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 = 105;
const int MAXK = 18;
const int SIZE = (1 << (MAXK + 1)) + 5;
int st[MAXN];
string str[MAXN];
struct data {
  int len;
  string pre, suf;
  bitset<SIZE> vis;
} s[MAXN << 1];
int main() {
  st[1] = 0;
  for (int i = 2; i <= MAXK; i++) st[i] = st[i - 1] + (1 << (i - 1));
  int n;
  cin >> n;
  for (int _ = 0; _ < n; _++) {
    string str;
    cin >> str;
    s[_].len = (int)str.size();
    s[_].vis.reset();
    for (int i = 0; i < (int)str.size(); i++) {
      int mask = 0;
      for (int j = i; j < i + MAXK && j < (int)str.size(); j++) {
        mask = mask << 1 | (str[j] - '0');
        s[_].vis.set(st[j - i + 1] + mask);
      }
    }
    if (s[_].len > MAXK) {
      s[_].pre = str.substr(0, MAXK);
      s[_].suf = str.substr(s[_].len - MAXK);
      s[_].len = MAXK;
    } else
      s[_].pre = s[_].suf = str;
  }
  int m;
  cin >> m;
  for (int _ = n; _ < n + m; _++) {
    int a, b;
    cin >> a >> b;
    a--, b--;
    string str = s[a].suf + s[b].pre;
    s[_].len = s[a].len + s[b].len;
    s[_].vis = s[a].vis | s[b].vis;
    for (int i = 0; i < (int)str.size(); i++) {
      int mask = 0;
      for (int j = i; j < i + MAXK && j < (int)str.size(); j++) {
        mask = mask << 1 | (str[j] - '0');
        s[_].vis.set(st[j - i + 1] + mask);
      }
    }
    if (s[_].len > MAXK) {
      if (s[a].len < MAXK)
        s[_].pre = str.substr(0, MAXK);
      else
        s[_].pre = s[a].pre;
      if (s[b].len < MAXK)
        s[_].suf = str.substr((int)str.size() - MAXK);
      else
        s[_].suf = s[b].suf;
      s[_].len = MAXK;
    } else
      s[_].pre = s[_].suf = str;
    int res = 0;
    for (int i = 1; i <= MAXK; i++) {
      bool flag = 1;
      for (int j = st[i]; j < st[i] + (1 << i); j++) flag &= s[_].vis[j];
      if (flag) res = i;
    }
    cout << res << endl;
  }
  return 0;
}