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<iostream>
using namespace std;

const int N=1e5+1e3+7;

int n,a[N],mx,mn=N*2;

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%d",&a[i]),mx=max(mx,a[i]),mn=min(mn,a[i]);
	if(mx-mn>=2)
	{
		cout<<"No";
		return 0;
	}
	if(mn>n/2&&mx==mn)
	{
		if(mx==n-1)
		{
			cout<<"Yes";
			return 0;
		}
		else
		{
			cout<<"No";
			return 0;
		}
	}
	else
	if(mx==mn)
	{
		cout<<"Yes";
		return 0;
	}
	int k=0;
	for(int i=1;i<=n;i++)
		if(a[i]==mx)
			k++;
	if(2*(mx-(n-k))>k||mx-(n-k)<=0)
	{
		cout<<"No";
		return 0;
	}
	cout<<"Yes";
}