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>
#define M 100005
#define INF 19260817
#define LHXAK {printf("Yes\n"); return 0;}
#define XFZSB {printf("No\n"); return 0;}
using namespace std;

int n,a[M]={0};

int main(){
	scanf("%d",&n);
	int maxn=0,minn=INF;
	for(int i=1;i<=n;i++){
		scanf("%d",a+i);
		maxn=max(maxn,a[i]);
		minn=min(minn,a[i]);
	}
	if(maxn-minn>1) XFZSB
	if(maxn==minn){
		if(maxn==n-1) LHXAK
		if(maxn*2<=n) LHXAK
		XFZSB
	}
	int cnt=0;
	for(int i=1;i<=n;i++) if(a[i]==minn) cnt++;
	if(cnt<maxn&&n-cnt>=(maxn-cnt)*2) LHXAK
	XFZSB
}