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;
#define rep(i,n) for(int i=0;i<n;i++)
typedef long long ll;
int main(){
    int n;
    cin>>n;
    vector<int> A(n);
    rep(i,n) cin>>A[i];
    sort(A.begin(),A.end());
    if(A[n-1]-A[0]>1){
        cout<<"No";
    }
    if(A[n-1]-A[0]==1){
        int a=0;
        rep(i,n) if(A[i]==A[0]) a++;
        if(a<A[n-1]&&A[n-1]<=a+(n-a)/2) cout<<"Yes";
        else cout<<"No";
    }
    if(A[n-1]==A[0]){
        if(A[0]==n-1||A[0]<=n/2) cout<<"Yes";
        else cout<<"No";
    }
}