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;
#define fr(i,n) for(int i=0;i<n;i++)

int main(){
  int n,a[100010],b,c;
  cin>>n;
  fr(i,n) cin>>a[i];
  sort(a,a+n);
  if(a[n-1]-a[0]>1){
    cout<<"No"<<endl;
    return 0;
  }
  b=a[0];
  if(a[0]==a[n-1]){
    if(b<=n/2 || b==n-1) cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
    return 0;
  }
  fr(i,n){
    if(a[i]>b){
      c=i;
      break;
    }
  }
  if(b-c+1<=0 || 2*(b-c+1)>n-c) cout<<"No"<<endl;
  else cout<<"Yes"<<endl;
}