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],m{100000},M;
int main(){
    cin.tie(0),ios_base::sync_with_stdio(0);
    cin>>N;
    for(int i{};i<N;++i){
        cin>>a[i];
        m=min(m,a[i]);
        M=max(M,a[i]);
    }
    if(M-m>1)
        cout<<"No"<<endl;
    else if(M-m){
        int s=count(a,a+N,M-1);
        cout<<((s<M&&(M-s)*2<=count(a,a+N,M))?"Yes":"No")<<endl;
    }
    else
        cout<<((m==N-1||m*2<=N)?"Yes":"No")<<endl;
}
