#include <bits/stdc++.h>
using namespace std;
const int inf = 0x3fffffff;
int num[32];
void solve(int ncase) {
  int n;
  scanf("%d", &n);
  vector<int> num(n);
  int cnt[32] = {0};
  for (int i = 0; i < n; i++) {
    scanf("%d", &num[i]);
    cnt[num[i]]++;
  }
  sort(num.begin(), num.end());
  if (cnt[2] || num[0] != 1 || num[n - 1] != n) {
    puts("NO");
    return;
  }
  vector<int> used(n);
  used[n - 1] = 1;
  for (int i = n - 1; i >= 0; i--) {
    if (used[i] != 1) {
      puts("NO");
      return;
    }
    int need = num[i] - 1;
    int cnt = 0;
    for (int j = i - 1; j >= 0; j--) {
      if (used[j] == 0) {
        if (cnt == 0) {
          if (num[j] < need) {
            used[j] = 1;
            need -= num[j];
            cnt++;
          }
        } else if (num[j] <= need) {
          cnt++;
          need -= num[j];
          used[j] = 1;
        }
      }
    }
    if (need != 0) {
      puts("NO");
      return;
    }
  }
  puts("YES");
}
int main() {
  int T = 1;
  int ncase = 0;
  while (T--) {
    solve(++ncase);
  }
}

### Prompt

In cpp, your task is to solve 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 inf = 0x3fffffff;
int num[32];
void solve(int ncase) {
  int n;
  scanf("%d", &n);
  vector<int> num(n);
  int cnt[32] = {0};
  for (int i = 0; i < n; i++) {
    scanf("%d", &num[i]);
    cnt[num[i]]++;
  }
  sort(num.begin(), num.end());
  if (cnt[2] || num[0] != 1 || num[n - 1] != n) {
    puts("NO");
    return;
  }
  vector<int> used(n);
  used[n - 1] = 1;
  for (int i = n - 1; i >= 0; i--) {
    if (used[i] != 1) {
      puts("NO");
      return;
    }
    int need = num[i] - 1;
    int cnt = 0;
    for (int j = i - 1; j >= 0; j--) {
      if (used[j] == 0) {
        if (cnt == 0) {
          if (num[j] < need) {
            used[j] = 1;
            need -= num[j];
            cnt++;
          }
        } else if (num[j] <= need) {
          cnt++;
          need -= num[j];
          used[j] = 1;
        }
      }
    }
    if (need != 0) {
      puts("NO");
      return;
    }
  }
  puts("YES");
}
int main() {
  int T = 1;
  int ncase = 0;
  while (T--) {
    solve(++ncase);
  }
}

```