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 = 'import sys\nfrom collections import defaultdict as dd\ninput = sys.stdin.readline\nI = lambda : list(map(int,input().split()))\n\nn,a,b=I()\nl=I()\ndic=dd(int)\nfor i in range(n):\n\tdic[l[i]]=1\nbs=[]\npa=dd(int)\nfor i in range(n):\n\tif dic[a-l[i]]==0:\n\t\tbs.append(l[i])\n\telse:\n\t\tpa[l[i]]=a-l[i]\nj=0\nwhile j<len(bs):\t\t\n\tfor i in range(j,len(bs)):\n\t\tcr=bs[i]\n\t\tdic[cr]=2\n\t\tif dic[b-cr]==0:\n\t\t\tprint("NO");return\n\t\tdic[b-cr]=2\n\t\tif dic[a-b+cr]==1:\n\t\t\tdic[a-b+cr]=2\n\t\t\tbs.append(a-b+cr)\n\t\tj+=1\n\t\t#ct=0;vt=a-b+cr\n\t\t#while vt!=pa[pa[vt]]:\n\t\t#\tvt=pa[vt];dic[b-vt]=2\n\t\t#\tdic[vt]=2\nan=[0]*n\nfor i in range(n):\n\tan[i]=dic[l[i]]-1\nprint("YES")\nprint(*an)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: