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=100005;
int n,a[N];
int main(){
	cin >> n;
	for (int i=1;i<=n;i++)
		cin >> a[i];
	sort(a+1,a+n+1);
	if (a[n]-a[1]>1)
		return puts("No"),0;
	if (a[1]==a[n])
		return puts(a[1]==n-1||(a[1]<n&&n%a[1]==0)?"Yes":"No"),0;
	int t=0;
	for (int i=1;i<=n;i++)
		if (a[i]==a[n])
			t++;
	if (n-t+1<=a[n]&&a[n]<=n-t+t/2)
		puts("Yes");
	else
		puts("No");
	return 0;
}