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[200100],n,mn,flag,p;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i)
		scanf("%d",&a[i]);
	mn=a[1];
	for(int i=1;i<=n;++i)mn=min(mn,a[i]);
	for(int i=1;i<=n;++i){
		if(a[i]!=mn)flag=true,p++;
		if(a[i]!=mn&&a[i]!=mn+1)return puts("No"),0;
	}
		
	if(flag){
		if(p==1)return puts("No"),0;
		int ans1=0;
		for(int i=1;i<=n;++i)if(a[i]==mn)ans1++;
		if(ans1+1>mn+1||ans1+(n-ans1)/2<mn+1)return puts("No"),0;
		else return puts("Yes"),0;
	} else {
		if(n/2<mn&&mn+1!=n)return puts("No"),0;
		else return puts("Yes"),0;
	}
}