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>
using namespace std;

int n, a = -1, b = -1, c, d;

int main () {
	scanf("%d", &n);
	for (int i = 1, j; i <= n; ++i) {
		scanf("%d", &j);
		if (~a && a == j) ++c;
		else if (~b && b == j) ++d;
		else if (a == -1) a = j, c = 1;
		else if (b == -1) b = j, d = 1;
		else return puts("No"), 0;
	}
	if (a > b) a ^= b ^= a ^= b, c ^= d ^= c ^= d;
	if (a == -1) {
		if (b == n - 1) return puts("Yes"), 0;
		a = b - 1;
	}
	if (a != b - 1) return puts("No"), 0;
	if ((a + 1 - c) * 2 > d || (a + 1 - c) <= 0) return puts("No"), 0;
	return puts("Yes"), 0;
}