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 wi, then 0 < w1 ≤ w2 ≤ ... ≤ wk 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 wi (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 w1 = 1, w2 = 2, w3 = 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.
#include <bits/stdc++.h>
using namespace std;
template <class T>
inline T __in() {
  T v;
  cin >> v;
  return v;
}
int main() {
  ios_base::sync_with_stdio(0);
  int n = __in<int>(), m = __in<int>(), k = __in<int>();
  map<int, int> aa, bb;
  for (__typeof(n) i = 0; i < (n); i++) aa[__in<int>()]++;
  for (__typeof(m) j = 0; j < (m); j++) bb[__in<int>()]++;
  for (__typeof((aa).begin()) it = (aa).begin(); it != (aa).end(); it++) {
    int am = it->second;
    am = min(am, bb[it->first]);
    aa[it->first] -= am;
    bb[it->first] -= am;
  }
  vector<pair<int, int> > A, B;
  for (__typeof((aa).begin()) it = (aa).begin(); it != (aa).end(); it++) {
    if (!it->second) continue;
    A.push_back(*it);
  }
  for (__typeof((bb).begin()) it = (bb).begin(); it != (bb).end(); it++) {
    if (!it->second) continue;
    B.push_back(*it);
  }
  sort(A.begin(), A.end());
  sort(B.begin(), B.end());
  if (A == B) {
    cout << "NO" << endl;
    return 0;
  }
  int i = 0, j = 0;
  int sm = 0;
  while (i < ((int)A.size()) && j < ((int)B.size())) {
    if (A[i].first > B[j].first)
      j++;
    else if (A[i].first < B[j].first && A[i].second >= B[j].second) {
      A[i].second -= B[j].second;
      if (!A[i].second) i++;
      j++;
    } else {
      B[j].second -= A[i].second;
      if (!B[j].second) j++;
      i++;
    }
  }
  if (j == ((int)B.size()) && i < ((int)A.size()))
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
  return 0;
}
