Problem:
Score : 300 points

Problem Statement

Snuke has an integer sequence A of length N.

He will freely choose an integer b.
Here, he will get sad if A_i and b+i are far from each other.
More specifically, the sadness of Snuke is calculated as follows:

abs(A_1 - (b+1)) + abs(A_2 - (b+2)) + ... + abs(A_N - (b+N))

Here, abs(x) is a function that returns the absolute value of x.

Find the minimum possible sadness of Snuke.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible sadness of Snuke.

Sample Input 1

5
2 2 3 5 5

Sample Output 1

2

If we choose b=0, the sadness of Snuke would be abs(2-(0+1))+abs(2-(0+2))+abs(3-(0+3))+abs(5-(0+4))+abs(5-(0+5))=2.
Any choice of b does not make the sadness of Snuke less than 2, so the answer is 2.

Sample Input 2

9
1 2 3 4 5 6 7 8 9

Sample Output 2

0

Sample Input 3

6
6 5 4 3 2 1

Sample Output 3

18

Sample Input 4

7
1 1 1 1 2 3 4

Sample Output 4

6

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int main() {
  int a, b, x, ar, ea;
  int cou = 0, cou_max = 0;
  string str;
  cin >> a;

  long long sum = 0, mi = 10000000000007;
  long long arr[a];
  for (int i = 0; i < a; i++) {
    cin >> arr[i];
    arr[i] = arr[i] - i - 1;
  }
  sort(arr, arr + a);
  for (int i = 0; i < a - 1; i++) {
    if (arr[i] == arr[i + 1]) {
      cou++;
      if (cou > cou_max) {
        cou_max = cou;
        ar = arr[i];
      }
    } else {
      cou = 0;
    }
  }
  if (a % 2 == 1) {
    b = arr[(a - 2) / 2];
    for (int j = b - 10000; j < b + 10000; j++) {
      for (int i = 0; i < a; i++) {
        sum += abs(arr[i] - j);
      }
      if (sum < mi) {
        mi = sum;
      }
      sum = 0;
    }
  } else {
    b = arr[(a - 4) / 2];
    for (int j = b - 10; j < arr[a / 2] + 10; j++) {
      for (int i = 0; i < a; i++) {
        sum += abs(arr[i] - j);
      }
      if (sum < mi) {
        mi = sum;
      }
      sum = 0;
    }
  }

  cout << mi << endl;
  return 0;
}