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;
  multiset<int> a;
  for(int i=0; i<N; i++){
    int tmp; cin >> tmp;
    a.insert(tmp);
  }
  int f=*(a.begin());
  int b=*(--a.end());
  if(f==b){
    if(f==N-1||f<=N/2) cout << "Yes" << endl;
    else cout << "No" << endl;
  }else if(f+1==b){
    int c=a.count(f);
    if(N-c>=2){
      if(b>=c+1&&b<=c+(N-c)/2){
        cout << "Yes" << endl;
      }else{
        cout << "No" << endl;
      }
    }else{
      cout << "No" << endl;
    }
  }else{
    cout << "No" << endl;
  }
}