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>
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
using namespace std;
inline int read() {
  int x = 0;
  char c = getchar();
  while (c < '0' || c > '9') c = getchar();
  while (c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
  return x;
}
struct node {
  set<string> s[12];
  string sf, sb;
  bool ok;
} s[205];
string tp;
set<string>::iterator it;
int main() {
  int i, j, l, n, m;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    cin >> tp;
    int sz = tp.size();
    for (j = 0; j < sz; j++) {
      string rp = "";
      for (l = j; l < sz; l++) {
        if (l - j + 1 > 11) {
          break;
        }
        rp += tp[l];
        s[i].s[l - j + 1].insert(rp);
      }
    }
    if (sz <= 11) {
      s[i].ok = 1;
    } else {
      s[i].ok = 0;
    }
    int f1 = (sz > 11 ? 11 : sz);
    s[i].sf = tp.substr(0, f1);
    s[i].sb = tp.substr(sz - f1, f1);
  }
  int a, b;
  scanf("%d", &m);
  for (i = 1; i <= m; i++) {
    scanf("%d%d", &a, &b);
    if (s[a].ok && s[b].ok) {
      string tp = s[a].sf + s[b].sf;
      int sz = tp.size();
      for (j = 0; j < sz; j++) {
        string rp = "";
        for (l = j; l < sz; l++) {
          if (l - j + 1 >= 11) {
            break;
          }
          rp += tp[l];
          s[n + i].s[l - j + 1].insert(rp);
        }
      }
      if (sz <= 11) {
        s[n + i].ok = 1;
      } else {
        s[n + i].ok = 0;
      }
      int f1 = (sz > 11 ? 11 : sz);
      s[n + i].sf = tp.substr(0, f1);
      s[n + i].sb = tp.substr(sz - f1, f1);
    } else {
      for (j = 1; j <= 11; j++) {
        if (s[a].s[j].size() > s[b].s[j].size()) {
          s[n + i].s[j] = s[a].s[j];
          for (it = s[b].s[j].begin(); it != s[b].s[j].end(); it++) {
            s[n + i].s[j].insert((*it));
          }
        } else {
          s[n + i].s[j] = s[b].s[j];
          for (it = s[a].s[j].begin(); it != s[a].s[j].end(); it++) {
            s[n + i].s[j].insert((*it));
          }
        }
      }
      if (s[a].ok && (!s[b].ok)) {
        s[n + i].ok = 0;
        string tp = s[a].sf + s[b].sf;
        int sz = tp.size();
        int f1 = (sz > 11 ? 11 : sz);
        s[n + i].sf = tp.substr(0, f1);
        s[n + i].sb = s[b].sb;
      }
      if ((!s[a].ok) && s[b].ok) {
        s[n + i].ok = 0;
        string tp = s[a].sb + s[b].sb;
        int sz = tp.size();
        int f1 = (sz > 11 ? 11 : sz);
        s[n + i].sf = s[a].sf;
        s[n + i].sb = tp.substr(sz - f1, f1);
      }
      if ((!s[a].ok) && (!s[b].ok)) {
        s[n + i].ok = 0;
        s[n + i].sf = s[a].sf;
        s[n + i].sb = s[b].sb;
      }
      int sa = s[a].sb.size(), sb = s[b].sf.size();
      for (j = 1; j <= sa; j++) {
        for (l = 1; l <= sb && j + l <= 11; l++) {
          string tp = s[a].sb.substr(sa - j, j) + s[b].sf.substr(0, l);
          s[n + i].s[j + l].insert(tp);
        }
      }
    }
    for (j = 1; j <= 11; j++) {
      if (s[n + i].s[j].size() != (1 << j)) {
        printf("%d\n", j - 1);
        break;
      }
      if (j == 11) {
        printf("%d\n", j);
      }
    }
  }
  return 0;
}