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.
a, b, _c = list(map(int, input().split()))
af = list(map(int, input().split()))
bf = list(map(int, input().split()))

af.sort(reverse = True)
bf.sort(reverse = True)

aflen = len(af)
bflen = len(bf)

i = 0
j = 0
cnt = 0
while i < aflen and j < bflen:
    if af[i] > bf[j]:
        cnt += 1
        i += 1
    elif af[i] < bf[j]:
        cnt -= 1
        j += 1
    else:
        i += 1
        j += 1
    if cnt > 0:
        print("YES")
        break
else:
    cnt += aflen - i
    if cnt > 0:
        print("YES")
    else:
        print("NO")




a, b, _c = list(map(int, input().split()))
af = list(map(int, input().split()))
bf = list(map(int, input().split()))

af.sort(reverse = True)
bf.sort(reverse = True)

aflen = len(af)
bflen = len(bf)

i = 0
j = 0
cnt = 0
while i < aflen and j < bflen:
    if af[i] > bf[j]:
        cnt += 1
        i += 1
    elif af[i] < bf[j]:
        cnt -= 1
        j += 1
    else:
        i += 1
        j += 1
    if cnt > 0:
        print("YES")
        break
else:
    cnt += aflen - i
    if cnt > 0:
        print("YES")
    else:
        print("NO")



