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;
const int km = 10;
int add(vector<unordered_set<string>>& substrings, string str) {
  int res = 0;
  for (int k = 0; k < km; ++k) {
    for (int i = 0; i < (int)(str).size(); ++i)
      if (i + k <= (int)(str).size()) {
        substrings[k].insert(str.substr(i, k));
      }
    if ((int)(substrings[k]).size() == (1 << k)) res = k;
  }
  return res;
}
int main() {
  int n;
  cin >> n;
  vector<vector<unordered_set<string>>> substrings(
      n, vector<unordered_set<string>>(km));
  vector<string> prefix(n), postfix(n);
  for (int i = 0; i < n; ++i) {
    string s;
    cin >> s;
    add(substrings[i], s);
    prefix[i] = s.substr(0, km);
    postfix[i] = s.substr(max(0, (int)(s).size() - km), km);
  }
  int m;
  cin >> m;
  for (int i = 0; i < m; ++i) {
    int ai, bi;
    cin >> ai >> bi;
    ai--, bi--;
    prefix.push_back((prefix[ai] + prefix[bi]).substr(0, km));
    postfix.push_back(
        (postfix[ai] + postfix[bi])
            .substr(max(0, (int)(postfix[ai] + postfix[bi]).size() - km), km));
    vector<unordered_set<string>> ab(km);
    for (int j = 0; j < km; ++j)
      ab[j].insert(substrings[ai][j].begin(), substrings[ai][j].end());
    for (int j = 0; j < km; ++j)
      ab[j].insert(substrings[bi][j].begin(), substrings[bi][j].end());
    int res = add(ab, postfix[ai] + prefix[bi]);
    cout << res << endl;
    substrings.push_back(ab);
  }
}