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],c,n;
void No()
{
	puts("No");
	exit(0);
}
void Yes()
{
	puts("Yes");
	exit(0);
}
int main(void)
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
	}
	stable_sort(a+1,a+1+n);
	if(a[n]>a[1]+1)
		No();
	if(a[n]==a[1])
	{
		if(a[n]==n-1)
			Yes();
		if(a[n]*2<=n)
			Yes();
		No();
	}
	for(int i=1;i<n;i++)
		c+=a[i]==a[1];
	if(a[n]*2-c<=n&&c<a[n])
		Yes();
	No();
}