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 a[100010];
int main()
{
	int n,maxx=0,minn=1e9,t=0,sum=0;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%d",a+i),maxx=max(maxx,a[i]),minn=min(minn,a[i]);
	if(maxx-minn>1)
	{
		puts("No");
		return 0;
	}
	if(maxx==minn&&minn==n-1)
	{
		puts("Yes");
		return 0;
	}
	for(int i=1;i<=n;i++)
		if(a[i]==maxx)t++;
		else sum++;
	if(sum>=maxx)
	{
		puts("No");
		return 0;
	}
	sum=maxx-sum;
	if(sum*2<=t)puts("Yes");
	else puts("No");
	return 0;
}