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 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

#define MAX 100000

void q_sort(int numbers[], int left, int right);

int main(void)
{
	int n, i, fac;
	int a[MAX];
	int b[MAX][2];
	int max;
	
	scanf("%d", &n);
	for(i=0; i<n; i++)
		scanf("%d", &a[i]);
	
	q_sort(a, 0, n-1);
	
	for(fac=0,i=0; i<n; i++){
		if(i == 0){
			b[fac][0] = a[i];
			b[fac][1] = 1;
			continue;
		}
		
		if(b[fac][0] == a[i])
			b[fac][1]++;
		else{
			b[++fac][0] = a[i];
			b[fac][1] = 1;
		}
	}
	fac++;
	
	for(max=0,i=0; i<fac; i++){
		int kari = b[i][1];
		
		if( (b[i-1][0] == b[i][0]-1) && (i != 0) ){
			kari += b[i-1][1];
		}
		
		if( (b[i+1][0] == b[i][0]+1) && (i != fac-1) ){
			kari += b[i+1][1];
		}
		
		if(max < kari){
			max = kari;
		}
	}
	
	printf("%d", max);
	
	
	return 0;
}

void q_sort(int numbers[], int left, int right)
{
    int pivot, l_hold, r_hold;
	
	l_hold = left;
	r_hold = right;
	pivot = numbers[left];
	
	while(left < right)
	{
		while( (numbers[right] >= pivot) && (left < right) )
			right--;
		if (left != right)
		{
			numbers[left] = numbers[right];
			left++;
		}
		while( (numbers[left] <= pivot) && (left < right) )
			left++;
		if(left != right)
		{
			numbers[right] = numbers[left];
			right--;
		}
	}
	
	numbers[left] = pivot;
	pivot = left;
	left = l_hold;
	right = r_hold;
	
	if(left < pivot)
		q_sort(numbers, left, pivot-1);
	if(right > pivot)
		q_sort(numbers, pivot+1, right);
}