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 9.2.1) (judge verdict: Wrong Answer)

#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) FOR(i,0,n)
#define BFOR(bit,a,b) for(int bit = (a); bit < (1<<(b)); ++bit)
#define BREP(bit,n) BFOR(bit,0,n)
using namespace std;
using ll = long long;

int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  REP(i,n) cin >> a[i];
  sort(a.begin(),a.end());
  
  vector<int> cnt(a[n-1]+1,0);
  
  REP(i,n){
    cnt[a[i]]++;
  }
  
  int ans = 0;
  
  REP(i,a[n-1]+1){
    int sum = 0;
    if(i != 0){
      if(i != a[n-1]){
        sum = cnt[i-1] + cnt[i] + cnt[i+1];
      }
  	}
    ans = max(sum,ans);
  }
  
  cout << ans << endl;

}