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>
#include<stdlib.h>
#include<string.h>
#include<math.h>

typedef long long ll;

int a[100007];
int cnt[100007];

int main(){
  int n;
  int i;
  int max;

  scanf("%d", &n);
  for(i = 0;i <= 100000;i++) cnt[i] = 0;
  for(i = 0;i < n;i++){
    scanf("%d", &a[i]);
    cnt[a[i]]++;
  }

  max = cnt[0]; // -1
  if((cnt[0] + cnt[1]) > max) max = cnt[0] + cnt[1]; // 0
  for(i = 1;i <= 100000;i++){
    if((cnt[i] + cnt[i - 1] + cnt[i + 1]) > max) max = cnt[i] + cnt[i - 1] + cnt[i + 1];
  }

  printf("%d\n", max);

  return 0;
}