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 rep(i,n) for(int i=0;i<n;i++)
int n,a[111111],x,y;
int main(){
	cin>>n;
	rep(i,n)cin>>a[i];
	sort(a,a+n);
	if(a[n-1]-a[0]>=2){
		puts("No");
		return 0;
	}
	if(a[n-1]-a[0]==0){
		if(a[0]==n-1||a[0]*2<=n)puts("Yes");
		else puts("No");
	}
	else{
		rep(i,n){
			if(a[i]==a[n-1])y++;
			else x++;
		}
		if(x<a[n-1]&&2*(a[n-1]-x)<=y)puts("Yes");
		else puts("No");
	}
	return 0;
}
