You are given n strings s_1, s_2, ..., s_{n} 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 s_{a}_{i}s_{b}_{i} is saved into a new string s_{n} + 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 2^{k} 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 s_1, s_2, ..., s_{n} (1 ≤ |s_{i}| ≤ 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 a_{i} abd b_{i} (1 ≤ a_{i}, b_{i} ≤ n + i - 1) — the number of strings that are concatenated to form s_{n} + 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.

Difficulty: competition

Starter code:

Solutions:
from sys import stdin, stdout

K = 20

def findAllStrings(s):
    n = len(s)
    sDict = {}
    for i in range(1,K+1):
        sDict[i]=set()
        for x in range(n-i+1):
            sDict[i].add(s[x:x+i])
    return sDict

n = int(stdin.readline().rstrip())
stringDicts = []
stringEnd = []
stringBegin = []

for i in range(n):
    s = stdin.readline().rstrip()
    stringDicts.append(findAllStrings(s))
    if len(s)<K:
        stringEnd.append(s)
        stringBegin.append(s)
    else:
        stringEnd.append(s[-20:])
        stringBegin.append(s[:20])

m = int(stdin.readline().rstrip())

for _ in range(m):
    a,b = list(map(int,stdin.readline().rstrip().split()))
    a-=1
    b-=1
    
    sDict1 = findAllStrings(stringEnd[a]+stringBegin[b])
    sDict2 = stringDicts[a]
    sDict3 = stringDicts[b]
    sDict={}
    for i in range(1,K+1):
        sDict[i] = sDict1[i]|sDict2[i]|sDict3[i]
    stringDicts.append(sDict)
    for i in range(1,K+1):
        if len(sDict[i])!=2**i:
            print(i-1)
            break
                
    if len(stringBegin[a])<K and len(stringBegin[a])+len(stringBegin[b])<K:
        stringBegin.append(stringBegin[a]+stringBegin[b])
    elif len(stringBegin[a])<K:
        s = stringBegin[a]+stringBegin[b]
        stringBegin.append(s[:K])
    else:
        stringBegin.append(stringBegin[a])
        
    if len(stringEnd[b])<K and len(stringEnd[a])+len(stringEnd[b])<K:
        stringEnd.append(stringEnd[a]+stringEnd[b])
    elif len(stringEnd[b])<K:
        s = stringEnd[a]+stringEnd[b]
        stringEnd.append(s[-K:])
    else:
        stringEnd.append(stringEnd[b])



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())




from sys import stdin, stdout
k = 20
def findAllStrings(s):
    n = len(s)
    sdict = {}
    for i in range(1,k+1):
        sdict[i]=set()
        for x in range(n-i+1):
            sdict[i].add(s[x:x+i])
    return sdict
n = int(stdin.readline().rstrip())
strdict = []
stringend = []
stringbegin = []
for i in range(n):
    s = stdin.readline().rstrip()
    strdict.append(findAllStrings(s))
    if len(s)<k:
        stringend.append(s)
        stringbegin.append(s)
    else:
        stringend.append(s[-20:])
        stringbegin.append(s[:20])
m = int(stdin.readline().rstrip())
for _ in range(m):
    a,b = list(map(int,stdin.readline().rstrip().split()))
    a-=1
    b-=1
    sdict1 = findAllStrings(stringend[a]+stringbegin[b])
    sdict2 = strdict[a]
    sdict3 = strdict[b]
    sdict={}
    for i in range(1,k+1):
        sdict[i] = sdict1[i]|sdict2[i]|sdict3[i]
    strdict.append(sdict)
    for i in range(1,k+1):
        if len(sdict[i])!=2**i:
            print(i-1)
            break
    if len(stringbegin[a])<k and len(stringbegin[a])+len(stringbegin[b])<k:
        stringbegin.append(stringbegin[a]+stringbegin[b])
    elif len(stringbegin[a])<k:
        s = stringbegin[a]+stringbegin[b]
        stringbegin.append(s[:k])
    else:
        stringbegin.append(stringbegin[a])
        
    if len(stringend[b])<k and len(stringend[a])+len(stringend[b])<k:
        stringend.append(stringend[a]+stringend[b])
    elif len(stringend[b])<k:
        s = stringend[a]+stringend[b]
        stringend.append(s[-k:])
    else:
        stringend.append(stringend[b])


from math import log
n = int(input())
p = [bin(p)[2:] for p in range(0,512)]
def mset(s):
    ss = set()
    for k in range(0,10):
        for pi in range(0,2 ** k):
            cs = p[pi]
            cs = (k - len(cs)) * "0" + cs
            if cs in s:
                ss.add(cs)
    return ss
def q(s):
    for k in range(0,10):
        for pi in range(0,2 ** k):
            cs = p[pi]
            cs = (k - len(cs)) * "0" + cs
            if not cs in s:
                return k - 1
s = [[v[:9], v[-9:], mset(v)] for v in [input() for i in range(n)]]
for qa, qb in [[int(v) - 1 for v in input().split()] for i in range(int(input()))]:
    v = [s[qa][0], s[qb][1], mset(s[qa][1] + s[qb][0]) | s[qa][2] | s[qb][2]]
    if len(v[0]) < 9:
        v[0] = (v[0] + s[qb][0])[:9]
    if len(v[1]) < 9:
        v[1] = (s[qa][1] + s[qb][1])[-9:]
    s += [v]
    print(max(q(v[2]),0))



# -*- coding: utf-8 -*-

import math
import collections
import bisect
import heapq
import time
import random

"""
created by shhuan at 2017/10/5 15:00

"""

N = int(input())
S = ['']
for i in range(N):
    S.append(input())
M = int(input())

# t0 = time.time()
# N = 3
# S = ["", "00010110000", "110101110101101010101101101110100010000001101101011000010001011000010101", "11100101100111010"]
# M = 1000

A = [[set() for _ in range(10)] for _ in range(M+N+1)]
D = collections.defaultdict(int)

for i in range(1, N+1):
    for j in range(1, 10):
        s = S[i]
        if j > len(s):
            break
        for k in range(len(s)-j+1):
            A[i][j].add(int(s[k:k+j], 2))

        if all(v in A[i][j] for v in range(2**j)):
            D[i] = j

for i in range(M):
    # a, b = random.randint(1, i+N), random.randint(1, i+N)
    a, b = list(map(int, input().split()))
    s, sa, sb = S[a] + S[b], S[a], S[b]
    if len(s) > 30:
        S.append(s[:10] + s[-10:])
    else:
        S.append(s)

    ai = i+N+1

    d = max(D[a], D[b]) + 1
    for dv in range(d, 10):
        if len(sa) + len(sb) < dv:
            break
        A[ai][dv] = A[a][dv] | A[b][dv] | {int(v, 2) for v in {sa[-i:] + sb[:dv-i] for i in range(1, dv+1)} if len(v) == dv}

    ans = d-1
    for dv in range(d, 10):
        if any(v not in A[ai][dv] for v in range(2**dv)):
            break
        ans = dv
    print(ans)
    D[ai] = ans





# print(time.time() - t0)






from math import log
n = int(input())
p = [bin(p)[2:] for p in range(0,512)]
def mset(s):
    ss = set()
    for k in range(0,10):
        for pi in range(0,2 ** k):
            cs = p[pi]
            cs = (k - len(cs)) * "0" + cs
            if cs in s:
                ss.add(cs)
    return ss
def q(s):
    for k in range(0,10):
        for pi in range(0,2 ** k):
            cs = p[pi]
            cs = (k - len(cs)) * "0" + cs
            if not cs in s:
                return k - 1
s = [[v[:9], v[-9:], mset(v)] for v in [input() for i in range(n)]]
for qa, qb in [[int(v) - 1 for v in input().split()] for i in range(int(input()))]:
    v = [s[qa][0], s[qb][1], mset(s[qa][1] + s[qb][0]) | s[qa][2] | s[qb][2]]
    if len(v[0]) < 9:
        v[0] = (v[0] + s[qb][0])[:9]
    if len(v[1]) < 9:
        v[1] = (s[qa][1] + s[qb][1])[-9:]
    s += [v]
    print(max(q(v[2]),0))