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;
int n,m,x,a[100005];
int main(void){
    scanf("%d",&n);
    for(int i=0;i<n;i++){
        scanf("%d",&x);
        a[x]++;
        m=max(m,x);
    }
    if((a[m]==n&&(m==n-1||m*2<=n))||(a[m]+a[m-1]==n&&2*m-n<=a[m-1]&&a[m-1]<m))cout<<"Yes\n";
    else cout<<"No\n";
}
