Little X has n distinct integers: p_1, p_2, ..., p_{n}. He wants to divide all of them into two sets A and B. The following two conditions must be satisfied:  If number x belongs to set A, then number a - x must also belong to set A.  If number x belongs to set B, then number b - x must also belong to set B. 

Help Little X divide the numbers into two sets or determine that it's impossible.


-----Input-----

The first line contains three space-separated integers n, a, b (1 ≤ n ≤ 10^5; 1 ≤ a, b ≤ 10^9). The next line contains n space-separated distinct integers p_1, p_2, ..., p_{n} (1 ≤ p_{i} ≤ 10^9).


-----Output-----

If there is a way to divide the numbers into two sets, then print "YES" in the first line. Then print n integers: b_1, b_2, ..., b_{n} (b_{i} equals either 0, or 1), describing the division. If b_{i} equals to 0, then p_{i} belongs to set A, otherwise it belongs to set B.

If it's impossible, print "NO" (without the quotes).


-----Examples-----
Input
4 5 9
2 3 4 5

Output
YES
0 0 1 1

Input
3 3 4
1 2 4

Output
NO



-----Note-----

It's OK if all the numbers are in the same set, and the other one is empty.

```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 = "class DisjointSet:\n    def __init__(self, n):\n        self._fa = list(range(n))\n\n    def union(self, x, y):\n        x = self.get_father(x)\n        y = self.get_father(y)\n        self._fa[x] = y\n        return y\n\n    def get_father(self, x):\n        y = self._fa[x]\n        if self._fa[y] == y:\n            return y\n        else:\n            z = self._fa[y] = self.get_father(y)\n            return z\n\n    def __repr__(self):\n        return repr([self.get_father(i) for i in range(len(self._fa))])\n\ndef solve(n, a, b, xs):\n    h = {x: i for i, x in enumerate(xs)}\n    if a == b:\n        if all(a - x in h for x in xs):\n            return [0] * n\n        return False\n    g1 = n\n    g2 = n + 1\n    ds = DisjointSet(n + 2)\n\n    for i, x in enumerate(xs):\n        for t in (a, b):\n            if t - x in h:\n                ds.union(i, h[t - x])\n\n    for i, x in enumerate(xs):\n        b1 = (a - x) in h\n        b2 = (b - x) in h\n        if b1 + b2 == 0:\n            return False\n        if b1 + b2 == 1:\n            if b1:\n                ds.union(i, g1)\n            else:\n                ds.union(i, g2)\n            if ds.get_father(g1) == ds.get_father(g2):\n                return False\n    group = [None] * n\n    for i, x in enumerate(xs):\n        f = ds.get_father(i)\n        if f < n:\n            return False\n        group[i] = f - n\n    return group\n\nn, a, b = list(map(int, input().split()))\nxs = list(map(int, input().split()))\ngroup = solve(n, a, b, xs)\nif isinstance(group, list):\n    print('YES')\n    print(' '.join(map(str, group)))\nelse:\n    print('NO')\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 16493