Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 2 2

Sample Output 1

Yes

For example, if cat 1, 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

Sample Input 2

3
1 1 2

Sample Output 2

No

From the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.
Also, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.
Therefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.

Sample Input 3

5
4 3 4 3 4

Sample Output 3

No

Sample Input 4

3
2 2 2

Sample Output 4

Yes

Sample Input 5

4
2 2 2 2

Sample Output 5

Yes

Sample Input 6

5
3 3 3 3 3

Sample Output 6

No

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define L long long
using namespace std;
int n,x[100010],l=1e9,r,a,b;
int main()
{
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	int i,j;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
	  {
	   scanf("%d",&x[i]);
	   l=min(l,x[i]);
	   r=max(r,x[i]);
	  }
	for(i=1;i<=n;i++)
	  if(x[i]==l)
	    a++;
	  else if(x[i]==r)
	    b++;
	if(a+b<n)
	  {
	   printf("No\n");
	   return 0;
	  }
	if(l==r)
	  i=1,j=n/2;
	else
	  i=a+1,j=a+b/2;
	if(i<=r && r<=j || l==r && l==n-1)
	  printf("Yes\n");
	else
	  printf("No\n");
	return 0;
}