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 = "parent = []\nranks = []\n\n\ndef make_set(n):\n    nonlocal parent, ranks\n    parent = [i for i in range(n + 5)]\n    ranks = [0 for i in range(n + 5)]\n\n\ndef find_set(u):\n    if parent[u] != u:\n        parent[u] = find_set(parent[u])\n    else:\n        parent[u] = u\n    return parent[u]\n\n\ndef union_set(u, v):\n    up = find_set(u)\n    vp = find_set(v)\n\n    if ranks[up] > ranks[vp]:\n        parent[vp] = up\n    elif ranks[up] < ranks[vp]:\n        parent[up] = vp\n    else:\n        parent[up] = vp\n        ranks[vp] += 1\n\n\ndef solution():\n    set_indicators = dict()\n    n, a, b = list(map(int, input().split()))\n    numbers = list(map(int, input().split()))\n    A = n + 1\n    B = A + 1\n\n    make_set(n)\n    for i in range(n):\n        set_indicators[numbers[i]] = i\n\n    for i in range(n):\n        if set_indicators.get(a - numbers[i]) is not None:\n            union_set(i, set_indicators.get(a - numbers[i]))\n        else:\n            union_set(i, B)\n        if set_indicators.get(b - numbers[i]) is not None:\n            union_set(i, set_indicators.get(b - numbers[i]))\n        else:\n            union_set(i, A)\n    if find_set(A) == find_set(B):\n        print('NO')\n        return\n\n    print('YES')\n    print(''.join('1 ' if find_set(i) == find_set(n + 2) else '0 ' for i in range(n)))\n\n\nsolution()\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: