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<vector>
#include<algorithm>

using namespace std;

int main(){
    int n;
    cin >> n;
    vector<int> a;
    for(int i=0;i<n;i++){
        int in;cin >> in;
        a.push_back(in);
    }
    a.push_back(1000000);
    sort(a.begin(),a.end());
    vector<int> b(100001,0);
    int tmp=1;
    for(int i=0;i<n;i++){
        if(a[i]!=a[i+1]){
            b[a[i]]+=tmp;
            tmp = 1;
        }
        else{
            tmp ++ ;
        }
    }
    int ans=0;
        for(int i=1;i<b.size()-1;i++){
            int t;
            t = b[i-1]+b[i] + b[i+1];
            if(t>ans){
                ans = t;
            }
        }
    cout << ans << endl;
    return 0;
}