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: Accepted)

#include <stdio.h>

#define MAX 100000

int main(void)
{
	int n, i, a, a_max;
	int b[MAX] = { 0 };
	int max;
	
	scanf("%d", &n);
	for(a_max=0,i=0; i<n; i++){
		scanf("%d", &a);
		
		if(a_max < a)
			a_max = a;
		
		b[a]++;
		
		if(a > 0)
			b[a-1]++;
		if(a < MAX-1)
			b[a+1]++;
	}
	
	for(max=0,i=0; i<a_max+1; i++){
		if(max < b[i])
			max = b[i];
	}
	
	printf("%d", max);
	
	
	return 0;
}