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
#include <bits/stdc++.h>
using namespace std;
int a[25];
bool vis[25];
int main(int argc, char *argv[]) {
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    a[i];
  }
  sort(a, a + n);
  if (a[n - 1] != n) {
    puts("NO");
    return 0;
  }
  for (int i = 0; i < n; ++i) {
    int k = 1;
    for (int j = i - 1; j >= 0 && a[i] != k; --j) {
      if (!vis[j] && a[i] >= a[j] + 2 && a[j] + k <= a[i]) {
        k += a[j];
        vis[j] = true;
      }
    }
    if (a[i] != k) {
      puts("NO");
      return 0;
    }
  }
  puts("YES");
  return 0;
}
