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 long long mod = 1000000007;
const unsigned gen_seed =
    std::chrono::system_clock::now().time_since_epoch().count();
std::mt19937_64 gen(gen_seed);
std::vector<int> a[201][20];
string l[201];
string r[201];
const int INF = 1e9;
void mer(std::vector<int>& a, std::vector<int>& b, std::vector<int>& c,
         std::vector<int>& to) {
  int pta = 0, ptb = 0, ptc = 0;
  a.push_back(INF);
  b.push_back(INF);
  c.push_back(INF);
  while (1) {
    if (a[pta] <= b[ptb] && a[pta] <= c[ptc]) {
      if (a[pta] == INF) break;
      to.push_back(a[pta]);
      if (b[ptb] == a[pta]) ptb++;
      if (c[ptc] == a[pta]) ptc++;
      pta++;
    } else if (b[ptb] <= a[pta] && b[ptb] <= c[ptc]) {
      to.push_back(b[ptb]);
      if (b[ptb] == a[pta]) pta++;
      if (c[ptc] == b[ptb]) ptc++;
      ptb++;
    } else {
      to.push_back(c[ptc]);
      if (c[ptc] == a[pta]) pta++;
      if (c[ptc] == b[ptb]) ptb++;
      ptc++;
    }
  }
  a.pop_back();
  b.pop_back();
  c.pop_back();
}
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    string s;
    cin >> s;
    l[i] = s;
    r[i] = s;
    for (int st = 0; st < s.size(); st++)
      for (int en = st; en < s.size(); en++) {
        if (en - st + 1 >= 20) continue;
        int cur = 0;
        for (int j = st; j < en + 1; j++) {
          cur = cur * 2 + (s[j] - '0');
        }
        a[i][en - st + 1].push_back(cur);
      }
    for (int j = 0; j < 20; j++) {
      std::vector<int> fil = a[i][j];
      sort((fil).begin(), (fil).end());
      a[i][j].clear();
      for (int k = 0; k < fil.size(); k++)
        if (k == 0 || fil[k] != fil[k - 1]) a[i][j].push_back(fil[k]);
    }
  }
  for (int i = 0; i < n; i++) {
    if (l[i].size() > 20) l[i] = l[i].substr(0, 20);
    if (r[i].size() > 20) r[i] = r[i].substr(r[i].size() - 20);
  }
  int m;
  cin >> m;
  for (int it = 0; it < m; it++) {
    int x, y;
    cin >> x >> y;
    x--;
    y--;
    l[n + it] = l[x];
    if (l[n + it].size() < 20) l[n + it] += l[y];
    if (l[n + it].size() > 20) l[n + it] = l[n + it].substr(0, 20);
    r[n + it] = r[y];
    if (r[n + it].size() < 20) r[n + it] = r[x] + r[n + it];
    if (r[n + it].size() > 20)
      r[n + it] = r[n + it].substr(r[n + it].size() - 20);
    int sl = r[x].size();
    int sr = l[y].size();
    for (int len = 1; len < 20; len++) {
      std::vector<int> addgr;
      for (int tl = 1; tl < len; tl++) {
        int tr = len - tl;
        if (tl > sl || tr > sr) continue;
        string p = r[x].substr(sl - tl) + l[y].substr(0, tr);
        int cur = 0;
        for (auto cx : p) cur = cur * 2 + (cx - '0');
        addgr.push_back(cur);
      }
      sort((addgr).begin(), (addgr).end());
      std::vector<int> add;
      for (int i = 0; i < addgr.size(); i++)
        if (i == 0 || addgr[i] != addgr[i - 1]) add.push_back(addgr[i]);
      mer(a[x][len], a[y][len], add, a[n + it][len]);
    }
    int k = 1;
    while (a[n + it][k].size() == (1 << k)) k++;
    printf("%d\n", k - 1);
  }
}