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 MAXN = 1005;
string a[MAXN];
string pref[MAXN], suff[MAXN];
int n, m, s[MAXN], e[MAXN];
bool dp[205][15][1 << 14];
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    pref[i] = a[i];
    suff[i] = a[i];
    if (a[i].size() > 15) pref[i] = pref[i].substr(0, 15);
    if (a[i].size() > 15) suff[i] = suff[i].substr(suff[i].size() - 15, 15);
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < a[i].size(); j++) {
      int ans = 0;
      for (int k = j; k < a[i].size(); k++) {
        if (k - j + 1 > 14) break;
        ans = ans * 2 + (a[i][k] - '0');
        dp[i][k - j + 1][ans] = 1;
      }
    }
  }
  cin >> m;
  for (int i = n + 1; i <= n + m; i++) {
    cin >> s[i] >> e[i];
    if (pref[s[i]].size() > 14)
      pref[i] = pref[s[i]];
    else
      pref[i] = pref[s[i]] + pref[e[i]];
    if (suff[e[i]].size() > 14)
      suff[i] = suff[e[i]];
    else
      suff[i] = suff[s[i]] + suff[e[i]];
    if (pref[i].size() > 15) pref[i] = pref[i].substr(0, 15);
    if (suff[i].size() > 15) suff[i] = suff[i].substr(suff[i].size() - 15, 15);
    for (int k = 1; k <= 14; k++) {
      for (int j = 0; j < (1 << k); j++) {
        dp[i][k][j] |= (dp[s[i]][k][j] | dp[e[i]][k][j]);
      }
    }
    auto k = suff[s[i]] + pref[e[i]];
    for (int j = 0; j < k.size(); j++) {
      int ans = 0;
      for (int l = j; l < k.size(); l++) {
        if (l - j + 1 > 14) break;
        ans = ans * 2 + (k[l] - '0');
        dp[i][l - j + 1][ans] = 1;
      }
    }
    int ret = 0;
    for (int k = 14; k; k--) {
      bool ok = 1;
      for (int j = 0; j < (1 << k); j++) {
        if (dp[i][k][j] == 0) ok = 0;
      }
      if (ok) {
        ret = k;
        break;
      }
    }
    cout << ret << endl;
  }
}