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>

using namespace std;

int n,a[100010],cnt[100010],k,k1,k2;

int main()
{
	scanf("%d",&n);
	for(int i=1; i<=n; i++)
	{
		scanf("%d",&a[i]);
		cnt[a[i]]++;
		if(k1==0)k1=a[i];
		if(k2==0)k2=a[i];
		if(cnt[a[i]]==1)k++;
	}
	if(k1>k2)swap(k1,k2);
	if(k>2||k==0)printf("No");
	else if(k2-k1>1)printf("No");
	else
	{
		if(k==1)
		{
			if((n/k1)>1)printf("Yes");
			else if(n==k1+1)printf("Yes");
			else printf("No");
		}
		else
		{
			int x=0,y=0;
			for(int i=1; i<=n; i++)
			{
				if(a[i]==k1)x++;
				else y++;
			}
			if(y>1&&x+1<=y&&k2<=x+y/2)printf("Yes");
			else printf("No");
		}
	}
	return 0;
}