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;
bitset<1 << (14 + 1)> possib[202][14 + 1];
vector<string> prefix, suffix;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  for (int i = 0; i < 202; i++)
    for (int j = 0; j < 14 + 1; j++) possib[i][j].reset();
  int n;
  cin >> n;
  string s;
  int pos = 0;
  while (n--) {
    cin >> s;
    int size = s.size();
    prefix.push_back(s.substr(0, min(14, size)));
    suffix.push_back(s.substr(max(0, size - 14), min(14, size)));
    for (int i = 1; i <= min(14, size); i++) {
      int temp = 0;
      for (int j = 0; j < i; j++) temp = temp * 2 + (s[j] - '0');
      possib[pos][i].set(temp, true);
      for (int j = i; j < size; j++) {
        temp = temp * 2 + (s[j] - '0');
        temp = temp % (1 << i);
        possib[pos][i].set(temp, true);
      }
    }
    pos++;
  }
  int m;
  cin >> m;
  int a, b;
  while (m--) {
    cin >> a >> b;
    a--;
    b--;
    for (int i = 1; i <= 14; i++) {
      for (int j = 0; j < (1 << i); j++) {
        if (possib[a][i][j] | possib[b][i][j]) {
          possib[pos][i].set(j, true);
        }
      }
    }
    s = suffix[a] + prefix[b];
    int size = s.size();
    for (int i = 1; i <= min(14, size); i++) {
      int temp = 0;
      for (int j = 0; j < i; j++) temp = temp * 2 + (s[j] - '0');
      possib[pos][i].set(temp, true);
      for (int j = i; j < size; j++) {
        temp = temp * 2 + (s[j] - '0');
        temp = temp % (1 << i);
        possib[pos][i].set(temp, true);
      }
    }
    s = prefix[a] + prefix[b];
    size = s.size();
    prefix.push_back(s.substr(0, min(14, size)));
    s = suffix[a] + suffix[b];
    size = s.size();
    suffix.push_back(s.substr(max(0, size - 14), min(14, size)));
    int k = 0;
    for (int i = 1; i <= 14; i++)
      if (possib[pos][i].count() == (1 << i)) k = i;
    cout << k << "\n";
    pos++;
  }
  return 0;
}