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 INF = 1e9 + 7;
struct T {
  set<string> tt;
  string prefix, suffix;
  bool all;
  T(string s = "") {
    int n = s.size();
    for (int i = 0; i < n; i++)
      for (int j = i; j < n && j - i + 1 <= 9; j++)
        tt.insert(s.substr(i, j - i + 1));
    if (n <= 9) {
      prefix = suffix = s;
      all = true;
    } else {
      prefix = s.substr(0, 9);
      suffix = s.substr(n - 9);
      all = false;
    }
  }
  int get() {
    int ans = 0;
    for (int len = 1; len <= 9; len++) {
      bool ok = true;
      for (int i = 0; i < (1 << len); i++) {
        string s;
        for (int j = 0; j < len; j++) {
          if (i >> j & 1)
            s += '1';
          else
            s += '0';
        }
        if (tt.count(s) == 0) {
          ok = false;
          break;
        }
      }
      if (!ok)
        break;
      else
        ans = len;
    }
    return ans;
  }
} a[202];
T add(T a, T b) {
  if (a.all && b.all) return T(a.prefix + b.prefix);
  T d;
  d.all = false;
  T c = T(a.suffix + b.prefix);
  for (string s : a.tt) d.tt.insert(s);
  for (string s : b.tt) d.tt.insert(s);
  for (string s : c.tt) d.tt.insert(s);
  if (a.all)
    d.prefix = (a.prefix + b.prefix).substr(0, 9);
  else
    d.prefix = a.prefix;
  if (b.all) {
    string r = (a.suffix + b.suffix);
    d.suffix = r.substr(r.size() - 9);
  } else
    d.suffix = b.suffix;
  return d;
}
signed main() {
  std::ios::sync_with_stdio(0);
  std::cin.tie(0);
  ;
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    string s;
    cin >> s;
    a[i] = T(s);
  }
  int m;
  cin >> m;
  for (int i = n + 1; i <= n + m; i++) {
    int x, y;
    cin >> x >> y;
    a[i] = add(a[x], a[y]);
    cout << a[i].get() << endl;
  }
}