D. Huge Stringstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given n strings s1, s2, ..., sn 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 saisbi is saved into a new string sn + 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 2k such strings) are substrings of the new string. If there is no such k, print 0.InputThe first line contains single integer n (1 ≤ n ≤ 100) — the number of strings. The next n lines contain strings s1, s2, ..., sn (1 ≤ |si| ≤ 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 ai abd bi (1 ≤ ai, bi ≤ n + i - 1) — the number of strings that are concatenated to form sn + i.OutputPrint m lines, each should contain one integer — the answer to the question after the corresponding operation.ExampleInput5011010111111031 26 54 4Output120NoteOn 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.
Input5011010111111031 26 54 4
Output120
['bitmasks', 'brute force', 'dp', 'implementation', 'strings', '*2200']