#include <bits/stdc++.h>
using namespace std;
const int MAXN = 8;
const int MAXR = 1;
const int MAXC = 1;
const int MAXBITS = 64;
const int INF = (int)1e9;
int dx[] = {-1, 0, 1, 0};
int dy[] = {0, 1, 0, -1};
int dx8[] = {-1, -1, -1, 0, 0, 1, 1, 1};
int dy8[] = {-1, 0, 1, -1, 1, -1, 0, 1};
priority_queue<int, vector<int>, greater<int>> q1;
priority_queue<int, vector<int>, less<int>> q2;
void l() { ; }
int arr[MAXN];
void printMultiSet(multiset<int> m) {
  l();
  for (auto it : m) {
    cout << it << " ";
  }
}
int main(void) {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  int n, m, k, x;
  cin >> n >> m >> k;
  multiset<int> s1, s2;
  for (int i = 0; i < n; ++i) {
    cin >> x;
    s1.insert(x);
  }
  for (int i = 0; i < m; ++i) {
    cin >> x;
    auto it = s1.find(x);
    if (it != s1.end()) {
      s1.erase(it);
    } else {
      s2.insert(x);
    }
  }
  if (s1.size() == 0) {
    cout << "NO";
    return 0;
  }
  vector<int> v1((s1).begin(), (s1).end());
  vector<int> v2((s2).begin(), (s2).end());
  ;
  ;
  int v1n = v1.size();
  int v2n = v2.size();
  int i = 0;
  int j = 0;
  while (i < v1n && j < v2n) {
    if (v1[i] > v2[j]) {
      j++;
    } else {
      i++;
      j++;
    }
  }
  if (i == v1n) {
    cout << "NO";
    return 0;
  }
  if (j == v2n) {
    cout << "YES";
  }
  return 0;
}

### Prompt

Please provide a CPP coded solution 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 = 8;
const int MAXR = 1;
const int MAXC = 1;
const int MAXBITS = 64;
const int INF = (int)1e9;
int dx[] = {-1, 0, 1, 0};
int dy[] = {0, 1, 0, -1};
int dx8[] = {-1, -1, -1, 0, 0, 1, 1, 1};
int dy8[] = {-1, 0, 1, -1, 1, -1, 0, 1};
priority_queue<int, vector<int>, greater<int>> q1;
priority_queue<int, vector<int>, less<int>> q2;
void l() { ; }
int arr[MAXN];
void printMultiSet(multiset<int> m) {
  l();
  for (auto it : m) {
    cout << it << " ";
  }
}
int main(void) {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  int n, m, k, x;
  cin >> n >> m >> k;
  multiset<int> s1, s2;
  for (int i = 0; i < n; ++i) {
    cin >> x;
    s1.insert(x);
  }
  for (int i = 0; i < m; ++i) {
    cin >> x;
    auto it = s1.find(x);
    if (it != s1.end()) {
      s1.erase(it);
    } else {
      s2.insert(x);
    }
  }
  if (s1.size() == 0) {
    cout << "NO";
    return 0;
  }
  vector<int> v1((s1).begin(), (s1).end());
  vector<int> v2((s2).begin(), (s2).end());
  ;
  ;
  int v1n = v1.size();
  int v2n = v2.size();
  int i = 0;
  int j = 0;
  while (i < v1n && j < v2n) {
    if (v1[i] > v2[j]) {
      j++;
    } else {
      i++;
      j++;
    }
  }
  if (i == v1n) {
    cout << "NO";
    return 0;
  }
  if (j == v2n) {
    cout << "YES";
  }
  return 0;
}

```