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;
const int N=1e5+10;
int n,a[N],cnt[N];
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++){
		scanf("%d",&a[i]);
		cnt[a[i]]++;
	}
	int m=n;
	while (!cnt[m]) m--;
	int s=n-cnt[m];
	if (cnt[m-1]!=s)
		return puts("No"),0;
	if (m==n-1&&cnt[m]==n)
		return puts("Yes"),0;
	if (2*m-s>n||m<=s)
		return puts("No"),0; 
	puts("Yes");
	return 0;
}