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 cnt[100005];
int main(){
	int n,a=0;
	scanf("%d\n",&n);
	for (int i=1;i<=n;i++){
		int x;
		scanf("%d",&x);
		cnt[x]++;
		if (x>a) a=x;
	}
	if ((cnt[a]+cnt[a-1]==n&&cnt[a-1]<a&&(a-cnt[a-1])*2<=cnt[a])
		||(cnt[a]==n && a==n-1)) printf("Yes\n");
		else printf("No\n");
}