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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define ll int64_t
 
const int N=1e5+5;
int n,cnt[N];
 
int main() {
	ios_base::sync_with_stdio(0);cin.tie(0);
	cin>>n;
	for(int i=0;i<n;++i){
		int x;
		cin>>x;
		cnt[x]++;
	}
	int res=0;
	for(int i=0;i<100000;++i){
		int sum=cnt[i]+cnt[i+1];
		if(i) sum+=cnt[i-1];
		res=max(res,sum);
	}
	cout<<res<<'\n';
}