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 <bits/stdc++.h>
using namespace std;


int main(){
    int N;
    cin >> N;
    vector<int> a(N), b(N), a1(N), a2(N);
    for(int i=0; i<N; i++){
        cin >> a[i];
        b[i] = a[i];
        a1[i] = a[i];
        a2[i] = a[i];
    }
    sort(b.begin(),b.end());
    int mid1 = b[b.size()/2];
    int mid2 = b[b.size()/2-1];
    
    for(int i=0; i<N; i++){
        if(a[i]<mid1) a1[i]++;
        else if(a[i]>mid1) a1[i]--;
        if(a[i]<mid2) a2[i]++;
        else if(a[i]>mid2) a2[i]--;
        //cout << b[i] <<" ";
    }
    //cout << endl;
    vector<int> c1(100000), c2(100000);
    for(int i=0; i<N; i++){
        c1[a1[i]]++;
        c2[a2[i]]++;
    }
    
    sort(c1.begin(),c1.end());
    reverse(c1.begin(),c1.end());
    sort(c2.begin(),c2.end());
    reverse(c2.begin(),c2.end());
    
    cout << (c1[0]>c2[0]?c1[0]:c2[0]) << endl;
}