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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>

int x[100003];

int f(int n, int *a) {
	int ans = 0;
	for (int i = 0; i < n; i++) {
		int ai = a[i];
		if (ai == 0) {
			x[0] += 1;
			x[1] += 1;
		} else {
			x[ai-1] += 1;
			x[ai] += 1;
			x[ai+1] += 1;
		}
	}
	for (int i = 1; i < 99999; i++) {
		if (x[i] > ans) ans = x[i];
	}
	return ans;
}

int main() {
	int ans;
	int n;
	scanf("%d", &n);
	int a[n];
	for (int i = 0; i < n; i++) scanf("%d", a+i);

	ans = f(n, a);
	
	printf("%d\n", ans);	
	return 0;
}