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 = "import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools\n\nsys.setrecursionlimit(10**7)\ninf = 10**20\neps = 1.0 / 10**15\nmod = 10**9+7\n\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\ndef LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]\ndef LF(): return [float(x) for x in sys.stdin.readline().split()]\ndef LS(): return sys.stdin.readline().split()\ndef I(): return int(sys.stdin.readline())\ndef F(): return float(sys.stdin.readline())\ndef S(): return input()\n\n\ndef main():\n    n = I()\n    t = [[S(), [set() for _ in range(151)]] for _ in range(n)]\n    m = I()\n    q = [LI_() for _ in range(m)]\n    for c in t:\n        s = c[0]\n        l = len(s)\n        for i in range(1,min(151,l+1)):\n            for j in range(l-i+1):\n                c[1][i].add(s[j:j+i])\n\n    rr = []\n    for li,ri in q:\n        l = t[li]\n        r = t[ri]\n        c = ['',[l[1][i]|r[1][i] for i in range(151)]]\n        for i in range(1,min(150,len(l[0])+1)):\n            ls = l[0][-i:]\n            for j in range(1,min(151-i,len(r[0])+1)):\n                c[1][i+j].add(ls+r[0][:j])\n\n        c[0] = l[0] + r[0]\n        if len(c[0]) > 300:\n            c[0] = c[0][:150] + c[0][-150:]\n        t.append(c)\n        r = 0\n        for i in range(1,151):\n            tt = len(c[1][i])\n            if tt != 2**i:\n                break\n            r = i\n        rr.append(r)\n\n\n    return '\\n'.join(map(str,rr))\n\n\nprint(main())\n\n\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 446050