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: Accepted)

#include <bits/stdc++.h>
#define ll long long
#define pii pair<int, int>
#define pll pair<ll, ll>
#define str string
#define fi first
#define se second
#define pb push_back
#define SET(a, b) memset(a, b, sizeof(a))
#define eps 1e-6
#define pi atan(1) * 4
#define mod 1000000007
#define inf 1000000000000000000
using namespace std;
int freq[100005];
int main () {
	int a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q;
	scanf("%d", &a);
	SET(freq, 0);
	for (i = 1; i <= a; i++) {
		scanf("%d", &b);
		freq[b]++;
	}
	c = 0;
	for (i = 1; i <= 100000; i++) {
		c = max(c, freq[i - 1] + freq[i] + freq[i + 1]);
	}
	printf("%d\n", c);
	return 0; 
}