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>
#pragma warning(disable : 4996)
using namespace std;
int n, a[100009];
int main() {
	scanf("%d", &n);
	for (int i = 0; i < n; i++) scanf("%d", &a[i]);
	int l = *min_element(a, a + n), r = *max_element(a, a + n);
	if (r - l >= 2) printf("No\n");
	else if (r - l == 0) printf(l + 1 == n || l * 2 <= n ? "Yes\n" : "No\n");
	else {
		int cnt = 0;
		for (int i = 0; i < n; i++) if (a[i] == l) cnt++;
		printf(cnt <= l && n - cnt >= 2 * (l + 1 - cnt) ? "Yes\n" : "No\n");
	}
	return 0;
}