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>
using namespace std;

#define FOR(i,a,b) for(int i = (a); i < (b); ++i)
#define REP(i,n) FOR(i,0,n)
using ll = long long;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vvvi = vector<vector<vector<int>>>;
using mii = map<int, int>;
using msi = map<string, int>;
using pii = pair<int, int>;

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int n;
    cin >> n;
    vi a(n);
    REP(i, n) cin >> a[i];

    map<int, int> mp;
    REP(i, n) mp[a[i]]++;

    int ans = 0;
    REP(i, 100000) {
        int cnt = 0;
        cnt += mp[i - 1];
        cnt += mp[i];
        cnt += mp[i + 1];
        ans = max(cnt, ans);
    }
    cout << ans << endl;
    return 0;
}