Vanja and Miksi really like games. After playing one game for a long time, they decided to invent another game!
In this game, they have a sequence $A_1, A_2, \dots, A_N$ and two numbers $Z_1$ and $Z_2$. The rules of the game are as follows:
- The players take turns alternately, starting with Vanja.
- There is an integer $S$; at the beginning, $S = 0$.
- In each turn, the current player must choose an arbitrary element of $A$ and either add that number to $S$ or subtract it from $S$. Each element can be selected multiple times.
- Afterwards, if $S = Z_1$ or $S = Z_2$, the current player (the player who made $S$ equal to $Z_1$ or $Z_2$) is the winner of the game.
- If the game lasts for $10^{10}$ turns, Vanja and Miksi decide to declare it a tie.
Can you help the boys determine the winner of the game? Please note that the game can end in a tie (if nobody can make $S = Z_1$ or $S = Z_2$ in the first $10^{10}$ moves).
Both players play optimally, i.e. if there is a move which guarantees the current player's victory regardless of the other player's moves, the current player will make such a move. If the current player cannot win and there is a move which guarantees that the game will end in a tie, the current player will make such a move.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains three space-separated integers $N$, $Z_1$ and $Z_2$.
- The second line contains $N$ space-separated integers $A_1, A_2, \dots, A_N$.

-----Output-----
- For each test case, print a single line containing one integer — the final result of the game:
- $1$ if Vanja (the first player) has a winning strategy
- $2$ if Miksi (the second player) has a winning strategy
- $0$ if the game ends in a tie

-----Constraints-----
- $1 \le T \le 50$
- $1 \le N \le 50$
- $|Z_1|, |Z_2| \le 10^9$
- $|A_i| \le 10^9$ for each valid $i$

-----Subtasks-----
Subtask #1 (25 points): $N = 2$
Subtask #2 (75 points): original constraints

-----Example Input-----
3
2 6 4
-4 10
1 1 -1
2
2 0 7
3 4

-----Example Output-----
1
0
2

-----Explanation-----
Example case 1: The first player can choose the value $A_1 = -4$, subtract it from $S = 0$ and obtain $S = - (-4) = 4 = Z_2$. The winner is the first player.  
Example case 2: It can be proven that neither player is able to reach $S = Z_1$ or $S = Z_2$. The result is a tie.

```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 sys\nfrom collections import defaultdict as dd\nfrom collections import deque\nfrom fractions import Fraction as f\nfrom copy import *\nfrom bisect import * \nfrom heapq import *\nfrom math import *\nfrom itertools import permutations \n \ndef eprint(*args):\n print(*args, file=sys.stderr)\nzz=1\n \n#sys.setrecursionlimit(10**6)\nif zz:\n input=sys.stdin.readline\nelse:   \n sys.stdin=open('input.txt', 'r')\n sys.stdout=open('all.txt','w')\ndef li():\n return [int(xx) for xx in input().split()]\ndef fli():\n return [float(x) for x in input().split()] \ndef comp(a,b):\n if(a>b):\n  return 2\n return 2 if a==b else 0 \ndef gi():   \n return [xx for x in input().split()]\ndef fi():\n return int(input())\ndef swap(a,i,j):\n a[i],a[j]=a[j],a[i] \ndef si():\n return list(input().rstrip()) \ndef mi():\n return map(int,input().split()) \ndef gh():\n sys.stdout.flush()\ndef graph(n,m):\n for i in range(m):\n  x,y=mi()\n  a[x].append(y)\n  a[y].append(x)\ndef bo(i):\n return ord(i)-ord('a')\n  \n \nt=fi()\nwhile t>0:\n t-=1\n n,z1,z2=mi()\n d={}\n a=li()\n flag=0\n for i in a:\n  d[i]=1\n  d[-i]=1\n  if i==z1 or i==z2 or i==-z1 or i==-z2:\n   flag=1\n   break\n if flag:\n  print(1)\n  continue \n for i in d:\n  p=[i-z1,i-z2]\n  c=1\n  for j in p:\n   if j in d:\n    c*=0\n  flag|=c \n print(0 if flag else 2) "
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 185073