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;
const int N=2e5+20;
int a[N],n;
int main()
{
	while(cin>>n)
	{
		int mx=0,mn=1e5;
		for(int i=1;i<=n;i++)
			scanf("%d",&a[i]),mx=max(mx,a[i]),mn=min(mn,a[i]);
		if(mx==mn)
		{
			if(a[1]==n-1||2*a[1]<=n)
				puts("Yes");
			else
				puts("No");
		}
		else if(mx-mn==1)
		{
			int x=0,y=0,A=mx;
			for(int i=1;i<=n;i++)
			{
				if(a[i]==mn)
					x++;
				if(a[i]==mx)
					y++;
			}
			if(A>=x+1&&A<=x+y/2)
				puts("Yes");
			else
				puts("No");
		}	
		else
			puts("No");
	}
	return 0;	
} 