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;
typedef long long ll;

int main() {
  int n;
  cin >> n;
  vector<ll> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    a[i] -= i + 1;
  }
  sort(begin(a), end(a));
  for (int i = n - 1; i >= 0; i--) {
    a[i] -= a[0];
  }
  for (int i = 0; i < n - 1; i++) {
    a[i + 1] += a[i];
  }
  /*
  for (auto e : a) {
    cerr << e << " ";
  }
  cerr << endl;
  */
  ll m = 1e15;
  for (int i = 0; i < n - 1; i++) {
    m = min(m, ((i + 1) * (a[i + 1] - a[i]) - a[i]) + (a[n - 1] - a[i] - (n - i - 1) * (a[i + 1] - a[i])));
  }
  cout << m << endl;
}