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>
using namespace std;
int n, i, nr, c;
int v[100005];
int main(){
    cin>> n;
    for(i = 1; i <= n; i++){
        cin>> v[i];
        c = max(v[i], c);
    }
    for(i = 1; i <= n; i++){
        if(c - v[i] > 1){
            cout<<"No";
            return 0;
        }
        if(c > v[i]){
            nr++;
        }
    }
    if(nr == 0 && c == n - 1){
        cout<<"Yes";
        return 0;
    }
    if(nr >= c || nr + (n - nr) / 2 < c){
        cout<<"No";
    }
    else{
        cout<<"Yes";
    }
}
