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<iostream>
#include<cstdio>
using namespace std;

int n,x,cnt=0;
int minv=1e9,maxv=-1e9;

int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&x);
		if(x==minv)cnt++;
		if(x<minv)minv=x,cnt=1;
		if(x>maxv)maxv=x;
	}
	if(maxv-minv>1)return printf("No"),0;
	if(maxv==minv){
		if(minv==n-1)return printf("Yes"),0;
		return printf(n/minv>=2?"Yes":"No"),0;
	}
	int a=n-cnt,b=maxv-cnt;
	if(b<1)return printf("No"),0;
	return printf(a/b>=2?"Yes":"No"),0;
}