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 arr[30], n, tmask;
int dp[30][30][30];
int rec(int p, int rem, int f, int pos, int mask) {
  if (p == pos) return (rem == 0 && f > 1);
  int &ret = dp[p][rem][f];
  if (ret != -1) return ret;
  ret = rec(p + 1, rem, f, pos, mask);
  if (rem >= arr[p] && (!(mask & (1 << p)))) {
    ret |= rec(p + 1, rem - arr[p], f + 1, pos, mask);
  }
  return ret;
}
void path(int p, int rem, int f, int pos, int mask) {
  if (p == pos) return;
  if (rec(p + 1, rem, f, pos, mask)) {
    path(p + 1, rem, f, pos, mask);
    return;
  }
  tmask |= (1 << p);
  path(p + 1, rem - arr[p], f + 1, pos, mask);
}
int fun(int pos, int mask) {
  if (pos == n + 1) {
    for (int i = 1; i < n; i++)
      if (!(mask & (1 << i))) return 0;
    return 1;
  }
  if (arr[pos] == 1) return fun(pos + 1, mask);
  memset(dp, -1, sizeof dp);
  if (rec(1, arr[pos] - 1, 0, pos, mask)) {
    tmask = 0;
    path(1, arr[pos] - 1, 0, pos, mask);
    return fun(pos + 1, mask | tmask);
  }
  return 0;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &arr[i]);
  sort(arr + 1, arr + n + 1);
  if (fun(1, 0))
    printf("YES\n");
  else
    printf("NO\n");
}
