e8495912c62894L,

0x8d3360f09cf6e4bdL, 0x64712dd7abbbd95cL,

0xb080392cc4349decL, 0xbd8d794d96aacfb3L,

0xdca04777f541c567L, 0xecf0d7a0fc5583a0L,

0x89e42caaf9491b60L, 0xf41686c49db57244L,

0xac5d37d5b79b6239L, 0x311c2875c522ced5L,

0xd77485cb25823ac7L, 0x7d633293366b828bL,

0x86a8d39ef77164bcL, 0xae5dff9c02033197L,

0xa8530886b54dbdebL, 0xd9f57f830283fdfcL,

0xd267caa862a12d66L, 0xd072df63c324fd7bL,

0x8380dea93da4bc60L, 0x4247cb9e59f71e6dL,

0xa46116538d0deb78L, 0x52d9be85f074e608L,

0xcd795be870516656L, 0x67902e276c921f8bL,

0x806bd9714632dff6L, 0xba1cd8a3db53b6L,

0xa086cfcd97bf97f3L, 0x80e8a40eccd228a4L,

0xc8a883c0fdaf7df0L, 0x6122cd128006b2cdL,

0xfad2a4b13d1b5d6cL, 0x796b805720085f81L,

0x9cc3a6eec6311a63L, 0xcbe3303674053bb0L,

0xc3f490aa77bd60fcL, 0xbedbfc4411068a9cL,

0xf4f1b4d515acb93bL, 0xee92fb5515482d44L,

0x991711052d8bf3c5L, 0x751bdd152d4d1c4aL,

0xbf5cd54678eef0b6L, 0xd262d45a78a0635dL,

0xef340a98172aace4L, 0x86fb897116c87c34L,

0x9580869f0e7aac0eL, 0xd45d35e6ae3d4da0L,

0xbae0a846d2195712L, 0x8974836059cca109L,

0xe998d258869facd7L, 0x2bd1a438703fc94bL,

0x91ff83775423cc06L, 0x7b6306a34627ddcfL,

0xb67f6455292cbf08L, 0x1a3bc84c17b1d542L,

0xe41f3d6a7377eecaL, 0x20caba5f1d9e4a93L,

0x8e938662882af53eL, 0x547eb47b7282ee9cL,

0xb23867fb2a35b28dL, 0xe99e619a4f23aa43L,

0xdec681f9f4c31f31L, 0x6405fa00e2ec94d4L,

0x8b3c113c38f9f37eL, 0xde83bc408dd3dd04L,

0xae0b158b4738705eL, 0x9624ab50b148d445L,

0xd98ddaee19068c76L, 0x3badd624dd9b0957L,

0x87f8a8d4cfa417c9L, 0xe54ca5d70a80e5d6L,

0xa9f6d30a038d1dbcL, 0x5e9fcf4ccd211f4cL,

0xd47487cc8470652bL, 0x7647c3200069671fL,

0x84c8d4dfd2c63f3bL, 0x29ecd9f40041e073L,

0xa5fb0a17c777cf09L, 0xf468107100525890L,

0xcf79cc9db955c2ccL, 0x7182148d4066eeb4L,

0x81ac1fe293d599bfL, 0xc6f14cd848405530L,

0xa21727db38cb002fL, 0xb8ada00e5a506a7cL,

0xca9cf1d206fdc03bL, 0xa6d90811f0e4851cL,

0xfd442e4688bd304aL, 0x908f4a166d1da663L,

0x9e4a9cec15763e2eL, 0x9a598e4e043287feL,

0xc5dd44271ad3cdbaL, 0x40eff1e1853f29fdL,

0xf7549530e188c128L, 0xd12bee59e68ef47cL,

0x9a94dd3e8cf578b9L, 0x82bb74f8301958ceL,

0xc13a148e3032d6e7L, 0xe36a52363c1faf01L,

0xf18899b1bc3f8ca1L, 0xdc44e6c3cb279ac1L,

0x96f5600f15a7b7e5L, 0x29ab103a5ef8c0b9L,

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};