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: Accepted)

#include <bits/stdc++.h>
#include <iostream>
#include<math.h>
using namespace std;
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
int main()
{
    int64_t N;
    cin >> N;
    map<int64_t,int64_t>d;
    for (int64_t i=0; i<N; i++) {
        int64_t n;
        cin >> n;
        if (d.count(n) > 0) {
            d[n] = d[n] + 1;
        } else {
            d[n] = 1;
        }
    }

    int64_t max_count = 0;
    for (auto s : d) {
        int64_t b_v = 0;
        if (d.count(s.first-1) > 0) {
            b_v = d[s.first-1];
        }

        int64_t a_v = 0;
        if (d.count(s.first+1) > 0) {
            a_v = d[s.first+1];
        }

        int64_t count = a_v + b_v + s.second;
        if (count > max_count) {
            max_count = count;
        }
    }

    cout << max_count << endl;
    return 0;
}