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<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
int n;
int a[100100];
int ma,mi=0x3f3f3f3f;
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",&a[i]),ma=max(ma,a[i]),mi=min(mi,a[i]);
	if(ma-mi>=2)
	{
		puts("No");
		return 0;
	}
	int c=0;
	if(ma==mi)
	{
		if(mi==n-1||mi*2<=n)
			puts("Yes");
		else puts("No");
	}
	else
	{
		for(int i=1;i<=n;++i)
			if(a[i]==mi)c++;
		if(2*(mi+1-c)>n-c||ma-c<=0)
			puts("No");
		else puts("Yes");
	}
	return 0;
}
