#include <bits/stdc++.h>
using namespace std;
int n;
int x[25];
int start;
bool dfs(int cur, int p, int mask, int sum) {
  if (1.0 * (clock() - start) / CLOCKS_PER_SEC > 0.9) return false;
  if (cur > n) return true;
  if ((mask & (1 << cur)) == 0) return false;
  if (sum == x[cur] - 1) return dfs(cur + 1, cur + 2, mask, 0);
  if (p > n) return false;
  if ((mask & (1 << p)) == 0) {
    if (!(x[p] == x[p - 1] && (mask & (1 << (p - 1)) == 0)))
      if (x[p] < x[cur] - 1 && sum + x[p] <= x[cur] - 1)
        if (dfs(cur, p + 1, mask | (1 << p), sum + x[p])) return true;
  }
  if (dfs(cur, p + 1, mask, sum)) return true;
  return false;
}
int MAIN() {
  start = clock();
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> x[i];
  sort(x + 1, x + 1 + n);
  reverse(x + 1, x + 1 + n);
  if (dfs(1, 2, 2, 0))
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
  return 0;
}
int main() {
  ios ::sync_with_stdio(false);
  cout << fixed << setprecision(16);
  return MAIN();
}

### Prompt

Your challenge is to write 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;
int x[25];
int start;
bool dfs(int cur, int p, int mask, int sum) {
  if (1.0 * (clock() - start) / CLOCKS_PER_SEC > 0.9) return false;
  if (cur > n) return true;
  if ((mask & (1 << cur)) == 0) return false;
  if (sum == x[cur] - 1) return dfs(cur + 1, cur + 2, mask, 0);
  if (p > n) return false;
  if ((mask & (1 << p)) == 0) {
    if (!(x[p] == x[p - 1] && (mask & (1 << (p - 1)) == 0)))
      if (x[p] < x[cur] - 1 && sum + x[p] <= x[cur] - 1)
        if (dfs(cur, p + 1, mask | (1 << p), sum + x[p])) return true;
  }
  if (dfs(cur, p + 1, mask, sum)) return true;
  return false;
}
int MAIN() {
  start = clock();
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> x[i];
  sort(x + 1, x + 1 + n);
  reverse(x + 1, x + 1 + n);
  if (dfs(1, 2, 2, 0))
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
  return 0;
}
int main() {
  ios ::sync_with_stdio(false);
  cout << fixed << setprecision(16);
  return MAIN();
}

```