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;

void fail(){
	cout<<"No"<<endl;
	exit(0);
}
int a[100001];
int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n,m=0,s=0;
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>a[i],m=max(m,a[i]);
	for(int i=1;i<=n;i++)
		if(a[i]<m-1)
			fail();
		else if(m-1==a[i])	
			s++;
	if(s==0){
		if(m==n-1||m<=n/2)	cout<<"Yes"<<endl;
		else fail();
		return 0;
	}
	if(s>=m)	fail();
	if((m-s)*2>n-s)
		fail();
	else
		cout<<"Yes"<<endl;
}

