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,a[100010],k1,k2;

int main()
{
	scanf("%d",&n);
	k1=n;
	k2=0;
	for(int i=1; i<=n; i++)
	{
		scanf("%d",&a[i]);
		k1=min(k1,a[i]);
		k2=max(k2,a[i]);
	}
	if(k2-k1>1)printf("No");
	else
	{
		if(k1==k2)
		{
			if((n/k1)>=2||n==(k1+1))printf("Yes");
			else printf("No");
		}
		else
		{
			int x=0,y=0;
			for(int i=1; i<=n; i++)
			{
				if(a[i]==k1)x++;
				else y++;
			}
			if(y>1&&x+1<=k2&&(y/(k2-x))>=2)printf("Yes");
			else printf("No");
		}
	}
	return 0;
}