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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'from sys import stdin, stdout\nk = 20\ndef findAllStrings(s):\n    n = len(s)\n    sdict = {}\n    for i in range(1,k+1):\n        sdict[i]=set()\n        for x in range(n-i+1):\n            sdict[i].add(s[x:x+i])\n    return sdict\nn = int(stdin.readline().rstrip())\nstrdict = []\nstringend = []\nstringbegin = []\nfor i in range(n):\n    s = stdin.readline().rstrip()\n    strdict.append(findAllStrings(s))\n    if len(s)<k:\n        stringend.append(s)\n        stringbegin.append(s)\n    else:\n        stringend.append(s[-20:])\n        stringbegin.append(s[:20])\nm = int(stdin.readline().rstrip())\nfor _ in range(m):\n    a,b = list(map(int,stdin.readline().rstrip().split()))\n    a-=1\n    b-=1\n    sdict1 = findAllStrings(stringend[a]+stringbegin[b])\n    sdict2 = strdict[a]\n    sdict3 = strdict[b]\n    sdict={}\n    for i in range(1,k+1):\n        sdict[i] = sdict1[i]|sdict2[i]|sdict3[i]\n    strdict.append(sdict)\n    for i in range(1,k+1):\n        if len(sdict[i])!=2**i:\n            print(i-1)\n            break\n    if len(stringbegin[a])<k and len(stringbegin[a])+len(stringbegin[b])<k:\n        stringbegin.append(stringbegin[a]+stringbegin[b])\n    elif len(stringbegin[a])<k:\n        s = stringbegin[a]+stringbegin[b]\n        stringbegin.append(s[:k])\n    else:\n        stringbegin.append(stringbegin[a])\n        \n    if len(stringend[b])<k and len(stringend[a])+len(stringend[b])<k:\n        stringend.append(stringend[a]+stringend[b])\n    elif len(stringend[b])<k:\n        s = stringend[a]+stringend[b]\n        stringend.append(s[-k:])\n    else:\n        stringend.append(stringend[b])\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 54700