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 <iostream>
#include <string>
#include <vector>
#include <climits>
#include <algorithm>
#include <set>
#include <unordered_map>
#include <queue>
#include <iomanip>

using namespace std;
int N;
int ma=0;
int a;
int ans=0;
vector<int> P(100005);

int main() {
  cin >> N;
  for (int i=0; i<N; i++) {
    cin >> a;
    P.at(a)++;
    ma = max(a, ma);
  }
  for (int i=1; i<=ma; i++) {
    ans = max(ans, P.at(i-1)+P.at(i)+P.at(i+1));
  }
  cout << ans << endl;
}