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 <algorithm>
using namespace std;
int arr[100005];
int main()
{
	int n;
	scanf("%d",&n);
	for (int i=0;i<n;i++)
	scanf("%d",&arr[i]);
	sort(arr,arr+n);
	if (arr[n-1]>arr[0]+1)
	printf("No");
	else if (arr[n-1]==arr[0])
	printf((arr[0]==n-1 || arr[0]<=n/2)? "Yes":"No");
	else
	{
		int tmp=0;
		while (arr[0]==arr[tmp])
		tmp++;
		printf((tmp<=arr[0] && arr[n-1]<=tmp+(n-tmp)/2)? "Yes":"No");
	}
}