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;
int a[200010];

int main()
{int i,j,k,s;
 
 scanf("%d",&n);
 for(i=1;i<=n;i++) scanf("%d",&a[i]);
 sort(a+1,a+n+1);
 k=0;
 for(i=2;i<=n;i++)
 	if(a[i]!=a[1])
 	{	k=i;
 		break;
 	}
 if(k==0)
 {	if(a[1]==n-1)
 		printf("Yes\n");
	else if(a[1]*2<=n)
		printf("Yes\n");
	else
		printf("No\n");
	return 0;
 }
 for(i=k+1;i<=n;i++)
 	if(a[i]!=a[k])
	{	printf("No\n");
		return 0;
	}
 if(a[k]!=a[1]+1)
 {	printf("No\n");
 	return 0;
 }
 s=a[k]-(k-1);
 if(s>0 && s*2<=(n-k+1))
 	printf("Yes\n");
 else
 	printf("No\n");
 return 0;
}