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 <iostream>
#include <string>
#include <cmath>

long long int n;
long long int a[200000] = {0};

int calc(int b) {
  int sum = 0;
  for (size_t i = 0; i < n; i++) {
    sum += abs(a[i] - (b + i + 1));
  }
  return sum;
}

int main(void) {
  std::cin >> n;

  for (size_t i = 0; i < n; i++) {
    std::cin >> a[i];
  }

  int sum = 0;
  long long int min = -1e10;
  long long int max = +1e10;
  for (size_t i = 0; i < n; i++) {
    int num = a[i] - (/*b + */ i + 1);
    if (i == 0) {
      max = num;
      min = num;
    } else {
      if (max < num) {
        max = num;
      }
      if (min > num) {
        min = num;
      }
    }
  }

  //std::cout << "MIN:" << min << std::endl;
  //std::cout << "MAX:" << max << std::endl;

  if (abs(max) < abs(min)) {
    max = abs(min);
    min = -max;
  } else {
    max = abs(max);
    min = -max;
  }

  long long int mid = (min + max) / 2;
  long long int b = mid;
  long long int resmin = calc(min);
  long long int resmid = calc(mid);
  long long int resmax = calc(max);
  long long int result = resmid;

  while(1) {
    //std::cout << "b : " << b << std::endl;

    int newb = 0;
    if (resmin == resmax) {
      if (result > resmid) {
        result = resmid;
      }
      break;
    } else {
      if (resmin < resmax) {
        newb = (min + b)/2;
        if (b == newb) {
          newb = min;
        }
        resmid = calc(newb);
        resmax = resmid;
      } else {
        newb = (max + b)/2;
        if (b == newb) {
          newb = max;
        }
        resmin = resmid;
        resmid = calc(newb);
      }
      if (result > resmid) {
        result = resmid;
      }
    }
    //std::cout << "newb : " << newb << " w/ " << resmid << std::endl;

    if (b == newb) {
      break;
    }
    b = newb;
  }

  std::cout << result << std::endl;

#if 0
  int result = 0;
  if (abs(max) < abs(min)) {
    max = abs(min);
  } else {
    max = abs(max);
  }
  for (int b = -max; b <= max; ++b) {
    int sum = 0;
    for (size_t i = 0; i < n; i++) {
      sum += abs(a[i] - (b + i + 1));
    }
    //std::cout << b << " : " << sum << std::endl;

    if (b == -max) {
      result = sum;
    } else {
      if (result > sum) {
        result = sum;
      }
    }
  }
  std::cout << result << std::endl;
#endif

  return 0;
}