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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <cstring>
#include <map>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <iostream>

using namespace std;

int arr[100010];

int main()
{

//    freopen("D:\\Code\\TestData\\data_in.txt","r",stdin);
//    freopen("D:\\Code\\TestData\\data_in.txt","w",stdout);
//    printf("100000\n");
//    for(int i=1;i<=100000;i++){
//        printf("%d ",i);
//    }
//    printf("\n");
    int loop;

    while(~scanf("%d", &loop))
    {
        for(int i=1;i<=loop;i++){
            scanf("%d",&arr[i]);
        }

        bool f=false;
        int pre=0;
        int res=0;
        for(int i=1;i<=loop;i++){
            if(arr[i]==i){
                if(f){
                   if(i-pre==1){
                        f=false;
                   }else{
                        res++;
                        f=false;
                   }
                }else{
                    pre=i;
                    f=true;
                    res++;
                }
            }else{
                f=false;
            }
        }
        printf("%d\n",res);

    }
    return 0;
}