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: Accepted)

#include<stdio.h>

int main()
{
  int n,x;
  int a[100001],b[100001],c[100001];
  int i;
  int ans=-1;
  scanf("%d",&n);
  for(i=0;i<=100000;i++){
    b[i]=0;
  }
  for(i=0;i<n;i++){
    scanf("%d",&a[i]);
    b[a[i]]++;
  }
  for(i=0;i<=100000;i++){
    c[i]=b[i];
  }
  b[0]+=b[1];
  b[n]+=b[n-1];
  for(i=1;i<100000;i++){
    b[i]+=c[i-1]+c[i+1];
    if(b[i]>ans) ans=b[i];
  }
  printf("%d\n",ans);
  return 0;
}