#include <bits/stdc++.h>
using namespace std;
const int maxN = 30;
const int maxS = maxN * maxN;
bool mark[maxN];
vector<int> could[maxS];
int sum[1 << 24], c[maxN], n;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> c[i];
  sort(c, c + n);
  if (c[0] != 1 || c[n - 1] != n) {
    cout << "NO\n";
    return 0;
  }
  for (int i = 0; i < n; i++) sum[1 << i] = c[i];
  for (int m = 0; m < (1 << n); m++) {
    if (!sum[m]) sum[m] = sum[m & (m - 1)] + sum[m - (m & (m - 1))];
    could[sum[m]].push_back(m);
  }
  for (int i = 0; i < n; i++)
    if (c[i] > 1) {
      bool can = 0;
      for (int j = (int)could[c[i] - 1].size() - 1; !can && j >= 0; j--) {
        bool fl = 0;
        int m = could[c[i] - 1][j], cnt = 0;
        for (int j = 0; !fl && j < n; j++)
          if (m & (1 << j))
            if (mark[j])
              fl = 1;
            else
              cnt++;
        if (!fl && cnt >= 2) {
          for (int j = 0; j < n; j++)
            if (m & (1 << j)) mark[j] = 1;
          can = 1;
        }
      }
      if (!can) {
        cout << "NO\n";
        return 0;
      }
    }
  cout << "YES\n";
}

### Prompt

Your task is to create 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 maxN = 30;
const int maxS = maxN * maxN;
bool mark[maxN];
vector<int> could[maxS];
int sum[1 << 24], c[maxN], n;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> c[i];
  sort(c, c + n);
  if (c[0] != 1 || c[n - 1] != n) {
    cout << "NO\n";
    return 0;
  }
  for (int i = 0; i < n; i++) sum[1 << i] = c[i];
  for (int m = 0; m < (1 << n); m++) {
    if (!sum[m]) sum[m] = sum[m & (m - 1)] + sum[m - (m & (m - 1))];
    could[sum[m]].push_back(m);
  }
  for (int i = 0; i < n; i++)
    if (c[i] > 1) {
      bool can = 0;
      for (int j = (int)could[c[i] - 1].size() - 1; !can && j >= 0; j--) {
        bool fl = 0;
        int m = could[c[i] - 1][j], cnt = 0;
        for (int j = 0; !fl && j < n; j++)
          if (m & (1 << j))
            if (mark[j])
              fl = 1;
            else
              cnt++;
        if (!fl && cnt >= 2) {
          for (int j = 0; j < n; j++)
            if (m & (1 << j)) mark[j] = 1;
          can = 1;
        }
      }
      if (!can) {
        cout << "NO\n";
        return 0;
      }
    }
  cout << "YES\n";
}

```