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 <queue>
#include <cmath>
#include <bitset>
#include <algorithm>

#define rep(i, N) for(int (i) = 0; (i) < (N); (i) ++)
typedef long long ll;

using namespace std;

int main(){
    int N;
    cin >> N;
    vector<int> as(N, 0);
    rep(i, N){
        cin >> as[i];
    }
    sort(as.begin(), as.end());
    int ans = 0;
    rep(i, as.size()){
        int x = as[i];
        auto iter1 = lower_bound(as.begin(), as.end(), x - 1);
        auto iter2 = lower_bound(as.begin(), as.end(), x + 2);
        int tmp = iter2 - iter1;
        ans = max(tmp, ans);
    }

    cout << ans << endl;
    return 0;
}