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: Time Limit Exceeded)

#include <bits/stdc++.h>
#define INF 1e9
#define endl '\n'
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define FORE(i, a, b) for (int i = (a), e = (b); i < e; ++i)
#define RFORE(i, a, b) for (int i = (b)-1, e = (a); i >= e; --i)
#define ALL(x) (x).begin(), (x).end()
#define SORT(c) sort((c).begin(), (c).end())
#define SORTR(c) sort((c).begin(), (c).end(), greater<int>())
using namespace std;
typedef long long ll;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int N;
    cin >> N;
    vector<int> a(N);
    for (int i = 0; i < N; i++) {
        cin >> a.at(i);
    }
    int         start = *min_element(ALL(a));
    int         end   = *max_element(ALL(a));
    int         tmp   = count(ALL(a), start);
    vector<int> c(end + 1, 0);
    c.at(start) = tmp;
    FORE(X, start + 1, end + 1) {
        c.at(X) += tmp;
        tmp = count(ALL(a), X);
        c.at(X - 1) += tmp;
        c.at(X) += tmp;
    }
    cout << *max_element(ALL(c)) << endl;
}