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;
const int MaxN = 100003;
int n,a[MaxN],a1,a2;
int s1,s2;
int main() {
	scanf("%d",&n);
	for (int i=1;i<=n;++i) scanf("%d",a+i);
	sort(a+1,a+n+1);
	if (a[n]-a[1]>1) {
		puts("No");
		return 0;
	}
	if (a[n]==a[1]) {
		if (a[n]==n-1) {
			puts("Yes");
			return 0;
		}
		if (a[n]>n/2) {
			puts("No");
		} else {
			puts("Yes");
		}
		return 0;
	}
	s1=s2=0;
	for (int i=1;i<=n;++i) {
		if (a[i]==a[1]) s1++;
		if (a[i]==a[n]) s2++;
	}
	int d1=a[n]-s1;
	if (d1<1 || d1>s2/2) puts("No");
	else puts("Yes");
	return 0;
}