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: Wrong Answer)

#include <stdio.h>
int main(void){
    int n;
    int a[100000+5];
    scanf("%d", &n);
    for(int i=0; i<n; i++)scanf("%d", &a[i]);
    int num[100000+5];
    
    for(int i=0; i<100000; i++)num[i]=0;
    for(int i=0; i<n; i++)num[a[i]-1]++;
    
    int ans=0;
    for(int i=1; i<100000-1; i++){
        if(num[i]!=0){
            ans=num[i-1]+num[i]+num[i+1]>ans?num[i-1]+num[i]+num[i+1]:ans;
        }
    }
    printf("%d\n", ans);
    return 0;
}