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 100010
using namespace std;
int n,a[N];

int main(){
	scanf("%d",&n);
	int mx=0,cnt=0;
	for (int i=1;i<=n;i++)
		scanf("%d",&a[i]),mx=max(a[i],mx);
	for (int i=1;i<=n;i++){
		if (a[i]<mx-1){
			puts("No");
			return 0;
		}
		cnt+=mx-a[i];
	}
	if (cnt==0){
		if ((n/mx>1) || mx==n-1)
			puts("Yes");
		else
			puts("No");
		return 0;
	}
	if ((mx>cnt) && ((n-cnt)/(mx-cnt)>1))
		puts("Yes");
	else
		puts("No");
	return 0;
}