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<algorithm>
using namespace std;
int m=1e9,M,n,a[1<<17];
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)
	{
		cin>>a[i];
		m=min(m,a[i]);
		M=max(M,a[i]);
	}
	if(M==m)
	{
		cout<<(m==n-1||m<=n/2?"Yes":"No")<<endl;
	}
	else if(M==m+1)
	{
		int cntm=0,cntM=0;
		for(int i=0;i<n;i++)cntm+=a[i]==m,cntM+=a[i]==M;
		cout<<(M<=(n-cntm)/2+cntm&&m>=cntm?"Yes":"No")<<endl;
	}
	else cout<<"No"<<endl;
}
