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 N = 205;
string pre[N], suf[N];
set<string> all[N][13];
void Extend(int id, string s) {
  for (int i = 0; i < s.size(); i++) {
    for (int j = 0; i + j < s.size() && j < 13; j++) {
      all[id][j].insert(s.substr(i, j + 1));
    }
  }
}
void Merge(int id, int l, int r) {
  for (int i = 0; i < 13; i++) {
    for (auto it : all[l][i]) all[id][i].insert(it);
    for (auto it : all[r][i]) all[id][i].insert(it);
  }
  Extend(id, suf[l] + pre[r]);
  pre[id] = pre[l];
  suf[id] = suf[r];
  for (int i = 0; i < pre[r].size(); i++)
    if (pre[id].size() < 13) pre[id] += pre[r][i];
  for (int i = (int)suf[l].size() - 1; i >= 0; i--)
    if (suf[id].size() < 13) suf[id] = suf[l][i] + suf[id];
}
int main() {
  int n, q, i;
  scanf("%i", &n);
  for (i = 1; i <= n; i++) {
    string s;
    cin >> s;
    Extend(i, s);
    if (s.size() < 13)
      pre[i] = suf[i] = s;
    else
      pre[i] = s.substr(0, 13), suf[i] = s.substr(s.size() - 13, 13);
  }
  scanf("%i", &q);
  while (q--) {
    n++;
    int l, r;
    scanf("%i %i", &l, &r);
    Merge(n, l, r);
    int sol = 0;
    for (i = 0; i < 13; i++) {
      if (all[n][i].size() != (1 << (i + 1))) break;
      sol = i + 1;
    }
    printf("%i\n", sol);
  }
  return 0;
}