#include <bits/stdc++.h>
using namespace std;
int n, c[25];
int mark[25];
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> c[i];
  sort(c + 1, c + 1 + n);
  reverse(c + 1, c + 1 + n);
  for (int i = 1; i <= n; i++) mark[i] = -1;
  mark[1] = 0;
  for (int i = 1; i <= n; i++) {
    if (c[i] == 1)
      if (mark[i] == -1) {
        cout << "NO";
        return 0;
      } else
        continue;
    int sum = 0;
    int cnt = 0;
    for (int j = i + 1; j <= n; j++) {
      if (mark[j] == -1 && sum + c[j] < c[i]) {
        mark[j] = mark[i] + 1;
        cnt++;
        sum += c[j];
      }
    }
    if (sum + 1 != c[i] || cnt == 1) {
      cout << "NO";
      return 0;
    }
  }
  cout << "YES";
}

### 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 n, c[25];
int mark[25];
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> c[i];
  sort(c + 1, c + 1 + n);
  reverse(c + 1, c + 1 + n);
  for (int i = 1; i <= n; i++) mark[i] = -1;
  mark[1] = 0;
  for (int i = 1; i <= n; i++) {
    if (c[i] == 1)
      if (mark[i] == -1) {
        cout << "NO";
        return 0;
      } else
        continue;
    int sum = 0;
    int cnt = 0;
    for (int j = i + 1; j <= n; j++) {
      if (mark[j] == -1 && sum + c[j] < c[i]) {
        mark[j] = mark[i] + 1;
        cnt++;
        sum += c[j];
      }
    }
    if (sum + 1 != c[i] || cnt == 1) {
      cout << "NO";
      return 0;
    }
  }
  cout << "YES";
}

```