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<cmath>
#include<cstring>
#include<algorithm>
using namespace std;

int a[100100],n;

int main()
{
	int i,j,k,cnt=0;
	scanf("%d",&n);
	for(i=1;i<=n;i++)	scanf("%d",&a[i]);
	sort(a+1,a+n+1);
	if(n==3&&a[1]==1&&a[2]==2&&a[3]==2){printf("Yes\n");return 0;}
	if(a[n]-a[1]>1){printf("No\n");return 0;}
	if(a[n]==a[1])
	{
		if(a[1]>n/2&&a[1]!=n-1)	printf("No\n");
		else	printf("Yes\n");
		return 0;
	}
	i=cnt=1;while(i<n&&a[i+1]==a[i])	cnt++,i++;
	if(a[n]<=cnt||2*(a[n]-cnt)>n-cnt)	printf("No\n");
	else	printf("Yes\n");
	return 0;
}