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;
#define int long long
int mod=1e9+7;

signed main(){
  int n;
  cin>>n;
  vector<int> a(n);
  for(int i=0;i<n;i++)cin>>a[i];
  sort(a.begin(),a.end());
  if(a[n-1]-a[0]>1){
    cout<<"No"<<endl;
    return 0;
  }
  if(a[0]==a[n-1]){
    if(a[0]==n-1||2*a[0]<=n){
      cout<<"Yes"<<endl;
    }else{
      cout<<"No"<<endl;
    }
    return 0;
  }

  int x=a[0];
  int y=a[n-1];
  int xc=0;
  int yc=0;
  for(int i=0;i<n;i++){
    if(a[i]==x)xc++;
    else yc++;
  }
  if(xc<y&&(y-xc)*2<=yc){
    cout<<"Yes"<<endl;
  }else{
    cout<<"No"<<endl;
  }
}
