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<stdio.h>
#include<stdlib.h>
int compare(const void *a, const void *b){
  if(*(int *)a < *(int *)b){
    return -1;
  }
  else if(* (int *)a == *(int *)b){
    return 0;
  }else{
    return 1;
  }
}
int main(){
  int a[100000];
  int i, j, N;
  int tmp;
  int count = 0;
  int kotae = 0;
  scanf("%d", &N);
  for(i = 0; i < N; i++){
    scanf(" %d", &a[i]);
  }
  
  size_t data_cnt;
  data_cnt = N;

  qsort((void *)a, data_cnt, sizeof(a[0]), compare);
  /*for(i = 0; i < N; i++){
    printf("%d", a[i]);
  }
  */
  j = 0;
  i = 0;
  for(j = 0; j < N; j++){
    tmp = a[j];
    if (a[j] == a[j+1] && j != N - 1){
      continue;
    }
    
    for(i = 0; i < N; i++){
      if(tmp == a[i] || tmp == a[i] - 1 || tmp == a[i] + 1){
        count = count + 1;
      }
      if(tmp > a[i] + 2 && count >= 1){
        break;
      } 
    }
    if(count > kotae){
      kotae = count;
    } 
    count = 0;
  }
  printf("%d", kotae); 
  return 0;
}