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 <iostream>
#include <algorithm>
using namespace std;

int main(){
  int n;
  cin >> n;
  int a[n];
  for(int i=0;i<n;i++){
    cin >> a[i];
  }
  sort(a,a+n);
  bool ans=true;
  if(a[n-1]-a[0]>1){
    ans=false;
  }
  else{
    int small=0;
    for(int i=0;i<n;i++){
      if(a[i]==a[0]){
        small++;
      }
    }
    if(small==n){
      if(a[0]!=n-1&&a[0]>n/2){
        ans=false;
      }
    }
    else{
      if(a[n-1]>small+(n-small)/2||a[n-1]<small+1){
        ans=false;
      }
      if(n-small==1){
        ans=false;
      }
    }
  }
  cout << (ans?"Yes":"No") << endl;
}