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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

int main(){

    long long N, i, j;
    int ans = 0;
    long long a[100010], cnt[100010];
    cin >> N;

    for (i = 1; i <= N; i++){
      cin >> a[i];
    }
    
    for (i = 1; i <= 100001; i++){
      cnt[i] = 0;
      for (j = 1; j <= 100000; j++){
        if(i == a[j])cnt[i]++;
      }
    }

    for (i = 2; i <= 100000; i++){
      int sum = 0;
      sum = cnt[i - 1] + cnt[i] + cnt[i + 1];
      ans = max(ans, sum);
    }
    cout << ans << endl;
}