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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
using namespace std;

int N;
int a[100007];

int main(){
    int max = -1;
    int min = -1;

    cin >> N;
    for(int i = 0;i < N;i++){
        cin >> a[i];

        if(a[i] >= max){
            max = a[i];
        }

        if(min <= a[i]){
            min = a[i];
        }
    }

    int true_ans = -1;
    int ans = 0;
    for(int X = min-1;X < max+1;X++){ 
        ans = 0;

        for(int i = 0;i < N;i++){
            if(X == a[i]-1 || X == a[i]+1 || X == a[i]){
                ans++;
            }
        }

        if(ans > true_ans){
            true_ans = ans;
        }

    }

    cout << true_ans << endl;

}