#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:102400000,102400000")
using namespace std;
int a[26], sum[26];
int n;
int dfs(int p) {
  int i, j, tem;
  if (a[p] == 1) return 1;
  for (i = n; i > p; i--)
    if (sum[i] + a[p] < a[i] && a[p] < a[i] - 1) {
      sum[i] += a[p];
      if (dfs(p - 1)) return 1;
      sum[i] -= a[p];
    }
  return 0;
}
int cau() {
  int i, j, tem;
  int num1 = 0;
  sort(a + 1, a + 1 + n);
  for (i = 1; i <= n; i++) {
    if (a[i] == 1) num1++;
    if (a[i] == 2) return 0;
  }
  if (n - num1 + 1 > num1) return 0;
  if (a[n] != n) return 0;
  memset(sum, 0, sizeof(sum));
  if (n == 1) return 1;
  return dfs(n - 1);
}
int main() {
  int i, j, tem;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) scanf("%d", &a[i]);
  int ans = cau();
  if (ans)
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}

### Prompt

Create a solution in Cpp for the following problem:

Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. 

Iahub asks Iahubina: can you build a rooted tree, such that

  * each internal node (a node with at least one son) has at least two sons; 
  * node i has ci nodes in its subtree? 



Iahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.

Input

The first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents ci (1 ≤ ci ≤ n).

Output

Output on the first line "YES" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output "NO" (without quotes). 

Examples

Input

4
1 1 1 4


Output

YES

Input

5
1 1 5 2 1


Output

NO

### Response

```cpp
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:102400000,102400000")
using namespace std;
int a[26], sum[26];
int n;
int dfs(int p) {
  int i, j, tem;
  if (a[p] == 1) return 1;
  for (i = n; i > p; i--)
    if (sum[i] + a[p] < a[i] && a[p] < a[i] - 1) {
      sum[i] += a[p];
      if (dfs(p - 1)) return 1;
      sum[i] -= a[p];
    }
  return 0;
}
int cau() {
  int i, j, tem;
  int num1 = 0;
  sort(a + 1, a + 1 + n);
  for (i = 1; i <= n; i++) {
    if (a[i] == 1) num1++;
    if (a[i] == 2) return 0;
  }
  if (n - num1 + 1 > num1) return 0;
  if (a[n] != n) return 0;
  memset(sum, 0, sizeof(sum));
  if (n == 1) return 1;
  return dfs(n - 1);
}
int main() {
  int i, j, tem;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) scanf("%d", &a[i]);
  int ans = cau();
  if (ans)
    printf("YES\n");
  else
    printf("NO\n");
  return 0;
}

```