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;
constexpr int MAX_K = 14;
struct Res {
  string last_k, first_k;
  bitset<(1 << MAX_K)> got[MAX_K];
};
Res init_calc(string s) {
  Res res;
  if (s.size() <= MAX_K) {
    res.last_k = s;
    res.first_k = s;
  } else {
    res.last_k = s.substr(s.size() - MAX_K, MAX_K);
    res.first_k = s.substr(0, MAX_K);
  }
  for (int k = 1; k < MAX_K; ++k) {
    for (int start = 0; start + k <= s.size(); ++start) {
      int val = 0;
      for (int i = start; i < start + k; ++i) {
        val *= 2;
        val += s[i] - '0';
      }
      res.got[k][val] = true;
    }
  }
  return res;
}
Res merge_res(Res &a, Res &b) {
  Res res;
  if (a.first_k.size() == MAX_K) {
    res.first_k = a.first_k;
  } else {
    string tmp = a.first_k + b.first_k;
    if (tmp.size() <= MAX_K) {
      res.first_k = tmp;
    } else {
      res.first_k = tmp.substr(0, MAX_K);
    }
  }
  if (b.last_k.size() == MAX_K) {
    res.last_k = b.last_k;
  } else {
    string tmp = a.last_k + b.last_k;
    if (tmp.size() <= MAX_K) {
      res.last_k = tmp;
    } else {
      res.last_k = tmp.substr(tmp.size() - MAX_K, MAX_K);
    }
  }
  for (int k = 1; k < MAX_K; ++k) {
    res.got[k] = a.got[k] | b.got[k];
  }
  string middle = a.last_k + b.first_k;
  for (int k = 1; k < MAX_K; ++k) {
    for (int start = 0; start + k <= middle.size(); ++start) {
      int val = 0;
      for (int i = start; i < start + k; ++i) {
        val *= 2;
        val += middle[i] - '0';
      }
      res.got[k][val] = true;
    }
  }
  return res;
}
int eval_res(Res &a) {
  int ans = 0;
  for (int k = 1; k < MAX_K; ++k) {
    if (a.got[k].count() == (1 << k))
      ans = k;
    else
      break;
  }
  return ans;
}
void debug_out(Res &a) {
  cout << endl;
  cout << "first: " << a.first_k << endl;
  cout << "last : " << a.last_k << endl;
  cout << "got  :" << endl;
  for (int k = 1; k < MAX_K; ++k) {
    cout << "  " << k << " " << a.got[k].count() << endl;
  }
  cout << endl;
}
int main() {
  int n;
  cin >> n;
  vector<string> s(n);
  for (int i = 0; i < n; ++i) {
    cin >> s[i];
  }
  vector<Res> res(n);
  for (int i = 0; i < n; ++i) {
    res[i] = init_calc(s[i]);
  }
  int m;
  cin >> m;
  for (int i = 0; i < m; ++i) {
    int a, b;
    cin >> a >> b;
    --a;
    --b;
    res.push_back(merge_res(res[a], res[b]));
    cout << eval_res(res.back()) << endl;
  }
  return 0;
}