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;
#define N 1111116

int n,a[N];

int read(){
	int x=0,f=1;char ch=getchar();
	for (;!isdigit(ch);ch=getchar()) if (ch=='-') f=-f;
	for (;isdigit(ch);ch=getchar()) x=x*10+ch-'0';
	return x*f;
}

int main(){
	n=read();
	for (int i=1;i<=n;i++) a[i]=read();
	sort(a+1,a+n+1);
	if (a[n]-a[1]>=2) printf("No\n");
	if (a[n]-a[1]==1){
		int t=upper_bound(a+1,a+n+1,a[1])-a-1;
		printf((a[n]>=t+1&&a[n]<=t+(n-t)/2)?"Yes\n":"No\n");
	}
	if (a[n]-a[1]==0)
		printf((a[n]<=n/2||a[n]==n-1)?"Yes\n":"No\n");
	return 0;
}