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<cstdlib>
#include<cstdio>
using namespace std;
int n,a[100010],mx,mn,y;
int main(){mn=200000;mx=0;
    scanf("%d",&n);
	for(int i=1;i<=n;++i)
	  {scanf("%d",&a[i]);
	   mn=min(a[i],mn);mx=max(mx,a[i]);}
	if(mx-mn<2)
	  if(mx-mn==0)
	    if(mx<=n/2||mx==n-1)cout<<"Yes"<<endl;
	    else cout<<"No"<<endl;
	  else
	    {for(int i=1;i<=n;++i)
	       if(a[i]==mn)y++;
	     if(mx-y>0&&mx-y<=(n-y)/2)cout<<"Yes"<<endl;
	     else cout<<"No"<<endl;}
	else cout<<"No"<<endl;
	return 0;}
		    