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<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int cnt[101010];
int main()
{
	int n,x,mi=100000,ma=0,k=0;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&x);
		cnt[x]++;
		mi=min(mi,x);
		ma=max(ma,x);
	}
	if(mi==ma&&mi==n-1)
	{
		printf("Yes");
		return 0;
	}
	if(ma-mi>1)
	{
		printf("No");
		return 0;
	}
	if(ma-mi==1)
	{
		k=cnt[mi];
		if(ma<=cnt[mi])
		{
			printf("No");
			return 0;
		}
	}
	if((ma-k)*2<=cnt[ma])
		printf("Yes");
	else
		printf("No");
	return 0;
}