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>
#include <stdlib.h>
#include <string.h>

int main()
{
	int i, j, imax, jmax = 0, count = 0;
	int *buf = calloc(1, 100001 * sizeof(int));
	
	scanf("%d", &imax);
	
	for (i = 0; i < imax; i++) {
		int tmp;
		scanf("%d", &tmp);
		if (jmax < tmp) {
			jmax = tmp;
		}
		if (tmp == 0) {
			buf[tmp] = buf[tmp] + 1;
			buf[tmp + 1] = buf[tmp + 1] + 1;
		} else {
			buf[tmp - 1] = buf[tmp - 1] + 1;
			buf[tmp] = buf[tmp] + 1;
			buf[tmp + 1] = buf[tmp + 1] + 1;
		}
	}
	
	for (j = 0; j < 100000; j++) {
		if (count <= buf[j]) {
			count = buf[j];
		}
	}
	
	printf("%d", count);
	return 0;
}