#include <bits/stdc++.h>
using namespace std;
int a[30], num, pp[30], p2;
void search(int k, int x) {
  int i;
  if (x == a[k] - 1) {
    p2 = 1;
    return;
  }
  for (i = k - 1; i >= 1; i--)
    if (pp[i] == 0 && a[i] != a[k] - 1 && a[i] + x < a[k]) {
      pp[i] = 1;
      search(k, a[i] + x);
      if (p2 == 0) {
        pp[i] = 0;
      } else
        return;
    }
}
int main() {
  int t, n, i, p;
  {
    scanf("%d", &n);
    memset(pp, 0, sizeof(pp));
    for (i = 1; i <= n; i++) scanf("%d", &a[i]);
    sort(a + 1, a + 1 + n);
    for (i = 2; i <= n; i++)
      if (a[i] != a[i - 1]) break;
    num = i;
    for (i = num; i <= n; i++) {
      p2 = 0;
      search(i, 0);
      if (p2 == 0) break;
    }
    p = 0;
    for (i = 1; i < n; i++)
      if (pp[i] == 0) p = 1;
    if (p == 1)
      printf("NO\n");
    else
      printf("YES\n");
  }
  return 0;
}

### Prompt

Please formulate a cpp solution to 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>
using namespace std;
int a[30], num, pp[30], p2;
void search(int k, int x) {
  int i;
  if (x == a[k] - 1) {
    p2 = 1;
    return;
  }
  for (i = k - 1; i >= 1; i--)
    if (pp[i] == 0 && a[i] != a[k] - 1 && a[i] + x < a[k]) {
      pp[i] = 1;
      search(k, a[i] + x);
      if (p2 == 0) {
        pp[i] = 0;
      } else
        return;
    }
}
int main() {
  int t, n, i, p;
  {
    scanf("%d", &n);
    memset(pp, 0, sizeof(pp));
    for (i = 1; i <= n; i++) scanf("%d", &a[i]);
    sort(a + 1, a + 1 + n);
    for (i = 2; i <= n; i++)
      if (a[i] != a[i - 1]) break;
    num = i;
    for (i = num; i <= n; i++) {
      p2 = 0;
      search(i, 0);
      if (p2 == 0) break;
    }
    p = 0;
    for (i = 1; i < n; i++)
      if (pp[i] == 0) p = 1;
    if (p == 1)
      printf("NO\n");
    else
      printf("YES\n");
  }
  return 0;
}

```