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;
template <class T>
void dbs(string str, T t) {
  cout << str << " : " << t << endl;
}
template <class T, class... second>
void dbs(string str, T t, second... s) {
  int idx = str.find(',');
  cout << str.substr(0, idx) << " : " << t << ",";
  dbs(str.substr(idx + 1), s...);
}
template <class second, class T>
ostream& operator<<(ostream& os, const pair<second, T>& p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& p) {
  os << "[ ";
  for (auto& it : p) os << it << " ";
  return os << "]";
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& p) {
  os << "[ ";
  for (auto& it : p) os << it << " ";
  return os << "]";
}
template <class second, class T>
ostream& operator<<(ostream& os, const map<second, T>& p) {
  os << "[ ";
  for (auto& it : p) os << it << " ";
  return os << "]";
}
template <class T>
void prc(T a, T b) {
  cout << "[";
  for (T i = a; i != b; ++i) {
    if (i != a) cout << ", ";
    cout << *i;
  }
  cout << "]";
  cout << endl;
}
const int MAGIC = 12;
struct HugeString {
  bitset<1 << MAGIC> bst[MAGIC + 1];
  string prefix, suffix;
};
HugeString hs[201];
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  for (int it = (1); it <= (n); ++it) {
    string s;
    cin >> s;
    hs[it].prefix = s.substr(0, min(int(s.size()), MAGIC));
    hs[it].suffix = s.substr(max(0, int(s.size()) - MAGIC));
    for (int i = (0); i <= (int(s.size()) - 1); ++i) {
      int x = 0;
      for (int j = (i); j <= (min(i + MAGIC - 1, int(s.size()) - 1)); ++j) {
        x <<= 1;
        x |= (s[j] - '0');
        hs[it].bst[j - i + 1].set(x);
      }
    }
  }
  int m;
  cin >> m;
  for (int cur = (n + 1); cur <= (n + m); ++cur) {
    int a, b;
    cin >> a >> b;
    for (int i = (0); i <= (MAGIC); ++i) {
      hs[cur].bst[i] = hs[a].bst[i];
      hs[cur].bst[i] |= hs[b].bst[i];
    }
    string t = hs[a].suffix + hs[b].prefix;
    for (int i = (0); i <= (int(t.size()) - 1); ++i) {
      int x = 0;
      for (int j = (i); j <= (int(t.size()) - 1); ++j) {
        if (j - i + 1 > MAGIC) break;
        x <<= 1;
        x |= (t[j] - '0');
        hs[cur].bst[j - i + 1].set(x);
      }
    }
    hs[cur].prefix = hs[a].prefix;
    if (hs[cur].prefix.length() < MAGIC) {
      hs[cur].prefix += hs[b].prefix.substr(0, MAGIC - hs[cur].prefix.length());
    }
    hs[cur].suffix = hs[b].suffix;
    if (hs[cur].suffix.length() < MAGIC) {
      int len = MAGIC - hs[cur].suffix.length();
      hs[cur].suffix =
          hs[a].suffix.substr(max(0, int(hs[a].suffix.size()) - len)) +
          hs[cur].suffix;
    }
    int ans = 0;
    for (int i = (1); i <= (MAGIC); ++i) {
      if (hs[cur].bst[i].count() == (1 << i)) {
        ++ans;
      } else {
        break;
      }
    }
    cout << ans << "\n";
  }
  return 0;
}