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

  int ans=0;
  for(int i=0;i<=100000;i++){
    int cnt=0;
    if(i==0) cnt=A[1]+A[0];
    else if(i==100000) cnt=A[100000-1]+A[100000];
    else cnt=A[i-1]+A[i]+A[i+1];
    if(cnt>ans) ans=cnt;
  }
  printf("%d",ans);
  return 0;
}