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 <stdio.h>
#include <stdlib.h>
#include <algorithm>
using namespace std;

int n,m,i,j,k;
int a[100005];

void fail()
{
	printf("No\n");
	exit(0);
}

int main()
{
	scanf("%d",&n);
	for(i=1;i<=n;++i)scanf("%d",&a[i]);
	sort(a+1,a+n+1);
	if(!(a[1]==a[n]||a[1]+1==a[n]))fail();
	if(a[1]==a[n])
	{
		if(a[1]*2>n&&a[1]!=n-1)fail();
	}
	else
	{
		for(i=1;i<=n;++i)if(a[i]==a[1])++k;
		if(k>=a[n])fail();
		if(k+(a[n]-k)*2>n)fail();
	}
	printf("Yes\n");
}