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: Accepted)

#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<string.h>


#define ZERO(p) memset(p, 0, sizeof(p))

int main() {
    int N;
    std::cin >> N;
    int MAXNUM = 100000;
    int max=0;
    int counter[MAXNUM+2];
    ZERO(counter);
    for(int i=0;i<N;i++) {
        int a;
        std::cin >> a;
        //counter[i]はi+1の数
        counter[a] = counter[a] + 1;
        counter[a+1] = counter[a+1] + 1;
        counter[a+2] = counter[a+2] + 1;
        int candidate;
        if(max < counter[a] ) {
            max = counter[a];
        }
        if(max < counter[a+1] ) {
            max = counter[a+1];
        }
        if(max < counter[a+2] ) {
            max = counter[a+2];
        }
    }
    std::cout << max << std::endl;
}