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<cstdio>

int a[100000];
int main()
{
	int i,n,c=1e9,f=0;scanf("%d",&n);
	for(i=0;i<n;i++)scanf("%d",a+i),a[i]<c&&(c=a[i]);
	for(i=0;i<n;i++)if(a[i]-c>1)return puts("No"),0;else f+=a[i]==c;
	if(f==n)return puts(n==a[0]+1||n>=a[0]<<1?"Yes":"No"),0;
	return puts(n-f>=c+1-f<<1&&c>=f?"Yes":"No"),0;
}