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 = 'from collections import defaultdict\n\ndef solve(n, a, b, xs):\n    group = [None] * n\n    id_ = {x: i for i, x in enumerate(xs)}\n    if a == b:\n        for x in xs:\n            if a - x not in id_:\n                return False\n        group = [0] * n\n    else:\n        for i, x in enumerate(xs):\n            if group[i] is not None:\n                continue\n            y = a - x\n            z = b - x\n            f1 = y in id_ and group[id_[y]] is None\n            f2 = z in id_ and group[id_[z]] is None\n            if f1 + f2 == 0:\n                return False\n            elif f1 + f2 == 1:\n                g = int(f2)\n                # End of link\n                link = []\n                t = a if f1 else b\n                while x in id_:\n                    link.append(x)\n                    x = t - x\n                    if x + x == t:\n                        break\n                    t = a + b - t\n                # print(link)\n                if len(link) % 2 == 0:\n                    for i, x in enumerate(link):\n                        group[id_[x]] = g\n                elif link[0] * 2 == (b, a)[g]:\n                    for i, x in enumerate(link):\n                        group[id_[x]] = 1 - g\n                elif link[-1] * 2 == (a, b)[g]:\n                    for i, x in enumerate(link):\n                        group[id_[x]] = g\n                else:\n                    # Found invalid link, answer is "NO"\n                    return False\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: 13819