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>
using namespace std;
string substr(const string& str, int idx, int count) {
  if (idx < 0) idx += str.size();
  if (idx < 0) idx = 0;
  count = min(count, (int)str.size() - idx);
  return str.substr(idx, count);
}
int main() {
  int n, m;
  cin >> n;
  vector<string> s(n), pre(n), post(n);
  vector<vector<unordered_set<string>>> subs(n,
                                             vector<unordered_set<string>>(10));
  for (int i = 0; i < n; ++i) {
    cin >> s[i];
    pre[i] = substr(s[i], 0, 9);
    post[i] = substr(s[i], -9, 9);
    for (int l = 1; l < 10; ++l)
      for (int j = 0; j + l <= (int)s[i].size(); ++j)
        subs[i][l].insert(s[i].substr(j, l));
  }
  cin >> m;
  for (int i = 0; i < m; ++i) {
    int a, b;
    cin >> a >> b;
    a--, b--;
    vector<unordered_set<string>> ns(10);
    int res = 0;
    for (int l = 1; l < 10; ++l) {
      ns[l].insert(subs[a][l].begin(), subs[a][l].end());
      ns[l].insert(subs[b][l].begin(), subs[b][l].end());
      for (int j = 1; j < l; ++j)
        if ((int)post[a].size() >= j && (int)pre[b].size() >= l - j)
          ns[l].insert(substr(post[a], -j, j) + substr(pre[b], 0, l - j));
      if (ns[l].size() == (1 << l)) res = l;
    }
    subs.push_back(ns);
    pre.push_back(substr(pre[a] + pre[b], 0, 9));
    post.push_back(substr(post[a] + post[b], -9, 9));
    cout << res << endl;
  }
}