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 n,a[100000],MIN,MAX;
int main(){
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>a[i];
        if(i){
            MIN=min(MIN,a[i]);
            MAX=max(MAX,a[i]);
        }
        else MIN=MAX=a[i];
    }
    if(MAX-MIN>1)cout<<"No\n";
    else if(MAX==MIN)cout<<(MAX==n-1||2*MAX<=n?"Yes\n":"No\n");
    else{
        int num=0;
        for(int i=0;i<n;i++)if(a[i]==MAX)num++;
        cout<<(n-num+num/2>=MAX&&n-num<=MIN?"Yes\n":"No\n");
    }
}