In the decimal system an autobiographical number is a natural number with no more than 10 digits, N =d0d1...dr−1 (1≤r≤10) suchthatd0 isthenumberof 0’sinN,d1 isthenumberof 1’sinN,d2 isthenumberof2’sinN,and so on. The notion of autobiographical number can be generalized to any base b ≥ 2. Let A = [s0,s1,...,sb−1] be an alphabet, whose symbols s0,s1,...,sb−1 correspond to the values 0, 1, . . . , b − 1, respectively: that is, value (si) = i. Then, an autobiographical number in base b (under the alphabet A) is a natural number with no more than b symbols, N =d0d1...dr−1 (1≤r≤b) such that value(d0) is the number of s0’s in N, value(d1) is the number of s1’s in N, ..., and value(dr−1) is the number of sr−1’s in N. For example: • 42101000 is an autobiographical number in base 10, under the alphabet [0, 1, 2, 3, 4, 5, 6, 7, 8,9], because it has four 0’s, two 1’s, one 2, zero 3’s, one 4, zero 5’s, zero 6’s, and zero 7’s; • A2100000001000 is an autobiographical number in base 16, under the alphabet [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F]. There are value(A)=10 0’s, two 1’s, etc. Given an alphabet A, with b symbols, determine all autobiographical numbers in base b under A. Input The first line contains a positive integer L (1 ≤ L ≤ 50), which is the number of subsequent lines. Each of the following L lines contains an alphabet. An alphabet is a contiguous sequence of b distinct symbols, where 2 ≤ b ≤ 100. A symbol is a printable character. Output For each input alphabet, the output is the sequence of all autobiographical numbers in increasing order. Each number is written on a different line. The outputs of two consecutive alphabets are separated by a blank line. Sample Input 2 0123 abcdefg
2/2 Sample Output 1210 2020 bcba caca cbcaa dcbbaaa