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>

using namespace std;

int cnt[100005];

int main() {
  int n;
  scanf("%d",&n);
  int maxn=0;
  for(int i=1;i<=n;i++) {
    int x;
	scanf("%d",&x);
	cnt[x]++;
	maxn=max(maxn,x);  	
  }
  int s=0;
  for(int i=1;i<=n;i++) s+=(cnt[i]>0);
  if (s==2&&cnt[maxn-1]>0) {
  	int p=maxn-cnt[maxn-1];
  	if (p>0&&p<=(cnt[maxn]>>1)) {
  		puts("Yes");
  		return 0;
	  }
  }
  else if (s==1) {
  	if (maxn==n-1||maxn<=(n>>1)) {
  		puts("Yes");
  		return 0;
	  }
  }
  puts("No");
  return 0;
}