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;
int a[N];
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	int mx=-1e9,mn=1e9;
	for(int i=1;i<=n;i++) mx=max(mx,a[i]),mn=min(mn,a[i]);
	if(mx-mn>=2) return puts("No"),0;
	if(mn==mx){
		if(n-1==mn||mn<=n/2) return puts("Yes"),0;
		return puts("No"),0;
	}
	int sm=0,bg=0;
	for(int i=1;i<=n;i++) if(a[i]==mn) sm++;
	bg=n-sm;
	int col=mx-sm;
	if(col<=0||col>bg/2) return puts("No"),0;
	return puts("Yes"),0;
} 