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 <stdio.h>
int n, x, y, z;
int a[100000];
int main() {
	scanf("%d", &n);
	x = n;
	for (int i = 0; i < n; i++) {
		scanf("%d", a + i);
		if (a[i] < x)x = a[i];
		if (a[i] > y)y = a[i];
	}
	if (y - x > 1) {
		printf("No\n");
		return 0;
	}
	if (y == x) {
		if (y == n - 1)printf("Yes\n");
		else if (y <= n / 2)printf("Yes\n");
		else printf("No\n");
		return 0;
	}
	for (int i = 0; i < n; i++) {
		if (a[i] == x)z++;
	}
	if (z < y && y <= z + (n - z) / 2)printf("Yes\n");
	else printf("No\n");
}