#include <bits/stdc++.h>
int a[100000], b[100000];
int tata(int p) { return (p - 1) >> 1; }
int fiust(int p) { return (p << 1) + 1; }
int fiudr(int p) { return (p << 1) + 2; }
void swap(int a, int b, int v[]) {
  int aux = v[a];
  v[a] = v[b];
  v[b] = aux;
}
void coborare(int p, int n, int v[]) {
  int f = 1, q;
  while ((f == 1) && (fiust(p) < n)) {
    q = fiust(p);
    if ((fiudr(p) < n) && (v[fiudr(p)] > v[q])) {
      q = fiudr(p);
    }
    if (v[q] > v[p]) {
      swap(p, q, v);
      p = q;
    } else {
      f = 0;
    }
  }
}
void heapify(int v[], int n) {
  int i;
  for (i = tata(n - 1); i >= 0; i--) {
    coborare(i, n, v);
  }
}
void heapSort(int v[], int n) {
  while (n > 1) {
    n--;
    swap(0, n, v);
    coborare(0, n, v);
  }
}
int main() {
  int n, m, k, i, j, f, s;
  fscanf(stdin, "%d%d%d", &n, &m, &k);
  for (i = 0; i < n; i++) {
    fscanf(stdin, "%d", &a[i]);
  }
  for (i = 0; i < m; i++) {
    fscanf(stdin, "%d", &b[i]);
  }
  heapify(a, n);
  heapSort(a, n);
  heapify(b, m);
  heapSort(b, m);
  f = 0;
  s = 0;
  i = n - 1;
  j = m - 1;
  while ((i >= 0) && (j >= 0)) {
    if (a[i] == b[j]) {
      i--;
      j--;
    } else if (a[i] > b[j]) {
      s--;
      i--;
    } else {
      s++;
      j--;
    }
    if (s < 0) {
      f = 1;
    }
  }
  while (i >= 0) {
    s--;
    i--;
  }
  while (j >= 0) {
    s++;
    j--;
  }
  if (s < 0) {
    f = 1;
  }
  if (f == 1) {
    fprintf(stdout, "YES\n");
  } else {
    fprintf(stdout, "NO\n");
  }
  fclose(stdin);
  fclose(stdout);
  return 0;
}

### Prompt

In CPP, your task is to solve the following problem:

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>
int a[100000], b[100000];
int tata(int p) { return (p - 1) >> 1; }
int fiust(int p) { return (p << 1) + 1; }
int fiudr(int p) { return (p << 1) + 2; }
void swap(int a, int b, int v[]) {
  int aux = v[a];
  v[a] = v[b];
  v[b] = aux;
}
void coborare(int p, int n, int v[]) {
  int f = 1, q;
  while ((f == 1) && (fiust(p) < n)) {
    q = fiust(p);
    if ((fiudr(p) < n) && (v[fiudr(p)] > v[q])) {
      q = fiudr(p);
    }
    if (v[q] > v[p]) {
      swap(p, q, v);
      p = q;
    } else {
      f = 0;
    }
  }
}
void heapify(int v[], int n) {
  int i;
  for (i = tata(n - 1); i >= 0; i--) {
    coborare(i, n, v);
  }
}
void heapSort(int v[], int n) {
  while (n > 1) {
    n--;
    swap(0, n, v);
    coborare(0, n, v);
  }
}
int main() {
  int n, m, k, i, j, f, s;
  fscanf(stdin, "%d%d%d", &n, &m, &k);
  for (i = 0; i < n; i++) {
    fscanf(stdin, "%d", &a[i]);
  }
  for (i = 0; i < m; i++) {
    fscanf(stdin, "%d", &b[i]);
  }
  heapify(a, n);
  heapSort(a, n);
  heapify(b, m);
  heapSort(b, m);
  f = 0;
  s = 0;
  i = n - 1;
  j = m - 1;
  while ((i >= 0) && (j >= 0)) {
    if (a[i] == b[j]) {
      i--;
      j--;
    } else if (a[i] > b[j]) {
      s--;
      i--;
    } else {
      s++;
      j--;
    }
    if (s < 0) {
      f = 1;
    }
  }
  while (i >= 0) {
    s--;
    i--;
  }
  while (j >= 0) {
    s++;
    j--;
  }
  if (s < 0) {
    f = 1;
  }
  if (f == 1) {
    fprintf(stdout, "YES\n");
  } else {
    fprintf(stdout, "NO\n");
  }
  fclose(stdin);
  fclose(stdout);
  return 0;
}

```