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<cstdio>
#include<vector>
#include<algorithm>


using namespace std;


int main(void)
{
	int n;

	while(scanf("%d", &n)==1)
	{
		vector<int> a(n);
		int ans=0;

		for(int i=0;i<n;i++)
		{
			scanf("%d", &a[i]);
		}
		sort(a.begin(), a.end());
		int a_min=a[0];
		int a_max=a.back();

		if(a_max==a_min)
		{
			// real=a[0]   real=a[0]+1
			if(a_min*2<=n || a_min==n-1) ans=1;
		}
		if(a_max==a_min+1)
		{
			int i;
			for(i=0;a[i]==a_min;i++)
				;
			if(i+2*(a_max-i)<=n) ans=1;
			if(a[n-2]!=a_max) ans=0;
		}

		printf("%s\n", ans?"Yes":"No");
	}

	return 0;
}