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<cstdio>
#include<cstring>
#include<algorithm>
#define rep(i,k,n) for(int i=k;i<=n;i++)
#define rep2(i,k,n) for(int i=k;i>=n;i--)
using namespace std;
const int N=1e5+7;

int n,a[N];
int main(){
	scanf("%d",&n);
	int vis=1,c=0;
	rep(i,1,n){
		scanf("%d",&a[i]);
		if(a[i]!=n-1)vis=0;
		c=max(c,a[i]);
	}
	if(vis){puts("Yes");return 0;}
	int cnt1=0,cnt2=0;
	rep(i,1,n){
		if(a[i] < c-1){puts("No");return 0;}
		if(a[i]==c-1)cnt1++;
		else cnt2++;
	}
	if(cnt1 + 1 > c){puts("No");return 0;}
	if(cnt1 + (cnt2>>1) < c){puts("No");return 0;}
	puts("Yes");
}