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 x first
#define y second

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;

ostream& operator<<(ostream &out, const pii &a) { return out << '(' << a.x << ", " << a.y << ')'; }
istream& operator>>(istream &in, pii &a) { return in >> a.x >> a.y; }

const int INF = 2147483647;
const ll LLINF = 9223372036854775807LL;

const int maxV = 1e5;

// lambda-expression: [] (args) -> retType { body }

int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	// cerr << boolalpha;
	(cout << fixed).precision(10);

	int N;
	cin >> N;
	vi cnt(maxV, 0);
	for (int i = 0; i < N; i++) {
		int a;
		cin >> a;
		cnt[a]++;
	}

	int best = cnt[0] + cnt[1] + cnt[2];
	int cur = best;
	int it = 1;
	while (it + 2 < maxV) {
		cur -= cnt[it - 1];
		it++;
		cur += cnt[it + 1];
		best = max(best, cur);
	}
	cout << best << endl;
	return 0;
}