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 int long long
#define f(i,n) for(int i=0;i<n;i++)
int x[100000];
signed main(){
	int n;
	cin>>n;
	f(i,n)cin>>x[i];
	sort(x,x+n);
	if(x[n-1]==x[0]&&(n>=x[0]*2||n<=x[0]+1)) puts("Yes");
	else if(x[n-1]-x[0]==1&&x[0]>=lower_bound(x,x+n,x[n-1])-x&&x[n-1]<=lower_bound(x,x+n,x[n-1])-x+(n-(lower_bound(x,x+n,x[n-1])-x))/2) puts("Yes");
	else puts("No");
	return 0;
}
		
