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;

const int MaxN=1e5+5;

int N,Mx,Mn=1<<30,Cnt;
int A[MaxN];

int main(){
	int i;
	scanf("%d",&N);
	for(i=1;i<=N;i++){
		scanf("%d",&A[i]);
		Mx=max(Mx,A[i]);
		Mn=min(Mn,A[i]);
	}
	if(Mx>Mn+1){
		puts("No");
		return 0;
	}
	if(Mn^Mx){
		for(i=1;i<=N;i++)
			Cnt+=(A[i]<Mx);
		puts(Cnt>=Mx||2*(Mx-Cnt)>N-Cnt?"No":"Yes");
	}
	else puts(Mx==N-1||2*Mx<=N?"Yes":"No");
	return 0;
}