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 <stdio.h>
#include <algorithm>

#define NBUF (100005)
int N;
int a[NBUF];

void input(void){
	scanf("%d",&N);
	for(int i=0;i<N;i++) scanf("%d",&a[i]);
}

int main(void){
	input();
	std::sort(a,a+N);
	//for(int i=0;i<N;i++)printf("%d ",a[i]);
		
	int max=0;
//	int X=-1;
	int lower;
	int upper;
	for(int i=0;i<N;i++){
		lower = i;
		upper = N;
		int index;
		while(1){
			index = (lower+upper)/2;
			//printf("i %d index %d",i,index);
			if(index==N-1) break;
			if(a[index]-a[i]<3){ 
				if(a[index+1]-a[i]>2)break;
				lower = index;	
			}else
			{
				upper = index;
			}
		}
		int cnt = index-i+1;
		if(max<cnt){
			max = cnt;
			if(cnt>N-i) break;
			//X=a[i]+1;
		}
	}

	printf("%d\n",max);
	return 0;
}