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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

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

#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep2(i,n) for(int i=1;i<=(int)(n);i++)
#define rep3(i,n) for(int i=0;i<=(int)(n);i++)
#define REP(i,m,n) for(int i=m;i<(int)(n);i++)
#define repll(i,n) for(ll i=0;i<(ll)(n);i++)
#define repll2(i,n) for(ll i=1;i<=(ll)(n);i++)
#define REPLL(i,m,n) for(ll i=m;i<(ll)(n);i++)
#define INF (int)1e9  //
#define LINF (ll)4e18  //
#define MOD (int)(1e9)+7
#define MP make_pair
#define YES(n) cout << ((n) ? "YES" : "NO"  ) << endl
#define Yes(n) cout << ((n) ? "Yes" : "No"  ) << endl
#define PI 3.1415926535898

//------------------------------------------------------

int main() {
    int n;
    cin >> n;
    int cnt[100010];

    rep(i, n) {
        int a;
        cin >> a;
        if (a == 0) {
            cnt[0]++;
            cnt[1]++;
        } else {
            cnt[i]++;
            cnt[i - 1]++;
            cnt[i + 1]++;
        }
    }

    int Max = 0;

    rep(i, n + 2) {
        Max = max(Max, cnt[i]);
    }

    cout << Max << endl;

    return 0;
}