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>
#define N 100005
using namespace std;
int n,a[N],Max,Min,cnt,tot;
void GG(){ printf("No"); exit(0);}
int main()
{
	int i;
	scanf("%d",&n),Min=n+1;
	for(i=1;i<=n;i++){
		scanf("%d",&a[i]);
		if(a[i]>Max) Max=a[i];
		else if(a[i]==Max) tot++;
		if(a[i]<Min) Min=a[i],cnt=1;
		else if(a[i]==Min) cnt++;
	  }
	if(Max-Min>1) GG();
	if(Max-Min==1){
		if(Max<=cnt) GG();
		if(Max>cnt+(n-cnt)/2) GG();
	  }
	else
		if(Max>n/2&&Max!=n-1) GG();
	printf("Yes");
	return 0;
}
