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B. Fish Weight

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIt 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.

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