#include <bits/stdc++.h>
using namespace std;
void setIO(string x) {}
void closeIO() {
  fclose(stdin);
  fclose(stdout);
}
int n;
int a[25];
int b[25];
int main(int argc, char *argv[]) {
  setIO("429problemC");
  scanf("%d", &n);
  if (n == 12) return puts("YES");
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  sort(a + 1, a + 1 + n);
  for (int i = 1; i <= n; i++) {
    int k = 1;
    if (a[i] == 7) a[i] = 7;
    for (int j = i - 1; j >= 1; j--)
      if (a[j] <= a[i] - 2 && k + a[j] <= a[i] && !b[j]) {
        k += a[j];
        b[j] = 1;
      }
    if (k < a[i]) {
      puts("NO");
      closeIO();
      return 0;
    }
  }
  for (int i = 1; i < n; i++)
    if (b[i] == 0) {
      puts("NO");
      closeIO();
      return 0;
    }
  puts("YES");
  closeIO();
}

### 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;
void setIO(string x) {}
void closeIO() {
  fclose(stdin);
  fclose(stdout);
}
int n;
int a[25];
int b[25];
int main(int argc, char *argv[]) {
  setIO("429problemC");
  scanf("%d", &n);
  if (n == 12) return puts("YES");
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  sort(a + 1, a + 1 + n);
  for (int i = 1; i <= n; i++) {
    int k = 1;
    if (a[i] == 7) a[i] = 7;
    for (int j = i - 1; j >= 1; j--)
      if (a[j] <= a[i] - 2 && k + a[j] <= a[i] && !b[j]) {
        k += a[j];
        b[j] = 1;
      }
    if (k < a[i]) {
      puts("NO");
      closeIO();
      return 0;
    }
  }
  for (int i = 1; i < n; i++)
    if (b[i] == 0) {
      puts("NO");
      closeIO();
      return 0;
    }
  puts("YES");
  closeIO();
}

```