Problem: You are given two positive integers a and b. There are two possible operations: 

  1. multiply one of the numbers by some prime p; 
  2. divide one of the numbers on its prime factor p. 



What is the minimum number of operations required to obtain two integers having the same number of divisors? You are given several such pairs, you need to find the answer for each of them.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of pairs of integers for which you are to find the answer.

Each of the next t lines contain two integers a_i and b_i (1 ≤ a_i, b_i ≤ 10^6).

Output

Output t lines — the i-th of them should contain the answer for the pair a_i, b_i.

Example

Input

8
9 10
100 17
220 70
17 19
4 18
32 20
100 32
224 385


Output

1
3
1
0
1
0
1
1

Note

These are the numbers with equal number of divisors, which are optimal to obtain in the sample test case: 

  * (27, 10), 4 divisors 
  * (100, 1156), 9 divisors 
  * (220, 140), 12 divisors 
  * (17, 19), 2 divisors 
  * (12, 18), 6 divisors 
  * (50, 32), 6 divisors 
  * (224, 1925), 12 divisors 



Note that there can be several optimal pairs of numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const char bs[] =
    "bcdefghcdefghefghighijijcdefghefghighiijefghghiighdefghifghijhijjfghihijjh"
    "ighijijijdefghifghihijjfghihihighijijighiiiefghijghijijkghijijihijjkjhijji"
    "jdefghfghihifghhihghiighihigefghighijijghiiihijjhiijhfghijhijjkhijjijijjfg"
    "hihijjhijjijijefghghiighhihfghihijhiiighijijijfghhihefgggfghhfgghgbcdefgbc"
    "defgdefghfghihibcdefgdefghfghhidefgfghhfgcdefghefghighiiefghghiighfghihihi"
    "cdefghefghghiiefghghghfghihihfghhhdefghifghihijfghihihghiijighiihicdefgefg"
    "hghefgghgfghhfghghfdefghfghihifghhhghiighhigefghighiijghiihihiiefghghiighi"
    "ihihidefgfghhfgghgefghghighhhfghihihiefgghgdefffefggeffgfbcdefbbcdefcdefge"
    "fghghabcdefcdefgefgghcdefefggefbcdefgdefghfghhdefgfghhfgefghghghbcdefgdefg"
    "fghhdefgfgfgefghghgefgggcdefghefghghiefghghgfghhihfghhghbcdefdefgfgdeffgfe"
    "fggefgfgecdefgefghghefgggfghhfgghfdefghfghhifghhghghhdefgfghhfghhghghcdefe"
    "fggeffgfdefgfghfgggefghghghdeffgfcdeeedeffdeefebcdecbbcdeccdefdefgfgbabcde"
    "bcdefdeffgbcdedeffdecbcdefcdefgefggcdefefggefdefgfgfgcbcdefcdefefggcdefefe"
    "fdefgfgfdefffbcdefgdefgfghdefgfgfefgghgefggfgabcdecdefefcdeefedeffdefefdbc"
    "defdefgfgdefffefggeffgecdefgefgghefggfgfggcdefefggefggfgfgbcdedeffdeefecde"
    "fefgefffdefgfgfgcdeefebcdddcdeecddedbcddcbbcdcccdeddefefcbabcdbbcdecdeefab"
    "cdcdeecddcbcdeccdefdeffbcdedeffdecdefefefdcbcdeccdedeffbcdededecdefefecdee"
    "ecbcdefcdefefgcdefefedeffgfdeffefbabcdbcdedebcddedcdeecdedeccbcdecdefefcde"
    "eedeffdeefddcdefdeffgdeffefeffdcdedeffdeffefefcbcdcdeecddeddcdedefdeeecdef"
    "efefbcddedabcccbcddccddebcedcbbcdcccddddeeedcbabccbbcdccddebabcbcddbcedcbc"
    "ddccdeddeecbcdcdeecddcdededeedcbcddccdddeecbcdcdcddcdededdcddddcbcdeccdede"
    "fbcdededcdeefecdeedecbabcbbcdcdabccdcbcddbcdcdbdcbcdccdedebcdddcdeecddeced"
    "cdeddeefcdeededeeedcdddeecdeedededcbcccddbccdcedcdddecddddcdededecbccdcbab"
    "bbcbccdcedfbfedcbbedcccddddeeedcbabdcbbccccddcbabbbccabfedcbcedccddddedcbc"
    "ccddbcedcdddcdfedcbcedccdddedcbcccbcedcdddcedcdcedcbcddccdddecbcdcdcdcdded"
    "dcddcddcbabcbbcccbabbcbcbcccbcbcaedcbcdccdddcbcccdcdddccdbfedcdeddeedcdded"
    "eddfedceddedcddedededcbdccdcbdcdfedcededceeedcdddcddcbccbcbabadcbcedfeggfe"
    "dcbfedccedddeefedcbaedcbbdccdddcbacbbcbagfedcbfedcceddeedcbdccdcbfedceddeg"
    "fedcbfedceddeedcbdccbfedceddfededfedcbcedccddedcbcccbedcddcedcddcedcbadcbb"
    "cccbabbadcbcdcccbbfedcbedccdddcbcbedcdeddccgfedcfedeeedcdfefeegfedfedeedcd"
    "fefefedcedcddcedegfedfeeedfffedceddeedcdccdcbcbedcdfegfhbcdefcdefgefghghbc"
    "defgcdefgefgghdefgefggfgcdefghdefghfghhefghfghhghfghighhibcdefgdefgfghhdef"
    "gfgfgefghghgefgggcdefghefghghiefghghgfghhihfghhghcdefgdefgfgefgfggfghgefgf"
    "gfcdefgefghghefgggfghhfgghfdefghfghhifghhghghhdefgfghhfghhghghcdefefggeffg"
    "fdefgfghfgggefghghghefgfggdefefefgfdeefebcdebcdefdefgfgbbcdefbcdefdeffgcde"
    "fdeffefbcdefgcdefgefggdefgefggfgefghfgghabcdefcdefefggcdefefefdefgfgfdefff"
    "bcdefgdefgfghdefgfgfefgghgefggfgbcdefcdefefdefeffefgfdefefebcdefdefgfgdeff"
    "fefggeffgecdefgefgghefggfgfggcdefefggefggfgfgbcdedeffdeefecdefefgefffdefgf"
    "gfgdefeffcdededefecddedbcdbbcdecdefefcbbcdeabcdecdeefbcdecdeedecbcdefbcdef"
    "deffcdefdeffefdefgeffgbabcdebcdedeffbcdededecdefefecdeeecbcdefcdefefgcdefe"
    "fedeffgfdeffefbbcdebcdedecdedeedefecdededcbcdecdefefcdeeedeffdeefdccdefdef"
    "fgdeffefeffbcdedeffdeffefefabcdcdeecddedbcdedefdeeecdefefefcdedeebcdcdcded"
    "bccdcbccbbcdccdededcbbcdbabcdbcddebbcdbcddcddcbcdecbcdecdeebcdecdeedecdefd"
    "eefcbabcdbbcdcdeeabcdcdcdbcdededbcddddcbcdebcdedefbcdededcdeefecdeedecbbcd"
    "abcdcdbcdcddcdedbcdcdcdcbcdbcdedebcdddcdeecddecdccdecdeefcdeededeecbcdcdee"
    "cdeededebabcbcddbccdccbcdcdecddddcdededeccdcddbbcbcccdccbdcdbdcbbccccddded"
    "cbbccbabcbbccdcbbcabccbcedcbcddcbcdccddcbcdbcddcddcdecddedcbabccbbcccddbab"
    "cbcbccbcdcdccbcccedcbcdcbcdcdecbcdcdcccddedbcddcddcbbcbabcbcbbcbccbcdcabcb"
    "cbedcbccbcdcdcbcccccddbccdbedccddcddeccddddcdddcbcccddbcddcdcdcbabbbccabbc"
    "bdcbcccdbcccedcdcdcddccbcccbbabdccbdcedeedcbbdcccddfedcbbdcbabcbbccdcbbbab"
    "bbbfedcbcedcbcdccddcbccbccbcedcddccdedcbabdcbbcccdcbabbbabdcbcccbdcbcbfedc"
    "bcdcbcccddcbcbcbdcccdccbccdcedcbbcbabbbcbbabbcbcbbabcbbfedcbdcbcccdcbbbdcc"
    "ccbdccfedccedcdddccceddcdedcbdccdcbccdcdcdcbacbbcbacbcedcbdcdcbddfedcdcdde"
    "dccbcdcbbbedccedfefbcdecdefefcccdefbcdefcdeefcdefdefeefccdefgcdefgdeffdefg"
    "efgffgefghfgghbbcdefbcdedeffcdefdeefdefgeffcdeeeccdefgcdefefgdefgeffefgfgg"
    "deffefbcdefcdefdedefeffefgfdeeefeabcdecdefefcdeeedeffdeefdbcdefdeffgdeffef"
    "effcdefdeffefgffgefbcdecdeedeefdcdefdefeffedefgeffgcdeefecdedecdeebccddbcd"
    "bcdededcccdebbcdebcddeccdecdeddedccdefbcdefcdeecdefdefeefdefgeffgcbbcdeabc"
    "dcdeebcdecddecdefdeebcddddccdefbcdedefcdefdeedefeffcdeedecbcdebcdecdcdedee"
    "defecdddedbabcdbcdedebcdddcdeecddeccbcdecdeefcdeededeeccdecdeedefeefdebbcd"
    "bcddcddecccdecdedeedddefdeefdcddedccdcdbcddabbccbcbbcdcdedcccdcbbcdabccdcc"
    "cdbcdccdedccdecbcdebcddccdecdeddecdefdeefdcbbcdbabcbcddbbcdbccdbcdecddabcc"
    "cedccdecbcdcdeccdecddcdedeebcddcddcbcdbbcdbcbcdcddcdedbcccdccbabcbbcdcdabc"
    "ccbcddbccdbdcbcdccddebcddcdcdddccdbcddcdeddecdcbbcabccbccdbdccdbcdcddcedde"
    "cddeddccdccccbccbccbacbdbcbbcccfedcccdcbbcbabbcdcccbbcbccfedccddcbcdcbccdc"
    "cdbcdccddcdecddeedcbbccbabbbcccbbcabbccbcdbccbabbbfedccddcbcbcddccdbccdcdc"
    "ddcbccdcedcbccbbcabcbcbccccdcbbbccbdcbabcbbcbcbabbbcbcccbbcaedcbcdcccdcbcc"
    "dccccedcccbccccdccdbcdcbbbabbbbbcaedcccbccccbfedddcddeddccddccbcdcbccbdced"
    "cbbccgfedccedcbbcbabbedcccbbaccgfedccedcbcdcbcedcccbcbccedcddccdfedcbbdcba"
    "cbbcdcbbbabbdcbccbbcbabagfedccedcbcbcedcccbcedccccdcbbedfedcbdcbbbadcbbbbd"
    "ccbcbadccedcbadcbbcbcbabadcbcdccbbfedcbedcdcdcbceddcdfedcdcbcdccbdccdedcbc"
    "babcbcbbfedcdccdcdcgfededeefeddcdedcccedcddcedfbcdcdeddddecccdebcdcddddecd"
    "eddeedddefccdefcdedddefdefeefdefgeffgdcccdebbcdbcddccdecddecdefdeebcdcdedd"
    "defccdecdeddefdeedefeffcdeddedccdebcdecdcdedeedefecdddedcbbcdabcdcdbcdcdcd"
    "edbccdcdccdebcddecdeddecdddddecdeddefeefdecccdbcdccddecdddecdddeedeeefdeef"
    "eddcdddddcdccdcbbccdbcbcfedddddcccdbbcbcddddccdcddfedddedccdebcdcdddecdedd"
    "eddefdeefedcccdcbbcabcccccdbccdccdecddbbcbcfedddedccdbcddddecddddedeeccdcd"
    "dedccdcbcdbcccdcddcdedbcccdcdcbbcbabcbcbbcbcbcdcabbcbedccdcbccdccdccdbcced"
    "ddccdcddeddecddcccbbcbcccdbedddcccdddcfeeeddeeeeddcddddcddccbcbdcebbbgfedd"
    "dedccccbbabedddcccbddgfedddedccdcbcbedddccdcddeddecddefedcccdcbbbabbdcccbb"
    "ccdccdbcccbbabgfedddedcccbcedddccdeddcdddccbedfedccdcbcbbdccbccdcdccbbdcce"
    "dcbbcbabbbcbbabcbcbbacbbfedccdcbccdccbdccbdfedddccbdddcddcdedcccbbaccccbfe"
    "dddcbdddcgfeeedeefeeddeeddcdedccdcedfcbhgfeddfedccdcbbafedddccbddhgfeddfed"
    "ccdcbcfedddccbddfedddcddgfedccedcbcbabedcccbccedcccbcdcbbbhgfeddfedcdcbfed"
    "ddcdfeddcdedccfegfedcedcbcbedccbcedccdcbeddfedcbdcbacbdcbbbdcbccbdccgfedce"
    "dcdcedcceddcegfededcceddceddefedcdcbbdcdccgfededcededhgfefeffgfeedefedddfe"
    "ddedfegbgfeeeeeddddcccbceeeedddceegfeeeeedddeccdceeeeddedeeeeefdeeffeddddd"
    "cccbbcbddddccdddddecddcccbcgfeeeeedddccceeeeddeeeedeedddceefeddddccdbcdddc"
    "ddddedcccddcedccccbbcabcccbcccdcbbccbfeddddccbcdddcddccdfeeedddceeedeedeed"
    "ddcccbddddcfeeeddceeedgfffeeffffeedeeeedeeddcdcedfhgfeeefeddddccbbfeeedddc"
    "eehgfeeefeddddccbfeeedddceefeeeddeegfedddedcccbbaedddccddedddccddccbchgfee"
    "efedddcbfeeeddefeeddeeddcfegfeddedcccbeddccdeddcdcbeddfedccdcbbbadccbcdccb"
    "cbdccgfeddedccbeddceddcegfeeeddceeedeedefedddccbddddcgfeeedceeedhgfffeffgf"
    "feeffeedefeddedfegbcdefcdefgefgghcdefefggefbcdefgdefghfghhdefgfghhfgefghgh"
    "ghccdefgdefgfghhdefgfgfgefghghgefgggcdefghefghghiefghghgfghhihfghhghbcdefd"
    "efgfgdeffgfefggefgfgecdefgefghghefgggfghhfgghfcdefgefgghefggfgfggdefgfghhf"
    "ghhghghcdefefggeffgfdefgfghfgggefghghghdeffgfcdeeedeffeeefdbcdebcdefdeffgb"
    "cdedeffdecbcdefcdefgefggcdefefggefdefgfgfgbbcdefcdefefggcdefefefdefgfgfdef"
    "ffbcdefgdefgfghdefgfgfefgghgefggfgabcdecdefefcdeefedeffdefefdbcdefdefgfgde"
    "fffefggeffgebcdefdeffgdeffefeffcdefefggefggfgfgbcdedeffdeefecdefefgefffdef"
    "gfgfgcdeefebcdddcdeedddecbcdbbcdecdeefabcdcdeecddcbcdeccdefdeffbcdedeffdec"
    "defefefcbbcdeccdedeffbcdededecdefefecdeeecbcdefcdefefgcdefefedeffgfdeffefb"
    "abcdbcdedebcddedcdeecdedeccbcdecdefefcdeeedeffdeefdcbcdecdeefcdeededeeccde"
    "deffdeffefefbbcdcdeecddedccdedefdeeecdefefefbcddedabcccbcddcccdbbccbbcdccd"
    "debabcbcddbcedcbcddccdeddeecbcdcdeecddcdedededcbbcdcccdddeebbcdcdcdccdeded"
    "ccddddcbcdeccdedefbcdededcdeefecdeedecbabcbbcdcdabccdcbcddbcdcdbdcbcdccded"
    "ebcdddcdeecddecdcbcdccddebcddcdcdddccdddeecdeededecbbcccddbccdcdccdddecddd"
    "dcdededecbccdcbabbbcbccdcdccbdcbbccccddcbabbbccabfedcbcedccddddedcbcccddbc"
    "edcdddcdedcbbcdcccdddecbbcccbcdccdddcdccdcedcbcddccdddecbcdcdcdcddedccddcd"
    "dcbabcbbcccbabbcbcbccbbcbcaedcbcdccdddcbcccdcddcccdbedcbcdccddcbccdcdccedc"
    "cdddeccdddddddcbbcccdbbcccedccddeccddedcdddcddcbccbcbabadcbcededdedcbbdccd"
    "ddcbacbbcbagfedcbfedcceddeedcbdccdcbfedceddefedcbbedccdddedcbbccbbedccddce"
    "dcdcfedcbcedccddedcbcccbedcddcdccddcedcbadcbbcccbabbadcbccbccbbfedcbedccdd"
    "dcbcbedcddcdccfedcbedcdddcbcededdfedceddedccdedededcbdccdcbdcdfedcededceef"
    "edceddeedcdccdcbcbedcdfefeebcdecdeefbcdecdeedecbcdefbcdefdeffcdefdeffefdef"
    "geffgbabcdebcdedeffbcdededecdefefecdeeecbcdefcdefefgcdefefedeffgfdeffefbbc"
    "debcdedecdedeedefecdededbccdecdefefcdeeedeffdeefdccdefcdeefdefeefdeebcdede"
    "ffdeffefefabcdcdeecddedbcdedefdeeecdefefefbcddedbcdcdcdedccddcbcdbcddebbcd"
    "bcddcddcbcdecbcdecdeebcdecdeedecdefdeefcbabcdbbcdcdeeabcdcdcdbcdededbcdddd"
    "cbcdebcdedefbcdededcdeefecdeedecbbcdabcdcdbcdcddcdedbcdcdccbbcdbcdedebcddd"
    "cdeecddecdccdebcddecdeddecddcbcdcdeecdeededebabcbcddbccdccbcdcdecddddcdede"
    "decbccdcbbcbcccdcbbcccbcbbccdcbbcabccbcedcbcddcbcdccddcbcdbcddcddcdecddedc"
    "babccbbcccddbabcbcbccbcdcdcbbcccedcbcdcbcdcdecbcdcdcccddedbcddcddcbbcbabcb"
    "cbbcbccbcdcabcbcbdcbbccbcdcdbbcccccddbccdbedccdcbccdccdccdbccdcbcccddbcddc"
    "dcdcbabbbccabbcbdcbcccdbcccedcdcdcddcbbcbcbbabdccbcbdcdbcbbccdcbbbabbbbfed"
    "cbcedcbcdccddcbccbccbcedcddccdedcbabdcbbcccdcbabbbabdcbcccbcbbcbfedcbcdcbc"
    "ccddcbcbcbdcccdccbccdcedcbbcbabbbcbbabbcbcbbabcbbedcbbdcbccccbbbbdccccbccb"
    "fedccdcbccdccbdccbdedcbdccdcbccdcccdcbacbbcbacbbedcbdcdcbdcfedcdcddedccbcd"
    "cbbbedccdcededcbccedcbcbabcbgfedcbfedcbedcdedcbdcbccbfedceddefedcbaedcbdcc"
    "ddcbacbbaedcbdccdcbcbgfedcbedcbdcdedcbcbcedcdccdcbcedfedcbdcbacbdcbbabdcbc"
    "cbbdccfedcbedcbdcdcbcbedcddcdccgfedcedcdcedcceddcefedcedcddcbcedddedcbdcbc"
    "cbdccfedcedddcedgfededeefeddcdedcccfeddedfefbccdcccdbcdccdedccdecbcdebcddc"
    "cdecdeddecdefdeefdcbbcdbabcbcddbbcdbccdbcdecddabcccedccdecbcdcdeccdecddcde"
    "deebcddcddcbcdbbcdbcbcdcddcdedbcccdccbabcbbcdcdabcccbcddcccdbdcbcdccdcdbcd"
    "dcdcdddccdbcddcdeddecdcbbcabccbccdbdccdbcdcddceddecddedccbcccccbccbccbacbd"
    "bbcdcccbbcbccfedccddcbcdcbccdccdbcdccddcdecddeedcbbccbabbbcccbbcabbccbcdbc"
    "cbabbbfedccddcbcbcddccdbccdcdcddcbccdcedcbccbbcabcbcbccccdcbbbccbdcbabcbbc"
    "bcbabbbcbccbbbcaedcbcdccbccbccdccccedcccbccccdccdbcdcbbbabbbbbcaedcccbcccc"
    "bfedddcddedccbcdccbcdcbccbdcebbedcccbbaccgfedccedcbcdcbcedcccbcbccedcddccd"
    "fedcbbdcbacbbcdcbbbabbdcbccbbcbabagfedccedcbcbcedcccbcedccccdcbbedfedcbdcb"
    "bbadcbbbbdccbcbadccedcbadcbbcbcbabadcbccbcbbfedcbedccbdcbceddcdfedcdcbcdcc"
    "bdccdedcbcbabcbcbbfedcdccdcdcgfededeefeddcdedcccedcddcedfbedddcccbddgfeddd"
    "edccdcbcbedddccdcddeddecddefedcccdcbbbabbdcccbbccdccdbcccbbabgfedddedcccbc"
    "edddccdeddcdddccbedfedccdcbcbbdccbccdcdccbbdccedcbbcbabbbcbbabcbcbbacbbfed"
    "ccdcbccdccbdccbdfedddccbdddcddcdedcccbbaccccbfedddcbdddcgfeeedeefeddcdeddc"
    "dedccdcedffedddccbddhgfeddfedccdcbcfedddccbddfedddcddgfedccedcbcbabedcccbc"
    "cedcccbcdcbbbhgfeddfedcdcbfedddcdfeddcdedccfegfedcedcbcbedccbcedccdcbeddfe"
    "dcbdcbacbdcbbbdcbccbdccgfedcedcdcedcceddcegfededcceddceddefedcdcbbdcdccgfe"
    "dedcededhgfefeffgfeedefedddfeddedfegbcdcdeecddcbcdeccdefdeffbcdedeffdecdef"
    "efefcbccdecddeeeffccdedededdefefedeefecbcdefcdefefgcdefefedeffgfdeffefbabc"
    "dbcdedebcddedcdeecdedeccbcdecdefefcdeeedeffdeefdcbcdecdeefcdeededeeccdedef"
    "fdeffefefbccdddeecddeecddeeefdeefcdefefefbcddedabcccbcddcdcdbbcbcddbcedcbc"
    "ddccdeddeecbcdcdeecddcdedededcbbcdcccdddeebbcdcdcdccdededcddeddcbcdeccdede"
    "fbcdededcdeefecdeedecbabcbbcdcdabccdcbcddbcdcdbdcbcdccdedebcdddcdeecddecdc"
    "bcdccddebcddcdcdddccdddeecdeededecbbcccddbccdddccdddecddedcdededecbccdcbab"
    "bbcbccccdccbbbccabfedcbcedccddddedcbcccddbcedcdddcdedcbbcdcccdddecbbcccbcd"
    "ccdddccccdcedcbcddccdddecbcdcdcdcddedccddcddcbabcbbcccbabbcbcbccbbcbcaedcb"
    "cdccdddcbcccdcddcccdbedcbcdccddcbccdccccedccdddeccdddddddcbbcccdbbcccedccd"
    "deccddedcdddcddcbccbcbabadcbcdceddcbbcbagfedcbfedcceddeedcbdccdcbfedceddef"
    "edcbbedccdddedcbbccbbedccddcdccdcfedcbcedccddedcbcccbedcddcdccddcedcbadcbb"
    "cccbabbadcbccbccbbfedcbedccdddcbcbedcddcdccfedcbedcdddcbceddcdfedceddedccd"
    "edddedcbdccdcbdccfedcededcedfedceddeedcdccdcbcbedcdedfeebccbcedcbcddcbcdcc"
    "ddcbcdbcddcddcdecddedcbabccbbcccddbabcbcbccbcdcdcbccdcedcbcdcbcdcdecbcdcdc"
    "ccddedbcddcddcbbcbabcbcbbcbccbcdcabcbcbdcbcccbcdcdbcccccdddbccdcedccdcbccd"
    "ccdccdbccdcbcccddbcddcdcdcbabbbccabbccdcbcccdbccdedcdcdcddcbbcbcbbabdccbcb"
    "dcdbbbbfedcbcedcbcdccddcbccbccbcedcddccdedcbabdcbbcccdcbabbbabdcbcccbcbbcb"
    "fedcbcdcbcccddcbcbcbdcccdccbccdcedcbbcbabbbcbbabbcbcbbabcbbedcbbdcbccccbbb"
    "bdccccbccbfedccdcbccdccbdccbdedcbdccdcbccdcccdcbacbbcbacbbedcbdcdcbdcfedcd"
    "cddedccbcdcbbbedccdcedebcbgfedcbfedcbedcdedcbdcbccbfedceddefedcbaedcbdccdd"
    "cbacbbaedcbdccdcbcbgfedcbedcbdcdedcbcbcedcdccdcbcedfedcbdcbacbdcbbabdcbccb"
    "bdccfedcbedcbdcdcbcbedcddcdccgfedcedcdcedcceddcefedcedcddcbcedddedcbdcbccb"
    "dccfedcedddcedgfededeefeddcdedcccfeddedfefccgfedccedcbcdcbcedcccbcbccedcdd"
    "ccdfedcbbdcbacbbcdcbbbabbdcbccbbcbabagfedccedcbcbcedcccbcedccccdcbbedfedcb"
    "dcbbbadcbbbbdccbcbadccedcbadcbbcbcbabadcbccbcbbfedcbedccbdcbceddcdfedcdcbc"
    "dccbdccdedcbcbabcbcbbfedcdccdcdcgfededeefeddcdedcccedcddcedfbfedcbcedccddd"
    "dedcbcccddbcedcdddcdedcbccdccdddeecbcccdccdcdddedcddededcbcddccdddecbcdcdc"
    "dcddedcddecddcbabcbbcccbabbcbcbccbcdbcaedcbcdccdddcbcccdcddcdcdbedcbcdccdd"
    "cbccdccdcedccdddeccdddddddcbcccddbccddedcdddecddeedcdddcddcbccbcbabadcbcdc"
    "eddgfedcbfedcceddeedcbdccdcbfedceddefedcbbedccdddedcbbccbbedccddcdccdcfedc"
    "bcedccddedcbcccbedcddcdccddcedcbadcbbcccbabbadcbccbccbbfedcbedccdddcbcbedc"
    "ddcdccfedcbedcdddcbceddcdfedceddedccdedddedcbdccdcbdccfedcededcedfedceddee"
    "dcdccdcbcbedcdedfeebcdefcdefgefggcdefefggefdefgfgfgbcdefgdefgfghhdefgfgfgd"
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    "bbcedcdccedcccfeddfefeeedcbdcddcbacbbedcdccedcddcgfedcedcbdcedccbcedcddccc"
    "bdhgfedfedcedfedddfedeeddcegfedcfedeeedcdfefeegfedfedeedcdfefefedcedcddced"
    "efedcedddceeedcbdccdfededdfedddgfeegfgffbcdcdebcdecddcdedeebcddcddccdebcde"
    "decdedeedefecdecddcbcdecdefefcdeeedeffdecdddcdefdeffgdeffefefddcdedeffdeff"
    "efedcbcdcdeecddedccdecdedeedbbcdbccdccdcddccdcdcdedbccdbbcbcdbbcdbccbcdcdd"
    "abccbcedccdcbcdcdccdcddcdedbcdbccdcbcdccdedebcdddcdeecdbccedcdecdeefcdeede"
    "decedcdcdeecdeededcdcbcbcddbccdcdccdbcdcddccbbcabbcdccbccdccbcdcdccbdccbbb"
    "ccbbcabbcbcbccbabbcbfedccdcbcbcdccbccdcdccbcbbcedcbcdccdcdcbcccdcdddccbbfe"
    "dcddcddedcddddcdcfedcdcdddcddddcbedcbcbcccbccbedcccbccccbdcbbbabbedccbcedc"
    "ccedcddceddcbcdcbbbabdcbcbbcbabdcgfedcedcbcbedccbcedccdcbcbdfedcbedccdcdcb"
    "cbedcdeddccgfedcedcddedcceddcdgfededcdedcceddcfedcdcbcdcdccfedcdccdcdcedcb"
    "cbccfeddcdfedddfedeedfeebccccdbccccdcddbbcbccfedcddccdbcdcdcddddedcccbcced"
    "cbccbcdcdcbcccccddbcabbfedcddcddedcddddcdbfedddcddddeddeccedcccbcccccdbedd"
    "dcccdddcdcccbbcceddccdeddcdedccdceddbdcccbbcdccbcccbbadcgfedcedcccbedcccce"
    "ddcdcbcbdfedcbdcbcccdcbbbdccccbbacgfedcedccdedcceddccgfededcceddceddcfedcd"
    "cbbdcdccfedddcbdddcedcccbccfeddcdfedddfeddedfeeedddccdeddccddccbedhgfedfed"
    "cdcfeddcdfeddedcdcegfedcedcbcbedcccedccdccbdhgfedfeddcfeddfeeddhgfefeddfee"
    "dfeedgfededccededdgfeeedceeedfedddcddgfeedegfeeegfeefegffbcdcdcbcddedccddc"
    "ddcbcdbcdedebcddedcdeecdebccdccdecdefefcdeeedeffdecdddccdecdeefcdeededecdc"
    "dedeffdeffefedcbcdcdeecddedcbcdcdecdddbabcbcbccbccdccbcccdcddccddcbcbcbcbc"
    "cdcbbccbcedcbccbcdcdcbccdcccddbcdabbedccddcdedeccdddddeecdbccedccddcddeccd"
    "dddcdbedcdddeecdeededcdcbcccddbccdcdcbcccdbccccbabbbabdcbccbdcbbbedccdcedd"
    "bbbadcbccbcbbccbfedcbdcbcccdcbbcbdccccbcbacfedccedcddddcccceddddccbcfedcce"
    "dcdddccceddccfedceddedcddeddcedcbdccdcbdccedcbdcdcbdcdcbacbbcedcdccedcccfe"
    "ddedfeecbbedcdccdcbcdcgfedcedcbdcedccbcedcddcccbdgfedcfedcededcdcfedeeddcd"
    "gfedcfedededcdfeeddgfedfedeedcdfeedfedcedcddceddfedcedddcededcbdccdfededdf"
    "edddgfeefegffbbcbcbccbabbcbfedccdcbcbcdccbccdcdccbcbbcedcbcdccdcdcbcccdcdd"
    "ccbcbfedcddcccddcdcddcccfedcdcdddcddddcbedcbcbcccbccbedcccbccccbdcbbbabbed"
    "ccbcedcccedcddceddbdcbcbbcbabdcgfedcedcbcbedccbcedccdcbcbdfedcbedccdcdcbcb"
    "edcddccbcgfedcedcdcedcceddcdgfededcdedcceddcfedcdcbcdcdccfedcdccdcdcedcbcb"
    "ccfeddcdfedddfedeedfeedcbccbcbcccbfedcbdcbcccdcbbcbdccccbcbacfedccedcddddc"
    "ccceddddccbcfedccedcdddccceddccfedceddedcddeddcedcbdccdcbdccedcbdcdcbdcdcb"
    "acbbcedcdccedcccfeddedfeebccdcbcddcdedcdeccdedecdedeebcddcdecddedcdecdefef"
    "cdeeecdeedecdddcbcdbcddebcddcdcdbedcdcdeecdeededcdccdcdeecdcdddcdecdedecdc"
    "bcdbccbcbccdcdcdcdededdcdccbbcbcbccccfedcddccdcddcdcddcbccccdbccfedcddcded"
    "edcddddcddcdbccedcbccbccdcbccccbcafedcdcdddcddcdcbedccdcddccbccedcddcdcdbc"
    "dcbccbbadcbccbedcccfeddededdbbadcbcdcgfedcedccdcedccccdcbbdcccbdgfedcedcdd"
    "dedcccedccdccbdfedcbdcbccdcbbdccbbgfededcdedccdcdcfedcedcddccbdfedcedddccd"
    "edcbdccbedcdccfedddgfeefefeebbcbcbdcgfeddedcdcceddcdddccbdccccdfedccedcdcd"
    "dcccccbccdccbcfedccdcbbcdccbdccbbgfededcceddcdcdcfedcdcccdccbcfedddccddcce"
    "dcccbcbedccbcfedddfedeedfeebdcbcedhgfedfedcdcfeddcdedccedcdcegfedcfedcdced"
    "cdcdcbceddcdgfedcedccbedcceddcchgfefeddfeddededgfededcdeddcdgfededdedddfed"
    "cdcdcfeddcdgfeeegfeffegffdcbcdcgfedcedccdcedccccdcbbdcccbdgfedcedcdddedccc"
    "dcccdccbdfedcbdcbccdcbbdccbbgfededcdedccdcdcfedcedcddccbdfedcedddccdedcbdc"
    "cbedcdccfedddgfeefefeebccbcedcdecbcdcdccdcddcdedbcdcdddcbcdccdedebcdddcdee"
    "cddccedcdecdeefcdeededecedcdcdeecdeededcdcbcbcddbccdcdccdbcdcddccbcdabbcdc"
    "dbccdcdbcdcdccbdccbbcbfedcddcbcbcdccbccdcdccbccccedcbcdccdcdcbcccdcdddccbb"
    "fedcddcddedcddddcdbfedcdcdddcddddcbedcbcbcccbccbedcccbcdccbdcbcbacbedccbce"
    "dccdedcddceddbdcgfedcedcbcbedccbcedccdcbcbdfedcbedccdcdcbcbedcdeddccgfedce"
    "dcddedcceddccgfededcdedcceddcfedcdcbcdcdccfedcdccdcdcedcbcbccfeddcdfedddfe"
    "deedfeedcgfedcedcccbedcccceddcdcbcbdfedcbdcbcccdcbbbdccccbbacgfedcedccdedc"
    "ceddccgfededcceddceddcfedcdcbbdcdccfedddcbeddcedcccbdcfeddcdfeddefeddedfee"
    "bfedcddcdededcddedddeecdebccedcdeddefefcdeeedeffdecddfedefdeffgdeffefefdfe"
    "dedeffdeffefededcdcdeecddededcdcdecddddcbcbcbcedccdcedccceddddceddgfedcedc"
    "dcdedccdceddddcdcbdfedcdeddededcdddedeeeddccgfedeedeefedeeeedecgfededeeede"
    "eeedcfedcdcdddcddcfedcdcddcdcedcbcbccfeddcdfedddfedeedfeebcdecdefefcdeefed"
    "effdefefdbcdefdefgfgdefffefggeffgecdefgefgghefggfgfggddefefggefggfgfgdcded"
    "effdeefeddefefgefffcdefefefcdeefebcdddcdeecddedbcdbcdedebcddedcdeecdedeccb"
    "cdecdefefcdeeedeffdeefddcdefdeffgdeffefeffdcdedeffdeffefefcbcdcdeecddedccd"
    "edefdeeebcdededebcddedabcccbcddbccdcbcbbcdcdabccdcbcddbcdcdbdcbcdccdedebcd"
    "ddcdeecddecedcdeddeefcdeededeeedcdcdeecdeedededcbcbcddbccdcdccdcdecdddcbcd"
    "cdcdcbccdcbabbbcbcccbdcdbcbbcbcbabbcbcbcccbcbcaedcbcdccdcdcbcccdcdddccdbfe"
    "dcdedddedcddeddddfedcdcdddcddddcdedcbcbcccbccbedccdcdccdcdcbcccbcdcbccbcba"
    "badcbcdcededcbbcbcbabbadcbcdcbcbbfedcbedccdcdcbcbedcdeddccgfedcfedededcdfe"
    "edegfededcdedcceddefedcdcbcdcdccfedcedddcededcbdccdedcdccdcbcbedcdedfefbcd"
    "cdbcdcddcdedbcdcdcdcccdbcdedeccdddddeecddecdccdecdeefcdeededeecbcdcdeecdee"
    "dedebabcbcddbccdccbcdcdecdddccdecddeccdcddbbcbcccdcccddcbcbcbbcbccbcdcabcb"
    "cbedcbccbcdcdcbcccccddbccdbedccddcddeccddddcdddcbcccddbcddcdcdcbabbbccabbc"
    "bdcbcccdbcccdccdbccddccbcccbbabdccbdceddbbbcbbabbcbcbbabcbbfedcbdcbcccdcbb"
    "bdccccbdccfedccedcdddccceddcdedcbdccccbccdcdcdcbacbbbbacbcedcbdcccbdcedccc"
    "bccedccbcdcbbbedccedfeecbdcbbabdcbccbbdccgfedcedcbdcedcccedcddceddgfedcfed"
    "ededcdfeedefedcedcddcbcedededcbdcbccbdcdfedcedddcedfedcdcddfeddcdedcccfedd"
    "fegffbcbcbccccdcbbbccbdcbabcbbcbcbabbbcbccccbcaedcbcdcccdcbccdccccedcccbcc"
    "ccdccdbcdcbbbabbbbbcaedcccbccccbedddccddeddccddccbcdcbccbdcedcbbbbdccbcbad"
    "ccedcbadcbbcbcbabadcbcdccbbfedcbedcdcdcbceddcdfedcdcbcdccbdccdedcbcbabcbcb"
    "bfedcdccdcdcfedddcddfeddcdedcccedcddcedfbccdcbcddccdcdbdcbcdccdedebcdddcde"
    "edddecdcbcdccddebcddcdddddccdcdeecdeededecbccbcddccddcdcddcdeddedcbcdcdcdc"
    "bccdcbabbbcbcccbdccbbcbcbccbbcbcaedcbcdccdcdcbcccdcddcccdbedcbcdcccdcbccdc"
    "dccedccdcddccddddcddcbbcbccbbccbedccdcdccdcdcbcccbcdcbccbcbabadcbcdceddbba"
    "dcbccbbcbbfedcbedccdcdcbcbedcddcdccfedcbedcdcdcbcededdfedcedcddcccedddedcb"
    "dcbccbdccfedcedddcededcbdccdedcdccdcbcbedcdedfeebbcbcbbabcbbedcbcdcbccccbc"
    "bcdcdccbccbfedccdcbccdccbdccbdedcbdccccbccdcccdcbacbbbbacbbedcbdcccbdcedcc"
    "cbccedccbcdcbbbedccdcedebdcbccbbdccfedcbedcbdcdcbcbedcddcdccgfedcedcdcedcc"
    "eddcefedcedcddcbcedddedcbdcbccbdccfedcedddcedfedcdcddfeddcdedcccfeddedfefd"
    "cbccbbcbbfedcbedccdcdcbcbedcddcdccfedcbedcdcdcbceddcdfedcedcddcccedddedcbd"
    "cbccbdccfedcedddcededcbdccdedcdccdcbcbedcdedfeebccbcdcdcdcbcdccdedebcdddbc"
    "ddcddeccbabcbbccdabccbccccdcbcccddbcddcddddcbcccddbcccdedcdddecddedccdcdcc"
    "dcdbcccbcbcdcdcdccbbbbcbcccbedcbcdccdcdcbccccbccdccdbdcbabcbbbcbabbcbcbbed"
    "cbdccccbccdcdcedcbdccccbcbcfedcedddccdedccdccbedccbcdcbcbedcdeddccbdccdccf"
    "edcbedccdcdcbcbdcbceddccedcbadcbcbcbabdcdccfedcedcddcbcededfedcedcddcdcdgf"
    "edfeeeddefedceddcfeddcdedcdcfedefeeddcbbdccfedcbdcbcccdcbbbdccbcbdccedcbbc"
    "babbcbbacbbacfedcdcbcdccbcbcdedcbdcbccbbacfedcedddccdedcbdcccdcbcbbedcccfe"
    "ddededdbcbccedcdccbcdcdccccccdddbccdddcbcdccddebcddcdcdddcbcccddbcddcdddcb"
    "abbbccabbccdcbcccdbccddcbcbcbcdccbcccbcabdcdbdcdccbcbcfedcbdcbcccdcbbbdccc"
    "cbdccedcbcdcccdcbccdcdccedcbdccccbccdcdcdcbacbbbbacbcedcbdcccbdcedcbcbcced"
    "ccbddcbbcedccededddccedcbadcbbcbcbabadcbcdccbbfedcbdcbccdcbbdccbdfedcdcbcd"
    "ccbdccdedcbcbabcbcbbfedcdccdcdcfedcdcddedcdccedccdedcddcedebbfedcddcdededc"
    "dddddeecdbccedcdeddeefcdeededecedcdddeecdeededddcbcccddbccdcdcbcccdbccdcba"
    "bbbabdcbccbdcbbbedccededdcgfedcedcdddedccceddddccbdfedcdedddedcddededdfedc"
    "eddddcddedededcbdccccbdcdedcbdcccbdddcbacbbcedcdccedcccfeddfefeeedcbcdccdc"
    "dcbcccdcddddcdbfedcdedddedcddeddedfedddcdddddddecdedcdcbcccccdbedcddcdcddc"
    "dcbcccbcdcbccbcbabadcbcdcedebcdecdefefcdeeedeffdeefdbcdefdeffgdeffefeffcde"
    "fdeffefgffgefddefcdeedeefdeefgdefeffedefgeffgddeefecdeeecdeebccdcbcdbcdede"
    "bcdddcdeecddeccbcdecdeefcdeededeedcdecdeedefeefdedcdebcddcddecddefcdedeedc"
    "defdeefccddedbcdddbcddabbcbbcbbcdcdabcccbcddbccdbdcbcdccddebcddcdcdddccdbc"
    "ddcdeddecdcbcdabccbccdbdcdebcdcddcdcdecddedccddccbccccbccbacbcbcbbcbcbabbb"
    "cbcccbbcaedcbcdcccdcbccdccccedcccbccdcdccdbcdcbcbabbcbbcaedcdcbcdccbedcddc"
    "cdedcddcdcbcbdcbccbdcddcbbcbcbabadcbcdccbbfedcbedcdcdcbceddcdfedcdcbcdccbd"
    "ccdedcbcbabcbcbbfedcdccdcdcfedceddefeddcdedcccedcddcedebcdcdbcdcdcdedbccdc"
    "dccdebcddecdeddecdddcdecdeddefededecbcdbcdccdcdcdcdecdddedddcdededecbccdcc"
    "cdcdccdcbbcccbcbcbbcbcbcdcabbcbedccdcbccdccdccdbccedcdccdccdedcdcddcbcbbcb"
    "bcbcbedcdccccdccedcdcdcddcbccbdccbcdccbcbdcdbbbcbbabcbcbbacbbfedccdcbccdcc"
    "bdccbdfedcdccbdcdcdccdedcbcbbacbcbbfedcdcbdcdcfedcdcddedcdccedcccedccdcede"
    "cbdcbbbdcbccbdccgfedcedcdcedcceddcegfededccedcceddefedcdcbbdcdccgfededcede"
    "dgfededeefededdfedddfeddedfefbcbcbccbccbbccbfedcddccbcdcdcdcccdfedddcdcdde"
    "dddcdedcccbcbccccbfedddccdddcfedddcddedccbceddcdedccdcededcbbbdcbbcbdccgfe"
    "dcedccbedcceddcegfededcceddceddefedcdcbbdcdccgfededcededgfededeefeddcdfedd"
    "dfeddedfefbcccbcddcccdbdcbcdccdcdbcddcdddddccdbcddcdeddecdcbcdabccbccdbdcd"
    "ebcdcddcdcdecddedcdbcccbccccbccbacbcbbbcbccbbbcaedcbcdccbccbccdccccedcccbc"
    "cdcdccdbcdcbcbabbcbbcaedcdcbcdccbedcddccdedccbcdcbcbdcbccbdcdbadcbccbcbbfe"
    "dcbedccbdcbceddcdfedcdcbcdccbdccdedcbcbabcbcbbfedcdccdcdcfedceddefeddcdedc"
    "ccedcddcedebcbcbbacbbfedccdcbccdccbdccbdfedcdccbdcdcdccdedcbcbbacbcbbfedcd"
    "cbdcdcfedcdcddedcdccedcccedccdcededcbccbcbbfedcbedccbdcbceddcdfedcdcbcdccb"
    "dccdedcbcbabcbcbbfedcdccdcdcfedceddefeddcdedcccedcddcedebccbccdcdcbcdccdbc"
    "bcdcbccddedcdcdeccdedcddedccdbcdccdcdceddecdddedddcdebccdcbcabbdcdbcdcdccb"
    "dccbbcbccbedcbccbcabcbcbcbdccfedcdcdbdcdcdccdedcccbcbdcccbfedddcceddcedcdc"
    "bdcdcbbacedcccedcddceddbdcdccfedcbdcbbadcbcdccbdgfededccedccdcdefedcdcbcdc"
    "cbcgfededdedddfedcdcddedccbcfedddfedeedfeecbdccfedccdcbbbdccbdccbdgfededcc"
    "eddcdcdefedcdccbdccbcgfededcedddfedcdcddedccbcfedddfeddedfeebbccedcdecbccd"
    "ccdccdbccedcddcdccdedcdcddcbcccdbbcbccedcdddccdcdedcdcdccdcbbcbdccbcdcdbcb"
    "dcdcbcfedcddcbbcdccbdccbdfedcdccbdcdcdcddedcbcbcacbcbcfedcdcbdcddfedcdcdde"
    "dccbcedccdedccdcedebbfedcddcddedcddddcdbfedddcddddeddeccedcdcbcccccdbedcdd"
    "cccdccdcbcccbbedccdcedcccedccdceddcgfedcedccdedcceddccgfededcceddcedddfedc"
    "dcbbdcdccfedcdcbdcddedcbcbccfeddcdfedddfeddedfeeedcbcdcccdcbccdccdcedcccbc"
    "cdcdccdbcdcbcbabbcbbcaedcdcbcdccbedcddcccedcdccdcbcbdcbccbdcdbcdecdeefcdee"
    "dedeebcdedeffdeffefefcdefdeffefdeedefgefgfgefedefefefdcddedddeeedeffcdcdbb"
    "cdbcddebcddcdcddcbcdcdeecdeedededcdecdeedecddedefdefefdedcdededecbccdcccdd"
    "dcdeebcbcabcbbccdabccbcbccdcbcccddbcddcdcddccdbcddcdbcceddecdedecdedcdddcd"
    "dcbccbdccccdcddcbcbbbcbbccbabbcbcbbedcbdccdcbccdcccedcccbccdccbbfedddcdedd"
    "cfedceddcedcdccedccbedcddcdccdcbcccbabdcdccfedcedcddcbcedddfedcdcbcdcdccgf"
    "ededdededgfedfeedfededdfeddcfedeededdbccdbcdccdbccdccdbcddcdedcdcddcdecded"
    "cdbccdcdedeedecdcbcdcdcdbabbcbcbcccdcddccccbbbcbbcbbcabbedcccbccccdcbcbced"
    "cdccdcbcabbedcddddcdbcdcbcccbccbabbadcbcbedccdcdccbbcbbacbbacfedcdcbcdccbc"
    "bcdfedcdccbcbbacfedcedcdccdedcbdccddcbcbbedcdcfeddededdbcccbcbbbcfedddccbd"
    "ddccccdfedddcdcccbbcfedddcdddccedcccbccdcbbabedcccfeddededddccbdccbdgfeded"
    "cceddcdcdegfededccdccbdgfededdedddfedcdcddedccbcfedddgfeefefeebccbccccdcbc"
    "ccddbcddcddddccdbcddcdccceddecdededddcdddeddcbccdcdcdccdcddcbcbbbbcbbbbedc"
    "bdccdcbccccccedcccbccccbbbfedddcdddccedccddccdcbccbedccbedcddcdccbdccbcfed"
    "cedcddcbcdcddfedcdcbcdccbcgfededdedddfedcedddedcdccfeddcfedeededdcbbacfedc"
    "dcbcdccbcbcdfedcdccbcbbacfedcedcdccdedcbdccddcbcbbedcdcfeddededdbbccedcddc"
    "ddcdedbccdeddecdedcdbccfededeedecdedcdcdccdcbbcbedccceddddcdcccbcfedcedccd"
    "cdccbddfedddcdcdccbcgfededdedddfedcdcddedccbcfeddcfedeededdbbedcdcbccccdcb"
    "cbcedcdccdcbcabbedcddddcdbcdcbcccbbcbabbadcbcbedccdcdcccfedcdcbcdccbcbcdfe"
    "dcdccbcbbacfedcedcdccdedcbdcccdcbcbbedcdcfeddededdfedcdcdddcddcdcbfedddcdd"
    "cdbccfededddcdbcedcdccbadcbccbedcdcfeddededdbcdcdeecdeededebcdedeffdeefecd"
    "efefgefffdefgfgfgedeefeeefdeeefedddecbcbcddbcddcdcdcbcdcdeecddeddcdedefdee"
    "eedefefefdcddedddecdddedcccdbbbbccabccbcbcdcbcccddbccdcedcdddecdddfededede"
    "edccdcdcdbceddcdcdcccbbcbabbcbcbedcbdccdcbdccfedcededcedgfedededfeddcdedcc"
    "cfeddededdbccbcdccdbcdccdbcddcdcdceddecdededddcdededecbccdcdcdcddcddcbdccb"
    "bbbcbbcabedcccbccccbcbfedddcdddccedcdddcddcbccbedcccedcddceddbcbbacbbcfedc"
    "dcbcdccbcgfededdedddfedceddeedcdccfedddfedeedfeecccbccbcfedddccbddcccgfeee"
    "dceeddfedddcddedccbcfedddfeddedfeebccbcccdcbcccddbccddedcdddecddeeddededed"
    "cccdcdcdbcedecdcdccbbcbbbedcbdccdcbcccfedcededcddfeddedddedcdccedcccfedded"
    "eddbdcccfedcedcddcdcdgfedfeeedeegfedfeeefededdfedddgfeefefeecbbcfedcdcbcdc"
    "cbcgfededdedddfedceddeedcdccfedddfedeedfeebbcedcddcddcdbccfedeededecdedcdd"
    "dcddcbccbedcccfeddededdccfedcedcddccbdgfedfeeeddefedceddeedcdccfedddgfeefe"
    "feebedcdcbccccbcbfededcdddccedcddcccdcbccbedcdcedcddceddfedcdcdddccdcfeddd"
    "cdddccedcdcbcbedcdccfedddfedeedfeebcdcdeecddedbcdedefdeeecdefefefdeedeeede"
    "cdededdceddbcbcddbccdccbcdcdecddddcdededeeddcdddcdbcdcdccbdccbbbccabbcbdcb"
    "cccdbcccedcdcdcddcdbcccbcabdccbdceddcbbcbacbcedcbdcdcbddfedcdcddedccbddcbb"
    "cedccedfeebccbccdbdccdbcdcddceddecddedcccdcdcdbccbccbacbdbbbbbcaedcccbcccc"
    "bfedddcddedccccdccbcdcbccbdcebcbcbbfedcdccdcdcgfededeefeddcdedccdedcddcedf"
    "ccccbfedddcbdddcgfeeedeefeddcdeddcdedccdcedfbbccdcbcccdbccdedcdcdcddcbbcbc"
    "bcabdcdbcbdcdcbbedcbdcdcbdcfedcdcddedccbcdcbbcedccdcedebbedcddcdcdbcdcbccc"
    "bccbabbadcbbbedccdcdcccfedcedddccdedcbdccddcbcbbedcccfeddededdedcdcbcdccbe"
    "dcdcbccdcbccbedcccdcbccbdcdbcdcdecdddbcdededecdeefedefdeeefeedfeebcbcdbccc"
    "cbcdcdcddcddededecdededdceddbbbcabbbdcbcccbcedccdcdcdbceddcedfeecbcbaccedc"
    "bdccdfeddcdedccdfeddfegffbcbccbdccdbccdeddcddedecddcddcbdcdbbbbaedcccbccfe"
    "ddcdeddcdedcddcedecccbfedddcddgfeedefeedefeddedfefbbcdcbcccbcedccdcdcdbced"
    "ecdcedecbedcbdccdfeddcdedccdfeddedfefbedcddccbdcbccbedcccfeddededdedcdcbdc"
    "edcdccfedddedcddcedebcdcdcdbcddedcdeeedeffeefeebcbcbccbccdcdcdddedeeededdb"
    "bbabdcbccbedcccfeddfeeddcbbcedcdccfedddgfeegffeebbcdccbcceddcdededdcdccbbe"
    "dccbcfedddfedeededdbdcbccbedcccfeddededdedcdccfedddgfeefefeebccdcbcdddcdee"
    "deeeebbcbcbcccdcddededdbbadcbcbedcdeddccbbdccbceddcededdbedcccfeddededddcb"
    "cbedcdeddccbcccbcddcddeebbbcbccdcedebadcbcededdbdccbedfeedcbcededdbccbccdd"
    "bbcbdcebdcededcedfbbcccbdbbc";
int ts[] = {2,   3,   5,   7,   11,  13,  17,  19,  23,  29,  31,  37,  41,
            43,  47,  53,  59,  61,  67,  71,  73,  79,  83,  89,  97,  101,
            103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167,
            173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239,
            241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313,
            317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397,
            401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467,
            479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569,
            571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643,
            647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733,
            739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823,
            827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
            919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997};
vector<int> sb[23333];
int sn = 0;
int ss[2333];
map<long long, int> ys;
long long hsh(vector<int> v) {
  long long a = 0;
  for (int i = 0; i < 7; ++i) a = a * 21 + v[i];
  return a;
}
void dfs(int b, int d, int u, int x) {
  ++sn;
  for (int p = 0; p < d; ++p) sb[sn].push_back(ss[p]);
  if (sb[sn].size() > 7) throw "GG";
  sb[sn].resize(7);
  ys[hsh(sb[sn])] = sn;
  for (int w = 1; w <= u && ts[d] <= b; ++w)
    ss[d] = w, b /= ts[d], x *= ts[d], dfs(b, d + 1, w, x);
}
int aa[2333];
int ans[555][555];
long long fac(int t) {
  vector<int> v;
  for (auto w : ts)
    if (t % w == 0) {
      int c = 0;
      while (t % w == 0) t /= w, ++c;
      v.push_back(c);
    }
  if (t > 1) v.push_back(1);
  sort(v.begin(), v.end(), greater<int>());
  v.resize(7);
  return hsh(v);
}
int main() {
  dfs(1e6, 0, 30, 1);
  int bn = 0;
  for (int i = 1; i <= sn; ++i)
    for (int j = i + 1; j <= sn; ++j) ans[i][j] = ans[j][i] = bs[bn++] - 'a';
  int T, a, b;
  scanf("%d", &T);
  while (T--) {
    scanf("%d%d", &a, &b);
    int x = fac(a), y = fac(b);
    cout << ans[ys[x]][ys[y]] << "\n";
  }
}