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>
#include<algorithm>
#define fo(i,a,b) for(i=a;i<=b;i++)
using namespace std;
int i,j,k,l,t,n,m,mx,mi,cnt;
bool czy;
int main(){
	scanf("%d",&n);
	czy=1;
	mi=n+1;mx=0;
	fo(i,1,n){
		scanf("%d",&t);
		//mi=min(mi,t);
		if (t<mi) mi=t,cnt=1;
		else if (t==mi) cnt++;
		if (i>1&&czy&&t!=mx) czy=0;
		mx=max(mx,t);
	}
	if (czy){
		if (mx==n-1) printf("Yes\n");
		else{
			k=mx;
			if (k*2<=n) printf("Yes\n");
			else printf("No\n");
		}
	}
	else{
		if (mx-mi>1) printf("No\n");
		else{
			k=mx;
			if (cnt<k&&n-cnt>=(k-cnt)*2) printf("Yes\n");
			else printf("No\n");
		}
	}
}