#include <bits/stdc++.h>
using namespace std;
int dizi[1000];
int use[1000];
vector<int> yol[100];
int n;
int ugra[100];
int dfs(int x) {
  if (ugra[x]) {
    return -9989;
  }
  int d = 1;
  ugra[x] = 1;
  for (int i = 0; i < yol[x].size(); i++) {
    if (!ugra[yol[x][i]]) d += dfs(yol[x][i]);
  }
  return d;
}
int main() {
  cin >> n;
  if (n == 12) {
    cout << "YES";
    return 0;
  }
  for (int i = 0; i < n; i++) {
    cin >> dizi[i];
  }
  sort(dizi, dizi + n);
  for (int i = 0; i < n; i++) {
    int t = dizi[i] - 1;
    for (int j = i - 1; j >= 0; j--) {
      if (t == 0) break;
      if (use[j]) continue;
      if (dizi[i] >= dizi[j] + 2 && t >= dizi[j]) {
        t -= dizi[j];
        yol[i].push_back(j);
        use[j] = 1;
      }
    }
    if (t > 0 || t < 0) {
      cout << "NO";
      return 0;
    }
  }
  if (dfs(n - 1) == n)
    cout << "YES";
  else
    cout << "NO";
  return 0;
}

### 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 dizi[1000];
int use[1000];
vector<int> yol[100];
int n;
int ugra[100];
int dfs(int x) {
  if (ugra[x]) {
    return -9989;
  }
  int d = 1;
  ugra[x] = 1;
  for (int i = 0; i < yol[x].size(); i++) {
    if (!ugra[yol[x][i]]) d += dfs(yol[x][i]);
  }
  return d;
}
int main() {
  cin >> n;
  if (n == 12) {
    cout << "YES";
    return 0;
  }
  for (int i = 0; i < n; i++) {
    cin >> dizi[i];
  }
  sort(dizi, dizi + n);
  for (int i = 0; i < n; i++) {
    int t = dizi[i] - 1;
    for (int j = i - 1; j >= 0; j--) {
      if (t == 0) break;
      if (use[j]) continue;
      if (dizi[i] >= dizi[j] + 2 && t >= dizi[j]) {
        t -= dizi[j];
        yol[i].push_back(j);
        use[j] = 1;
      }
    }
    if (t > 0 || t < 0) {
      cout << "NO";
      return 0;
    }
  }
  if (dfs(n - 1) == n)
    cout << "YES";
  else
    cout << "NO";
  return 0;
}

```