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 N=100005;
int n,cnt[N],mx,mn,x;

void chk(bool f){if(f)puts("Yes");else puts("No");}

int main(){
	scanf("%d",&n);mn=n;
	for(int i=1;i<=n;i++)scanf("%d",&x),cnt[x]++,mx=max(mx,x),mn=min(mn,x);
	if(mn==mx)chk(mn==n-1||mn<=n/2);
	else if(mx-mn==1)chk(cnt[mn]<=mn&&mn<=cnt[mn]+cnt[mx]/2-(cnt[mx]?1:0));
	else puts("No");
	return 0;
}