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;

using Lint=long long;

int main()
{
   int N; cin>>N;
   vector<int> a(N);
   for(int i=0;i<N;i++) cin>>a[i];

   sort(a.begin(),a.end());
   int mn=a[0];
   int mx=a[N-1];

   bool ok=false;
   if(mx-mn==1){
      int K=count(a.begin(),a.end(),mn);
      if(mx>K and N>=K+(mx-K)*2) ok=true;
   }else if(mx-mn==0){
      if(mn==N-1 or N>=2*mn) ok=true;
   }
   cout<<(ok? "Yes":"No")<<endl;
   return 0;
}
