Problem:
Score : 300 points

Problem Statement

You are given an integer sequence of length N, a_1,a_2,...,a_N.

For each 1≤i≤N, you have three choices: add 1 to a_i, subtract 1 from a_i or do nothing.

After these operations, you select an integer X and count the number of i such that a_i=X.

Maximize this count by making optimal choices.

Constraints

1≤N≤10^5

0≤a_i<10^5 (1≤i≤N)

a_i is an integer.

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N

Output

Print the maximum possible number of i such that a_i=X.

Sample Input 1

7
3 1 4 1 5 9 2

Sample Output 1

4

For example, turn the sequence into 2,2,3,2,6,9,2 and select X=2 to obtain 4, the maximum possible count.

Sample Input 2

10
0 1 2 3 4 5 6 7 8 9

Sample Output 2

3

Sample Input 3

1
99999

Sample Output 3

1

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

#include <stdio.h>
int main(void){
	int n;
	int a[100000];
	int num[100000]={0};
	int i;
	scanf("%d",&n);
	for(i=0;i<n;i++){
		scanf("%d",&a[i]);
	}
	for(i=0;i<n;i++){
		num[a[i]]++;
	}
	int max = 0;
	int maxi = 0;
	for(i=0;i<n;i++){
		if(max < num[a[i]]){
			max = num[a[i]];
			maxi = a[i];
		}
	}
	int max_n[3];
	max_n[0] = num[maxi]+num[maxi+1]+num[maxi+2];
	max_n[1] = num[maxi]+num[maxi-1]+num[maxi+1];
	max_n[2] = num[maxi]+num[maxi-1]+num[maxi-2];
	max = max_n[0];
	int maxii;
	for(i=0;i<3;i++){
		if(maxi == 0 && i == 1)break;
		if(maxi == 1 && i == 2)break;
		if(max < max_n[i]){
			max = max_n[i];
			maxii = i;
		}
	}
	if(maxi == 99999){
		printf("%d",max_n[2]);
		return 0;
	}
	if(maxi == 99998){
		if(max_n[1] < max_n[2]){
			printf("%d",max_n[2]);
		}else{
			printf("%d",max_n[1]);
		}
		return 0;
	}
	printf("%d",max);
	return 0;
}