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 JAVA):

Solution:
import java.util.*;

public class Problem868D {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        List<String> strings = new ArrayList<>(n);
        List<HashSet<String>> sets = new ArrayList<>(n);
        for (int i = 0; i < n; i++) {
            strings.add(in.next());
            HashSet<String> set = new HashSet<>();
            subsets(strings.get(i), set);
            sets.add(set);
        }

        int m = in.nextInt();
        for (int i = 0; i < m; i++) {
            int ai = in.nextInt() - 1;
            int bi = in.nextInt() - 1;
            String s = strings.get(ai) + strings.get(bi);
            HashSet<String> subset = new HashSet<>();

            subset.addAll(sets.get(ai));
            subset.addAll(sets.get(bi));

            subsets(s, subset);
            if (s.length() >= 10) {
                String prefix = s.substring(0, 10);
                String suffix = s.substring(s.length() - 10);
                s = prefix + '$' + suffix;
            }
            strings.add(s);
            sets.add(subset);

            int k = 1;
            while (true) {
                boolean valid = true;
                for (int j = 0; j < (1 << k); j++) {
                    char[] t = new char[k];
                    Arrays.fill(t, ' ');
                    for (int l = 0; l < k; l++) {
                        t[l] = "01".charAt(j >> l & 1);
                    }
                    if (!subset.contains(new String(t))) {
                        valid = false;
                        break;
                    }
                }
                if (!valid) {
                    break;
                }
                k++;
            }
            System.out.println(k - 1);
        }
    }

    private static void subsets(String s, Set<String> set) {
        for (int i = 0; i < s.length() + 1; i++) {
            for (int j = i + 1; j < s.length() + 1; j++) {
                if (j - i <= 10) {
                    set.add(s.substring(i, j));
                }
            }
        }
    }
}