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: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
int main()
{
	int n;
	scanf("%d",&n);
	int a[n],b[n],c[n],d[n];
	for(int i=0;i<n;i++)
	{
		scanf("%d",&a[i]);
	}
	for(int i=0;i<n;i++)
	{
		b[i]=a[i]+1;
		c[i]=a[i]-1;
	}
	for(int i=0;i<n;i++)
	{
		int x=0,y=0,t=0,max;
		for(int j=0;j<n;j++)
		{
			if(a[i]==a[j]||a[i]==b[j]||a[i]==c[j])x++;
			if(b[i]==a[j]||b[i]==b[j]||b[i]==c[j])y++;
			if(c[i]==a[j]||c[i]==b[j]||c[i]==c[j])t++;
			if(x>y)max=x;
			if(x<=y)max=y;
			if(max<t)max=t;
			d[i]=max;
		}
	}
	for(int i=0;i<n-1;i++)
	{
		if(d[i]>d[i+1])d[i+1]=d[i];
	}
	printf("%d\n",d[n-1]);
}