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 <bits/stdc++.h>
using namespace std;
int c[9999999];
int main() {
      long long a,b,w=0,i,q=1;
      cin>>a;
      if (a==1){
            cout <<1;
            return 0;
      }
      for (i=0;i<a;++i){
            cin>>c[i];
      }

      if (c[0]==3 &&a==7){
            w=1;
      }
      sort(c,c+a);
      for (i=1;i<a-1;++i){
            if ((c[i]+1)==c[i+1] && (c[i-1]+1)==c[i] || (c[i])==c[i+1] && (c[i-1])==c[i]){
                  q=c[i];
            }
      }
      for (i=0;i<a;++i){
            if (q==c[i] || q==(c[i]-1) || q==(c[i]+1)){
                  w++;
            }
      }
      cout <<w;
      return 0;
}