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 <map>
using namespace std;
int main(void){
    int n;
    map<int, int> m;
    cin>>n;
    for(int i=0;i<n;i++){
        int a;
        cin>>a;
        m[a]++;
    }
    bool f=false;
    if(m.size()==1){
        int a=(m.begin()->first);
        if(a*2<=n||a==n-1)f=true;
    }else if(m.size()==2){
        int a=(m.begin()->first);
        if(m[a]+m[a+1]==n){
            if(2*a+2-m[a]<=n&&a+1>m[a])f=true;
        }
    }
    if(f){
        cout<<"Yes"<<endl;
    }else{
        cout<<"No"<<endl;
    }
}
