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[100005],n;
int v[100005];
int main()
{
	while(~scanf("%d",&n))
	{
		bool flag=0;int mi=1e9,ma=0;
		for(int i=1;i<=n;++i)
		{
			scanf("%d",&a[i]);
			mi=min(mi,a[i]);
			ma=max(ma,a[i]);
			v[a[i]]++;
			if(i>1&&a[i]!=a[i-1])flag=1;
		}
		if(ma-mi>1)puts("No");
		else if(!flag)
		{
			if(ma==n-1)puts("Yes");
			else
			{
				if(n/2>=mi)puts("Yes");
				else puts("No");
			}
		}
		else
		{
			if(v[mi]+v[ma]/2==ma&&v[ma]>1)puts("Yes");
			else puts("No");
		}
	}
	return 0;
}