#include <bits/stdc++.h>
using namespace std;
const int N = 1003;
int n, h, len;
int c[N], sum[N], p[N];
void go(int v) {
  if (v == len - 1) {
    cout << "YES\n";
    exit(0);
  }
  for (int i = v + 1; i < len; i++) {
    p[v] = i;
    sum[i] += c[v];
    if (sum[i] < c[i] && c[i] > c[v] + 1) go(v + 1);
    sum[i] -= c[v];
  }
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> h;
    if (n == 1 && h == 1) {
      cout << "YES\n";
      return 0;
    }
    if (h == 2) {
      cout << "NO\n";
      return 0;
    }
    if (h != 1) c[len++] = h;
  }
  sort(c, c + len);
  if (c[len - 1] != n || len > 11) {
    cout << "NO\n";
    return 0;
  }
  if (n == 1) {
    cout << "YES\n";
    return 0;
  }
  go(0);
  cout << "NO\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;
const int N = 1003;
int n, h, len;
int c[N], sum[N], p[N];
void go(int v) {
  if (v == len - 1) {
    cout << "YES\n";
    exit(0);
  }
  for (int i = v + 1; i < len; i++) {
    p[v] = i;
    sum[i] += c[v];
    if (sum[i] < c[i] && c[i] > c[v] + 1) go(v + 1);
    sum[i] -= c[v];
  }
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> h;
    if (n == 1 && h == 1) {
      cout << "YES\n";
      return 0;
    }
    if (h == 2) {
      cout << "NO\n";
      return 0;
    }
    if (h != 1) c[len++] = h;
  }
  sort(c, c + len);
  if (c[len - 1] != n || len > 11) {
    cout << "NO\n";
    return 0;
  }
  if (n == 1) {
    cout << "YES\n";
    return 0;
  }
  go(0);
  cout << "NO\n";
  return 0;
}

```