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;
int n,a[100005];
vector<int> k;
map<int,int> mp;

int main()
{
	cin >> n;a[0]=1000000;
	for(int i=1;i<=n;i++) cin >> a[i];
	
	sort(a+1,a+n+1);
	
	for(int i=1;i<=n;i++)
	{
		if(a[i]!=a[i-1]) k.push_back(a[i]);
		mp[a[i]]++;
	}
	
	int sum=0,res=0;
	for(int i=0;i<=int(k.size()-3);i++)
	{
		sum=mp[k[i]];
		if(k[i+1]==k[i]+1 && k[i+2]==k[i]+2) sum+=(mp[k[i+1]]+mp[k[i+2]]);
		else if (k[i+1]==k[i]+1) sum+=mp[k[i+1]];
		res=max(res,sum);
	}
	
	if(k.size()==1) res=mp[k[0]];
	if(k.size()==2)
	{
		if(k[0]+1==k[1]) res=mp[k[0]]+mp[k[1]];
		else res=max(mp[k[0]],mp[k[1]]);
	}
	cout << res;
	return 0;
}