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
// Colorful Hats
// * frank_c1
// * 2017 / 10 / 01

#include <bits/stdc++.h>
using namespace std;

int main() {
	int n, mx = 0, mi = (int)(1e9), cmx = 0;
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) {
		int x; scanf("%d", &x);
		if (x > mx) mx = x, cmx = 1;
		else if (x == mx) ++cmx; 
		if (x < mi) mi = x; 
	} 
	if (mx == mi && mx == n - 1) return printf("Yes\n"), 0;
	if (mx - mi > 1 || !(mx >= n - cmx + 1 && mx <= n - cmx + (cmx >> 1))) return printf("No\n"), 0;
	return printf("Yes\n"), 0;
}