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: Accepted)

#include <iostream>
#include <algorithm>
#include <vector>

using namespace std;

int main(void) {
  int n;
  cin >> n;
  vector<int> a;
  for(int i = 0; i < n; i++) {
    int x;
    cin >> x;
    a.push_back(x);
  }

  sort(a.begin(), a.end());

  int mx = 0;
  for(int i = a[0]; i <= a[n - 1]; i++) {
    vector<int>::iterator ulim = upper_bound(a.begin(), a.end(), i + 1);
    vector<int>::iterator dlim = lower_bound(a.begin(), a.end(), i - 1);
    mx = max(mx, (int)(ulim - dlim));
  }

  cout << mx << endl;
}