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: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#define max(a,b) (a>b)?a:b;

int n[100000] = { 0 };

int sort(const void *a, const void *b) {
	return *(int*)a - *(int*)b;
}

int main(void) {
	int N;
	int ans = 1, cnt1 = 1, cnt2 = 0, flag = 1, def = 2;

	scanf("%d", &N);
	for (int i = 0; i < N; i++) scanf("%d", &n[i]);
	qsort(n, N, sizeof(int), sort);

	for (int i = 0; i < N; i++) {
		if (n[i] == n[i + 1]) cnt1++;
		else if ((n[i + 1] - n[i]) <= def) {
			cnt2 = cnt1;
			cnt1++;
			def = def - (n[i + 1] - n[i]);
		}
		else {
			ans = max(ans, cnt1);
			cnt1 = cnt1 - cnt2;
			cnt2 = 0;
			def = 2;
		}
	}

	printf("%d\n", ans);

	return 0;
}