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: Accepted)

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

typedef long long Int;

constexpr Int INF = 10000000000;
Int a[200005];

int main(){
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }

  auto f = [&a, &n](Int x) -> Int {
      Int sum = 0;
      for (int i = 0; i < n; ++i) {
          sum += abs(a[i] - (x + (i + 1)));
      }
      return sum;
  };

  auto tenary_search = [&f]() -> Int {
      Int l = -INF, r = INF;
      Int a, b;

      for (int i = 0; i < 100; ++i) {
          a = (2 * l + r) / 3;
          b = (l + 2 * r) / 3;
          if (f(a) < f(b)) r = b;
          else l = a;
      }

      Int res = f(r);
      for (Int i = l; i < r; ++i) {
        Int temp = f(i);
        if (temp < res) {
          res = temp;
        }
      }
      return res;
  };

  cout << tenary_search() << "\n";
}