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[1000005];
bool check(){
	int i,ans=0,tmp=0;
	for (i=1; i<=n; i++) ans=max(ans,a[i]);
	for (i=1; i<=n; i++) if (ans>a[i]+1) return 0;
	for (i=1; i<=n; i++) if (ans>a[i]) tmp++;
	int x,y;
	if (tmp==n) return ans==n; else{
		if (!tmp && ans==n-1) return 1;
		x=1; y=(n-tmp)/2;
		if (x+tmp<=ans && ans<=y+tmp) return 1; else return 0;
	}
}
int main(){
	scanf("%d",&n);
	int i;
	for (i=1; i<=n; i++) scanf("%d",&a[i]);
	puts(check()?"Yes":"No");
	return 0;
}
