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 PYTHON3):

Solution:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**15
mod = 10**9+7

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()


def main():
    n = I()
    t = [[S(), [set() for _ in range(151)]] for _ in range(n)]
    m = I()
    q = [LI_() for _ in range(m)]
    for c in t:
        s = c[0]
        l = len(s)
        for i in range(1,min(151,l+1)):
            for j in range(l-i+1):
                c[1][i].add(s[j:j+i])

    rr = []
    for li,ri in q:
        l = t[li]
        r = t[ri]
        c = ['',[l[1][i]|r[1][i] for i in range(151)]]
        for i in range(1,min(150,len(l[0])+1)):
            ls = l[0][-i:]
            for j in range(1,min(151-i,len(r[0])+1)):
                c[1][i+j].add(ls+r[0][:j])

        c[0] = l[0] + r[0]
        if len(c[0]) > 300:
            c[0] = c[0][:150] + c[0][-150:]
        t.append(c)
        r = 0
        for i in range(1,151):
            tt = len(c[1][i])
            if tt != 2**i:
                break
            r = i
        rr.append(r)


    return '\n'.join(map(str,rr))


print(main())