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>
bool debug = 0;
const double PI = acos(-1.0);
const double eps = 1e-9;
using namespace std;
string pre[202];
string suf[202];
bool num[202][14][10000];
void cria(string s, int i) {
  for (int k = 1; k <= min(13, (int)s.size()); k++) {
    int r = 0;
    for (int j = 0; j < k; j++) {
      r += (1 << j) * (s[s.size() - 1 - j] - '0');
    }
    num[i][k][r] = 1;
    for (int j = s.size() - k - 1; j >= 0; j--) {
      r /= 2;
      r += (1 << (k - 1)) * (s[j] - '0');
      num[i][k][r] = 1;
    }
  }
}
int main() {
  int n, m;
  cin >> n;
  string s;
  for (int i = 0; i < n; i++) {
    cin >> s;
    pre[i] = s.substr(0, min(13, (int)s.size()));
    suf[i] = s.substr(((int)s.size()) - min(13, (int)s.size()),
                      min(13, (int)s.size()));
    if (debug)
      cout << "pre[i]"
           << " = " << (pre[i]) << endl;
    if (debug)
      cout << "suf[i]"
           << " = " << (suf[i]) << endl;
    cria(s, i);
  }
  cin >> m;
  int a, b;
  for (int i = n; i < n + m; i++) {
    cin >> a >> b;
    a--;
    b--;
    pre[i] = pre[a];
    if (pre[i].size() < 13) {
      int falta = 13 - (int)pre[i].size();
      pre[i] += pre[b].substr(0, min(falta, (int)pre[b].size()));
    }
    suf[i] = suf[b];
    if (suf[i].size() < 13) {
      int falta = 13 - (int)suf[i].size();
      suf[i] =
          suf[a].substr(((int)suf[a].size()) - min(falta, (int)suf[a].size()),
                        min(falta, (int)suf[a].size())) +
          suf[i];
    }
    if (debug)
      cout << "pre[i]"
           << " = " << (pre[i]) << endl;
    if (debug)
      cout << "suf[i]"
           << " = " << (suf[i]) << endl;
    cria(suf[a] + pre[b], i);
    for (int k = 1; k <= 13; k++) {
      for (int j = 0; j <= (1 << k); j++) {
        num[i][k][j] |= num[a][k][j] or num[b][k][j];
      }
    }
    int res = 0;
    for (int k = 13; k > 0; k--) {
      bool aux = 1;
      for (int j = 0; j < (1 << k); j++) {
        if (num[i][k][j] == 0) {
          aux = 0;
          break;
        }
      }
      if (aux) {
        res = k;
        break;
      }
    }
    cout << res << endl;
  }
  return 0;
}