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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
$N = trim(fgets(STDIN));
$A = explode(' ',trim(fgets(STDIN)));
// $b = max($A) - $N;
// if($b < 0) $b = $b * (-1);

for($b = -max($A); $b <= max($A); $b++) {
  $total = 0;
  for($i = 0; $i < $N; $i++) {
    $abs = ($A[$i] - ($b + $i + 1));
    if($abs < 0) $abs = $abs * (-1);

    $total = $total + $abs;
  }
  if($b == -max($A)) {
    $ans = $total;
    // echo "(1)$b $ans\n";
  }
  if($total < $ans) {
    $ans = $total;
    // echo "(2)$total\n";
  }
  if($total == 0) {
    echo "$ans\n";
    exit;
  }
}
// echo "$b\n";
echo "$ans\n";
?>