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 = '# -*- coding: utf-8 -*-\n\nimport math\nimport collections\nimport bisect\nimport heapq\nimport time\nimport random\n\n"""\ncreated by shhuan at 2017/10/5 15:00\n\n"""\n\nN = int(input())\nS = [\'\']\nfor i in range(N):\n    S.append(input())\nM = int(input())\n\n# t0 = time.time()\n# N = 3\n# S = ["", "00010110000", "110101110101101010101101101110100010000001101101011000010001011000010101", "11100101100111010"]\n# M = 1000\n\nA = [[set() for _ in range(10)] for _ in range(M+N+1)]\nD = collections.defaultdict(int)\n\nfor i in range(1, N+1):\n    for j in range(1, 10):\n        s = S[i]\n        if j > len(s):\n            break\n        for k in range(len(s)-j+1):\n            A[i][j].add(int(s[k:k+j], 2))\n\n        if all(v in A[i][j] for v in range(2**j)):\n            D[i] = j\n\nfor i in range(M):\n    # a, b = random.randint(1, i+N), random.randint(1, i+N)\n    a, b = list(map(int, input().split()))\n    s, sa, sb = S[a] + S[b], S[a], S[b]\n    if len(s) > 30:\n        S.append(s[:10] + s[-10:])\n    else:\n        S.append(s)\n\n    ai = i+N+1\n\n    d = max(D[a], D[b]) + 1\n    for dv in range(d, 10):\n        if len(sa) + len(sb) < dv:\n            break\n        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}\n\n    ans = d-1\n    for dv in range(d, 10):\n        if any(v not in A[ai][dv] for v in range(2**dv)):\n            break\n        ans = dv\n    print(ans)\n    D[ai] = ans\n\n\n\n\n\n# print(time.time() - t0)\n\n\n\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 31133