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[100005];
int main() {
	scanf("%d",&n);
	int v1=1e9,v2=-1e9,c1=0,c2=0;
	for (int i=1;i<=n;++i) {
		scanf("%d",a+i);
		v1=min(v1,a[i]);
		v2=max(v2,a[i]);
	}
	if (v2-v1>1) return puts("No"),0;
	if (v1==v2) {
		puts(v1<=n/2||v1==n-1?"Yes":"No");
	}
	else {
		for (int i=1;i<=n;++i) {
			a[i]==v1?++c1:++c2;
		}
		puts(c2>1&&c1+1<=v2&&v2<=c1+c2/2?"Yes":"No");
	}
}