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 <bits/stdc++.h>
//---------------------------
using namespace std;
//---------------------------
#define REP(i,n) for(int i = 0; i < (n); i++)
#define P(x) cout << (x) << "\n"

#define MOD 1e9+7
#define PI acos(-1.0)
#define ll long long
#define INF 1000000001

int dx[4]={1,-1,0,0};
int dy[4]={0,0,1,-1};
//---------------------------

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

  // ifstream in("input.txt");
  // cin.rdbuf(in.rdbuf());

  int n;cin>>n;
  if(n==1){
    P(1);
    return 0;
  }else if(n==2){
    int x1,x2;cin>>x1>>x2;
    if(x2-x1<3 && x2-x1>-3){
      P(2);return 0;
    }
    P(1);return 0;
  }
  int a[100000];
  int b[100000];
  int mx=0;
  REP(i,n)cin>>a[i];
  sort(a,a+n);
  REP(i,100000){
    // iの個数を求める→b[i]に入れる
    int t1=lower_bound(a,a+n,i)-a;
    int t2=upper_bound(a,a+n,i)-a;
    int t=t2-t1;
    b[i]=t;
  }
  for(int i=0;i<n-2;i++){
    mx=max(mx, b[i]+b[i+1]+b[i+2]);
  }
  P(mx);
  return 0;
}