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: Accepted)

#include "bits/stdc++.h"
using namespace std;
const int N = 1e5 + 5;
int n;
int arr[N];
int cnt[N];
int mini , maxi;
int main(){
	scanf("%d" , &n);
	mini = n;
	maxi = 0;
	for(int i = 1 ; i <= n ; ++i){
		scanf("%d" , arr + i);
		++cnt[arr[i]];
		maxi = max(maxi , arr[i]);
		mini = min(mini , arr[i]);
	}
	if(maxi - mini > 1){
		printf("No\n");
		return 0;
	}
	if(maxi == mini){
		if(maxi == n - 1){
			printf("Yes\n");
			return 0;
		}
		if(maxi <= (n >> 1)){
			printf("Yes\n");
			return 0;
		}
		printf("No\n");
		return 0;
	}
	if(cnt[1] > 1){
		printf("No\n");
		return 0;
	}
	if(maxi == n - 1){
		if(cnt[maxi] > 2){
			printf("No\n");
			return 0;
		}
	}
	if(cnt[mini] >= maxi){
		printf("No\n");
		return 0;
	}
	if((maxi - cnt[mini]) * 2 <= cnt[maxi]){
		printf("Yes\n");
	}
	else{
		printf("No\n");
	}
}