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 <iostream>
#include <map>
using namespace std;

int N;

int main(){
	cin >> N;
	int a,mi = 1e9,ma = 0;
	map<int,int> m;
	for(int i=0;i<N;i++){
		cin >> a;
		m[a]++;
		mi = min(mi,a);
		ma = max(ma,a);
	}
	if(ma-mi>=2){
		cout << "No" << endl;
	}else if(mi==ma){
		if(ma==N-1 || m[mi]/2>=mi){
			cout << "Yes" << endl;
		}else{
			cout << "No" << endl;
		}
	}else{
		int a = m[mi];
		if((N-a)/2>=ma-a && ma!=a){
			cout << "Yes" << endl;
		}else{
			cout << "No" << endl;
		}
	}
}