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<cstring>

bool judge(int m,int a,int b)
{
	if(m>b+a/2)return 0;
	else if(m<b+(a!=0))return 0;
	else return 1;
}

int n,m,a,b;

int main()
{
	scanf("%d",&n);
	a=b=0,m=-1;
	for(int i=1,x;i<=n;i++)
	{
		scanf("%d",&x);
		if(m==-1)m=x,a++;
		else if(x==m)a++;
		else if(x==m-1)b++;
		else if(x==m+1 && !b)m=x,b=a,a=1;
		else {printf("No\n");return 0;}
	}
	if(judge(m,a,b) || (!b && judge(m+1,0,a)))printf("Yes\n");
	else printf("No\n");

	return 0;
}
