You are given n strings s 1 , s 2 , ..., s n consisting of characters 0 and 1 . m operations are performed, on each of them you concatenate two existing strings into a new one. On the i -th operation the concatenation s a i s b i is saved into a new string s n + i (the operations are numbered starting from 1 ). After each operation you need to find the maximum positive integer k such that all possible strings consisting of 0 and 1 of length k (there are 2 k such strings) are substrings of the new string. If there is no such k , print 0 . The first line contains single integer n ( 1 ≤ n ≤ 100 ) — the number of strings. The next n lines contain strings s 1 , s 2 , ..., s n ( 1 ≤ | s i | ≤ 100 ), one per line. The total length of strings is not greater than 100 . The next line contains single integer m ( 1 ≤ m ≤ 100 ) — the number of operations. m lines follow, each of them contains two integers a i abd b i ( 1 ≤ a i , b i ≤ n + i - 1 ) — the number of strings that are concatenated to form s n + i . Print m lines, each should contain one integer — the answer to the question after the corresponding operation. On the first operation, a new string " 0110 " is created. For k = 1 the two possible binary strings of length k are " 0 " and " 1 ", they are substrings of the new string. For k = 2 and greater there exist strings of length k that do not appear in this string (for k = 2 such string is " 00 "). So the answer is 1 . On the second operation the string " 01100 " is created. Now all strings of length k = 2 are present. On the third operation the string " 1111111111 " is created. There is no zero, so the answer is 0 .