#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 5;
vector<pair<long long, int> > v;
bool cmp(pair<long long, int> p1, pair<long long, int> p2) {
  if (p1.first != p2.first) return p1.first > p2.first;
  return p1.second > p2.second;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, m;
  long long k;
  cin >> n >> m >> k;
  map<long long, int> pos, neg;
  for (int i = 0; i < n; i++) {
    long long x;
    cin >> x;
    pos[x]++;
  }
  for (int i = 0; i < m; i++) {
    long long x;
    cin >> x;
    neg[x]++;
  }
  for (map<long long, int>::iterator it = pos.begin(); it != pos.end(); it++) {
    long long minn = min(pos[it->first], neg[it->first]);
    pos[it->first] -= minn;
    neg[it->first] -= minn;
  }
  for (map<long long, int>::iterator it = pos.begin(); it != pos.end(); it++) {
    if (it->second == 0) continue;
    for (int j = 0; j < it->second; j++) {
      v.push_back(make_pair(it->first, 2));
    }
  }
  for (map<long long, int>::iterator it = neg.begin(); it != neg.end(); it++) {
    if (it->second == 0) continue;
    for (int j = 0; j < it->second; j++) {
      v.push_back(make_pair(it->first, 1));
    }
  }
  sort(v.begin(), v.end(), cmp);
  int cnt_neg = 0;
  for (int i = 0; i < v.size(); i++) {
    if (v[i].second == 1)
      cnt_neg++;
    else
      cnt_neg--;
    if (cnt_neg < 0) {
      break;
    }
  }
  if (cnt_neg < 0) {
    cout << "YES\n";
  } else
    cout << "NO\n";
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 5;
vector<pair<long long, int> > v;
bool cmp(pair<long long, int> p1, pair<long long, int> p2) {
  if (p1.first != p2.first) return p1.first > p2.first;
  return p1.second > p2.second;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, m;
  long long k;
  cin >> n >> m >> k;
  map<long long, int> pos, neg;
  for (int i = 0; i < n; i++) {
    long long x;
    cin >> x;
    pos[x]++;
  }
  for (int i = 0; i < m; i++) {
    long long x;
    cin >> x;
    neg[x]++;
  }
  for (map<long long, int>::iterator it = pos.begin(); it != pos.end(); it++) {
    long long minn = min(pos[it->first], neg[it->first]);
    pos[it->first] -= minn;
    neg[it->first] -= minn;
  }
  for (map<long long, int>::iterator it = pos.begin(); it != pos.end(); it++) {
    if (it->second == 0) continue;
    for (int j = 0; j < it->second; j++) {
      v.push_back(make_pair(it->first, 2));
    }
  }
  for (map<long long, int>::iterator it = neg.begin(); it != neg.end(); it++) {
    if (it->second == 0) continue;
    for (int j = 0; j < it->second; j++) {
      v.push_back(make_pair(it->first, 1));
    }
  }
  sort(v.begin(), v.end(), cmp);
  int cnt_neg = 0;
  for (int i = 0; i < v.size(); i++) {
    if (v[i].second == 1)
      cnt_neg++;
    else
      cnt_neg--;
    if (cnt_neg < 0) {
      break;
    }
  }
  if (cnt_neg < 0) {
    cout << "YES\n";
  } else
    cout << "NO\n";
  return 0;
}

```