#include <bits/stdc++.h>
using namespace std;
int n, a[25], tot;
int st[12], top;
void dfs(int d) {
  if (d > tot) cout << "YES", exit(0);
  for (int i = 1; i <= top; ++i) {
    if (st[i] >= a[d] && (st[i] > a[d] || st[i] != a[i] - 1)) {
      st[i] -= a[d];
      st[++top] = a[d] - 1;
      dfs(d + 1);
      st[i] += a[d];
      --top;
    }
  }
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    if (a[i] == 2) return cout << "NO", 0;
    if (a[i] > 1) ++tot;
  }
  sort(a + 1, a + n + 1, greater<int>());
  if (a[1] != n) return cout << "NO", 0;
  st[top = 1] = a[1] - 1;
  dfs(2);
  cout << "NO";
}

### Prompt

Construct a CPP code solution to the problem outlined:

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, a[25], tot;
int st[12], top;
void dfs(int d) {
  if (d > tot) cout << "YES", exit(0);
  for (int i = 1; i <= top; ++i) {
    if (st[i] >= a[d] && (st[i] > a[d] || st[i] != a[i] - 1)) {
      st[i] -= a[d];
      st[++top] = a[d] - 1;
      dfs(d + 1);
      st[i] += a[d];
      --top;
    }
  }
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    if (a[i] == 2) return cout << "NO", 0;
    if (a[i] > 1) ++tot;
  }
  sort(a + 1, a + n + 1, greater<int>());
  if (a[1] != n) return cout << "NO", 0;
  st[top = 1] = a[1] - 1;
  dfs(2);
  cout << "NO";
}

```