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;
  int A[100000];
  cin >> N;
  
  int s=100001,l=0;
  for(int i=0;i<N;i++){
    cin >> A[i];
    if(A[i]>l) l=A[i];
    if(A[i]<s) s=A[i];
  }
  if(l-s==0){
    if(l+1==N || l*2<=N)
      cout << "Yes" << endl;
    else cout << "No";
    return 0;
  }else if(l-s==1){
    int C=l;
    int uni=0;
    for(int i=0;i<N;i++){
      if(A[i]==s) uni++;
    }
    if(C>uni && (C-uni)*2<=N-uni)
      cout << "Yes" << endl;
    else cout << "No" << endl;
    return 0;
  }else{
    cout << "No" << endl;
  }
  
  return 0;
}