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 <cstdio>
int n,a[100005],ok=1,mx,mn,tot;
int main()
{
	scanf("%d",&n);mn=n+1;
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	for(int i=1;i<=n;i++)
	{
		if(a[i]<mn) mn=a[i],tot=1;else if(mn==a[i]) tot++;
		if(a[i]!=mx&&i>1) ok=0;if(a[i]>mx) mx=a[i];
	}
	if(ok) (mx==n-1||(mx!=n-1&&mx*2<=n))?puts("Yes"):puts("No");
	else (mx!=mn+1||(mx==mn+1&&!(mx>tot&&n-tot>=(mx-tot)*2)))?puts("No"):puts("Yes");
}