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"
using namespace std;
#define rep(i,a,n) for(int i=a;i<n;i++)
#define ALL(s) s.begin(),s.end()
const int M=100010;
const int INF=1000000007;
using ll=long long;

int main(){
	int n,a[M],b[M]={},c[M]={};
	cin>>n;
	rep(i,0,n){
		cin>>a[i];
		b[a[i]]++;
		rep(j,0,3)c[a[i]+j]++;
	}
	int ans=0;
	rep(i,0,M)ans=max(ans,b[i]);
	rep(i,ans-3,ans+4){
		ans=max(ans,c[i-1]);
	}
	cout<<ans<<endl;
}