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)

/*
"IOI 2018" Japan, Tokyo.
*/
#include <bits/stdc++.h>

#define fr first
#define sc second
#define mk make_pair
#define pb push_back
#define pp pop_back()
#define ll long long
#define ld long double
#define ok puts("OK");
#define sz(s) (int)s.size()
#define all(s) s.begin(), s.end()

using namespace std;

inline ll min(ll a, ll b) {
    return (a > b) ? b : a;
}

inline ll max(ll a, ll b) {
    return (a > b) ? a : b;
}

const int N = 1e5 + 7;
const int inf = 1e9 + 7;
const ll linf = 1e18 + 9;

int a[N], b[N], freq[N];

main() {
    int n; scanf ("%d", &n);
    for (int i = 1; i <= n; i++) {
        scanf ("%d", a + i);
        b[i] = i;
        freq[a[i]]++;
    }
    sort (b + 1, b + n + 1);
    int mx = 1;
    for (int i = 1; i <= n; i++) {
        int dif = b[i] - b[i - 1];
        int aa = 0, bb = 0;
        if (b[i] - dif >= 0) aa = freq[b[i] - dif];
        if (b[i] + dif < N) bb = freq[b[i] + dif];
        mx = max(mx, bb + freq[b[i]] + aa);
    }
    cout << mx;
}