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 <cstdlib>
#include <cstring>
#include <algorithm>
#include <math.h>
using namespace std;

const int MAXN = 1e5 + 10;
int N;
int A, c[MAXN];

int main() {
	register int i; int x;
	scanf("%d", &N);
	for(i = 1; i <= N; ++i)
		scanf("%d", &x), ++c[x], A = max(A, x);
	if((c[A] + c[A - 1] == N && c[A - 1] < A && (A - c[A - 1]) * 2 <= c[A]) || (c[A] == N && A == N - 1))
		puts("Yes");
	else
		puts("No");
	return 0;
}