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: Time Limit Exceeded)

#include <stdio.h>

int main()
{
    int i,j,n,count1,count2,count3,max=0;
    scanf("%d",&n);
    int a[n];
    for(i=0; i<n; i++)
    {
        scanf("%d",&a[i]);
    }
    for(i=0; i<n; i++)
    {
        count1=count2=count3=0;
        for(j=i+1; j<n; j++)
        {
            if( a[i] - 1 == a[j] - 1 || a[i] - 1 == a[j] || a[i] - 1 == a[j] + 1)
            {
                count1++;
            }
            if( a[i] == a[j] - 1 || a[i] == a[j] || a[i] == a[j] + 1)
            {
                count2++;
            }
            if( a[i] + 1 == a[j] - 1 || a[i] + 1 == a[j] || a[i] + 1 == a[j] + 1)
            {
                count3++;
            }
        }
        if(count1 > max)
        {
            max=count1;
        }
        else if(count2 > max)
        {
            max=count2;
        }
        else if(count3 > max)
        {
            max=count3;
        }
    }
    printf("%d",max+1);
    return 0;
}