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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <cmath>

using namespace std;

int main()
{
    int countNum[100001];
    int maxCount = 0;

    int n; cin >> n;
    for (int i = 0; i < n; i++) {
        int a; cin >> a;
        countNum[a]++;
        if (a > 0) countNum[a - 1]++;
        countNum[a + 1]++;
        maxCount = max(max(maxCount, countNum[a]), max(countNum[a - 1], countNum[a + 1]));
    }
    cout << maxCount << endl;

    return 0;
}