Huge Strings

有n+m个01串，前n个串由输入给出，长度和不超过100，后m个串由前面两个串（不一定是前n个串中的串）拼接而成，对于后m个串中的每个串，求出最大的k，使得所有长度为k的01串均被它包含

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_{ai}s_{bi} $ 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.

5
01
10
101
11111
0
3
1 2
6 5
4 4

1
2
0

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 $ .