Problem: You 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.

Input

The 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.

Output

Print m lines, each should contain one integer — the answer to the question after the corresponding operation.

Example

Input

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


Output

1
2
0

Note

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.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
const int cHalfLim = 1000;
int GetAns(std::string str) {
  for (int i = 1; i < 10; i++) {
    for (int j = 0; j < (1 << i); j++) {
      std::string tmp = "";
      for (int l = 0; l < i; l++) {
        if ((1 << l) & j)
          tmp += "1";
        else
          tmp += "0";
      }
      if (str.find(tmp) == -1) return i - 1;
    }
  }
  return 10;
}
int main() {
  int n;
  scanf("%d", &n);
  std::vector<std::string> strs;
  std::vector<int> outs;
  for (int i = 0; i < n; i++) {
    std::string tmp;
    std::cin >> tmp;
    strs.push_back(tmp);
    outs.push_back(GetAns(tmp));
  }
  int m;
  scanf("%d", &m);
  while (m--) {
    int l, r;
    std::cin >> l >> r;
    std::string tmp;
    l--, r--;
    tmp = strs[l] + strs[r];
    if (tmp.size() > 2 * cHalfLim) {
      std::string ntmp =
          tmp.substr(0, cHalfLim) + tmp.substr(tmp.size() - cHalfLim, cHalfLim);
      tmp = ntmp;
    }
    strs.push_back(tmp);
    outs.push_back(std::max(std::max(outs[l], outs[r]), GetAns(tmp)));
    std::cout << outs[outs.size() - 1] << std::endl;
  }
}