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: Wrong Answer)

#include<stdio.h>

int MAX(int a, int b){return a>b?a:b;}
int MIN(int a, int b){return a<b?a:b;}

int main(void){
    int n;
    scanf("%d", &n);
    int a[100002];
    for(int i=0; i<100002; i++){
        a[i] = 0;
    }
    int min = 100000;
    int max = 0;
    for(int i=0; i<n; i++){
        int tmp;
        scanf("%d", &tmp);
        a[tmp] += 1;
        min = MIN(min, tmp);
        max = MAX(max, tmp);
    }

    int ans;
    if(n == 1){
        ans = 1;
    }
    if(n == 2){
        if((a[min]+a[min+1]==2)||(a[min]+a[min+2]==2)||(a[min]==2)){
            ans = 2;
        }else{
            ans = 1;
        }
    }
    if(n > 2){
        ans = -1;
        for(int i=1; i<=max; i++){
            ans = MAX(ans, a[i-1]+a[i]+a[i+1]);
        }
    }

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

    return 0;
}