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 5.4.1) (judge verdict: Accepted)


#include <stdio.h>
 
int
main(int argc, char *argv[])
{
  int n, a[100000]; int max = 0, min = 100000; int cnt[100001] = {};
  scanf("%d", &n);
  for(int i = 0; i < n; i++){
    scanf("%d", &a[i]);
    max = (max > a[i] ? max : a[i]);
    min = (min > a[i] ? a[i] : min);
    cnt[a[i]]++; cnt[a[i] + 1]++;
    if(a[i] >= 1) cnt[a[i] - 1]++;
  }
 
  int ans = 0;
 
  for(int i = min; i <= max; i++){
    ans = (ans > cnt[i] ? ans : cnt[i]);
  }
 
  printf("%d\n", ans);
 
  return 0;
}