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 n,a;
int main(){
	scanf("%d",&n);
	int mx=0,mxc,mn=n,mnc;
	for(int i=0,a;i<n;i++){
		scanf("%d",&a);
		if (a>mx)mx=a,mxc=1;
		else if (a==mx)mxc++;
		if (a<mn)mn=a,mnc=1;
		else if (a==mn)mnc++;
	}
	if (mx==mn&&(mx==n-1||mx<=n/2)||mx==mn+1&&mx-mnc>0&&mx-mnc<=mxc/2)puts("Yes");
	else puts("No");
}
