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>

const int maxn = 1e5 + 100;

int a[maxn], n;

int main() {
	scanf("%d", &n);
	for (int i = 0; i < n; ++i) {
		scanf("%d", a + i);
	}
	std::sort(a, a + n);
	if(a[0] == a[n - 1]) {
		if(a[n - 1] <= n / 2 || a[n - 1] == n - 1) {
			puts("Yes");
		}
		else {
			puts("No");
		}
	}
	else if(a[0] == a[n - 1] - 1) {
		for (int i = 0; i < n; ++i) {
			if(a[i] != a[0]) {
				if(a[n - 1] <= i + (n - i) / 2 && a[n - 1] >= i + 1) {
					puts("Yes");
				}
				else {
					puts("No");
				}
				break;
			}
		}
	}
	else {
		puts("No");
	}
	return 0;
}