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 s[2000];
int n, m, ans[2000];
int solve() {
  for (int l = 1; l <= 10; l++)
    for (int t = 0; t < (1 << l); t++) {
      string v;
      for (int k = 0; k < l; k++) v += (t >> k & 1 ? "1" : "0");
      if (s[n].find(v) == -1) return l - 1;
    }
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> s[i];
  cin >> m;
  for (; m--;) {
    int l, r;
    cin >> l >> r;
    s[++n] = s[l] + s[r];
    int len = s[n].length();
    if (len > 1000) s[n] = s[n].substr(0, 500) + s[n].substr(len - 500, 500);
    cout << (ans[n] = max(solve(), max(ans[l], ans[r]))) << "\n";
  }
}