Fish Weight

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 ≤ 10⁵, 1 ≤ k ≤ 10⁹) — 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.

Solution:

#include <iostream>
#include <iomanip>
#include <stdio.h>
#include <set>
#include <vector>
#include <map>
#include <cmath>
#include <algorithm>
#include <memory.h>
#include <string>
#include <sstream>

using namespace std;

int a[4444444], b[4444444];

int main() {
int n, m, k;
scanf("%d %d %d", &n, &m, &k);
for (int i=0;i<n;i++) scanf("%d", a+i);
  for (int i=0;i<m;i++) scanf("%d", b+i);
  sort(a, a+n);
  sort(b, b+m);
  int ok = 0;
  if (n > m) ok = 1; else {
for (int i=0;i<n;i++)
      if (a[i] > b[m-n+i]) ok = 1;
}
if (ok) printf("YES\n");
else printf("NO\n");
return 0;
}