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>
#include<algorithm>
using namespace std;

int a[100005];
int main()
{
	int n,Max=-1,Min=100005,k=0;
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]),Min=min(Min,a[i]),Max=max(Max,a[i]);
	if(Max-Min>1) return !printf("No");
	if(Max==Min)
	{
		if(Max==n-1) return !printf("Yes");
		if(n>=2*Max) return !printf("Yes");
		return !printf("No");
	}
	for(int i=1;i<=n;i++) if(a[i]==Max) k++;
	int M=Max-(n-k);
	if(M>0&&k>=2*M) return !printf("Yes");
	return !printf("No");
}