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 <cstdio>
#include <algorithm>
using namespace std;
int n, x, y, a[100005];

int f(int p, int q) {
	if(x+y<n || q-p>1) return 0;
	if(x==n) return p==n-1 || p<=n/2;
	return x+1<=q && q<=x+y/2;
}

int main() {
	int i, j;
	scanf("%d", &n);
	for(i=0; i<n; i++) scanf("%d", a+i);
	sort(a, a+n);
	for(i=0; a[i]==a[0]; i++, x++);
	for(j=i; a[j]==a[i]; j++, y++);
	puts(f(a[0], a[n-1]) ? "Yes":"No");
	return 0;
}