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

int compare(const void *a, const void *b) {
    return *(int *)a - *(int *)b;
}

int main(void){
    int n, j=0;
    int *a, *t;
    int ans, cnt, min;
    
    scanf("%d", &n);
    a = malloc(sizeof(int) * n);
    t = malloc(sizeof(int) * n);
    for(int i=0;i<n;i++) t[i] = 0;

    for(int i=0;i<n;i++){
        scanf("%d", a+i);
    }

    qsort(a, n, sizeof(int), compare);

    min = a[0];
    for(int i=0;i<n;i++){
        if(a[i] > min){
            min = a[i];
            j++;
        }
        t[j]++;

    }

    for(int i=0;i<n;i++){

        if(i == 0) ans = t[i];
        else if(i == 1) ans = t[i-1] + t[i];
        else{
            cnt = t[i] + t[i+1] + t[i+2];
            if(cnt > ans) ans = cnt;
        }
    }
    printf("%d\n", ans);
    return 0;
}