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;

const int N = 1e5 + 3;

int p, n;

int main() {
  #ifdef GG
    freopen("a.in", "r", stdin);
    freopen("a.out", "w", stdout);
  #endif
  scanf("%d", &n); int ans = 0, x = 0;
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &p);
    if (p == i) {
      ++x;
    } else {
      ans += x / 2 + x % 2;
      x = 0;
    }
  }
  ans += x / 2 + x % 2;
  printf("%d", ans);
  return 0;
}