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,mx,mn,a[100005];
int main()
{
	scanf("%d",&n);
	mx=-1e9+7;
	mn=1e9+7;
	for(int i=0;i<n;i++)
	{
		int x;
		scanf("%d",&x);
		a[x]++;
		mx=max(mx,x);
		mn=min(mn,x);
	}
	if(mx-mn>1)puts("No");
	else if(mx==mn)
	{
		if(mx==n-1||n>=2*mx)puts("Yes");else puts("No");
	}
	else
	{
		if(mx>a[mn]&&a[mx]>=2*(mx-a[mn]))puts("Yes");else puts("No");
	}
	return 0;
}