It is known that there are k fish species in the polar ocean, numbered from 1 to k. They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the i-th type of fish be w_{i}, then 0 < w_1 ≤ w_2 ≤ ... ≤ w_{k} holds.

Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights w_{i} (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?


-----Input-----

The first line contains three integers n, m, k (1 ≤ n, m ≤ 10^5, 1 ≤ k ≤ 10^9) — the number of fish caught by Alice and Bob respectively, and the number of fish species.

The second line contains n integers each from 1 to k, the list of fish type caught by Alice. The third line contains m integers each from 1 to k, the list of fish type caught by Bob.

Note that one may have caught more than one fish for a same species.


-----Output-----

Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.


-----Examples-----
Input
3 3 3
2 2 2
1 1 3

Output
YES

Input
4 7 9
5 2 7 3
3 5 2 7 3 8 7

Output
NO



-----Note-----

In the first sample, if w_1 = 1, w_2 = 2, w_3 = 2.5,  then Alice has a total of 2 + 2 + 2 = 6 weight units, while Bob only has 1 + 1 + 2.5 = 4.5.

In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish.

```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 copy\nimport itertools\nimport string\nimport sys\n\n###\n\ndef powmod(x, p, m):\n\tif p <= 0:\n\t\treturn 1\n\tif p <= 1:\n\t\treturn x%m\n\treturn powmod(x*x%m, p//2, m) * (x%m)**(p%2) % m\n\n###\n\ndef to_basex(num, x):\n\twhile num > 0:\n\t\tyield num % x\n\t\tnum //= x\n\ndef from_basex(it, x):\n\tret = 0\n\tp = 1\n\tfor d in it:\n\t\tret += d*p\n\t\tp *= x\n\treturn ret\n\n###\n\ndef core():\n\t_ = input()\n\ta = [int(x) for x in input().split()]\n\tr = [int(x) for x in input().split()]\n\ta.sort()\n\tr.sort()\n\t# print(a)\n\t# print(r)\n\t\n\twhile (\n\t\tlen(a) > 0 and\n\t\tlen(r) > 0 and\n\t\tr[-1] >= a[-1]\n\t):\n\t\ta.pop()\n\t\tr.pop()\n\t\n\t\n\tans = "YES" if len(a) > 0 else "NO"\n\tprint(ans)\n\n\ncore()\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 177174