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 <vector>
#include <algorithm>

using namespace std;

int main(){
  int N;
  vector<int> a;
  cin >> N;
  int b;
  for(int i=0;i<N;i++){
    cin >> b;
    a.push_back(b);
  }
  sort(a.begin(),a.end());
  int c=-1;
  int count;
  int ans=0;
  for(int i=0;i<N;i++){
    count=0;
    if(c!=a[i]){
      c=a[i];
      for(int j=i;c+2>=a[j]&&j<N;j++){
        count++;
      }
      ans=max(ans,count);
    }
  }
  cout << ans << endl;
}