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>
#define rep(i,n) for (ll i = 0; i < n; ++i)
#define sz(x) int(x.size())
#define ALL(c) (c).begin(), (c).end()
#define SUM(x) std::accumulate(ALL(x), 0LL)
#define MIN(v) *std::min_element(v.begin(), v.end())
#define MAX(v) *std::max_element(v.begin(), v.end())
#define EXIST(v, x) (std::find(v.begin(), v.end(), x) != v.end())
#define FORV(i, v) for (auto i = v.begin(); i != v.end(); i++)
using namespace std;

using ll = long long;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
const int INF = 1001001001;
const long long INFL = LLONG_MAX / 3;
const double eps = (1e-9);

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  int n; cin >> n;
  vector<int> a(n);
  rep(i, n) cin >> a[i];
  int max_a = MAX(a);

  vector<ll> b(max_a+3, 0);
  rep(i, n) {
    b[a[i]]++;
  }

  ll ans = 0;
  for (int i = 0; i < max_a; i++) {
    chmax(ans, b[i] + b[i+1] + b[i+2]);
  }

  cout << ans << endl;

  return 0;
}