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>
int n, a, m, fl, c[100005];
int main() {
	scanf("%d", &n);
	for(int i=0; i<n; i++) {
		scanf("%d", &a);
		c[a]++;
		if(a>m) m=a;
	}
	if(c[m]+c[m-1]==n) {
		if(c[m]==n) {
			if(m==n-1 || m<=n/2) fl = 1;
		} else {
			if(c[m-1]<m && m<=c[m-1]+c[m]/2) fl = 1;
		}
	}
	puts(fl ? "Yes":"No");
	return 0;
}