There are N cats. We number them from 1 through N.

Each of the cats wears a hat. Cat i says: "there are exactly a_i different colors among the N - 1 hats worn by the cats except me."

Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.

Constraints

* 2 ≤ N ≤ 10^5
* 1 ≤ a_i ≤ N-1

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print `Yes` if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print `No` otherwise.

Examples

Input

3
1 2 2


Output

Yes


Input

3
1 1 2


Output

No


Input

5
4 3 4 3 4


Output

No


Input

3
2 2 2


Output

Yes


Input

4
2 2 2 2


Output

Yes


Input

5
3 3 3 3 3


Output

No
#include <bits/stdc++.h>
using namespace std;

int main()
{
  int n;
  scanf("%d",&n);
  static int a[100000];
  for(int i=0;i<n;i++){
    scanf("%d",a+i);
  }
  int M=a[0],X=a[0];
  for(int i=0;i<n;i++){
    M=min(M,a[i]);
    X=max(X,a[i]);
  }
  bool F;
  if(M<X-1){
    F=0;
  }
  else if(M==X-1){
    int Y=0;
    for(int i=0;i<n;i++){
      if(a[i]==M){
	Y++;
      }
    }
    F=(Y<X&&2*(X-Y)<=n-Y);
  }
  else{
    F=(2*X<=n||X==n-1);
  }
  puts(F?"Yes":"No");
  return 0;
}
