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 = 222, K = 15;
void push(string s, bool a[K][1 << K]) {
  int n = s.size();
  for (int i = 0; i < n; i++) {
    int x = 0;
    for (int j = i; j < n && j - i + 1 < K; j++) {
      x |= (s[j] == '1') << (j - i);
      a[j - i + 1][x] = true;
    }
  }
}
void push(bool a[K][1 << K], bool b[K][1 << K]) {
  for (int i = 0; i < K; i++) {
    for (int j = 0; j < 1 << i; j++) b[i][j] |= a[i][j];
  }
}
bool a[N][K][1 << K];
string s[N], pre[N], suf[N];
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> s[i];
    push(s[i], a[i]);
    pre[i] = suf[i] = s[i];
  }
  int lim = 1 << K;
  int m;
  cin >> m;
  for (int i = n + 1; i <= n + m; i++) {
    int x, y;
    cin >> x >> y;
    push(a[x], a[i]), push(a[y], a[i]);
    push(suf[x] + pre[y], a[i]);
    pre[i] = pre[x], suf[i] = suf[y];
    if ((int)pre[i].length() < lim)
      pre[i] =
          (pre[i] + pre[y])
              .substr(0, min(lim, (int)(pre[i].length() + pre[y].length())));
    if ((int)suf[i].length() < lim)
      suf[i] =
          (suf[x] + suf[i])
              .substr(max(0, (int)(suf[x].length() + suf[i].length() - lim)));
    int k;
    for (k = 1; k < K; k++) {
      int ok = 1;
      for (int j = 0; j < 1 << k; j++)
        if (!a[i][k][j]) ok = 0;
      if (!ok) break;
    }
    cout << k - 1 << endl;
  }
}