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;cin>>n;
  int a[n];
  int ma=0,mi=1000000000;
  for(int i=0;i<n;i++){
    cin>>a[i];
    ma=max(a[i],ma);
    mi=min(a[i],mi);
  }
  if(ma-mi>=2){
    cout<<"No"<<endl;
    return 0;
  }
  if(ma==mi){
    if(a[0]<=n/2||a[0]==n-1)cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
    return 0;
  }
  if(ma==mi+1){
    int k=0;
    for(int i=0;i<n;i++){
      if(a[i]==ma)k++;
    }
    if(ma-1>=n-k&&k<=2*(n-ma))cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
  }
}
  