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 PHP (5.6.30) (judge verdict: Time Limit Exceeded)

<?php
  fscanf(STDIN,"%d",$a);
  $array = explode(" ",fgets(STDIN));
  $order_array = $array;
  $total_cnt = 0;
  $total_cnt_abs = 0;
  $sign  = 0;
  $through = 0;
  $ans = 0;
  $sort_array = array();//ソート用配列

  //数からiを引いて均す
  for($i=0;$i<$a;$i++)
  {
    $order_array[$i] = (int)$array[$i] - ($i+1);
    $total_cnt_abs += abs($order_array[$i]);
    if($order_array[$i] > 0)
    {
      $total_cnt++;
    }
    else if($order_array[$i] < 0)
    {
      $total_cnt--;
    }
  }
  if($total_cnt > 0)
  {
    $sign = 1;
  }
  else if($total_cnt < 0)
  {
    $sign = -1;
  }
  else
  {
    //同数だった場合は合計を出力
    $ans = $total_cnt_abs;
    $through = 1;
  }
  if($through == 0)
  {
    //正or負のみ抜き出す
    for($i=0;$i<$a;$i++)
    {
      if($order_array[$i] * $sign > 0)
      {
        $sort_array[] = $order_array[$i];
      }
    }
    //重複除外
    $sort_array = array_unique($sort_array);
    //ソートする
    if($sign == 1)
    {
      sort($sort_array);//昇順でソート
    }
    else
    {
      rsort($sort_array);//降順でソート
    }
    
    //本計算
    $total_cnt_old = $total_cnt_abs;
    $total_cnt_abs = 0;
    
    for($j=0;$j<count($sort_array);$j++)
    {
      $tmp_array = $order_array;
      for($i=0;$i<$a;$i++)
      {
        $tmp_array[$i] -= $sort_array[$j];
        $total_cnt_abs += abs($tmp_array[$i]);
      }
      if($total_cnt_old <= $total_cnt_abs)
      {
        $ans = $total_cnt_old;
        break;
      }
      else
      {
        $total_cnt_old = $total_cnt_abs;
        $ans = $total_cnt_old;//配列の末端だった場合対策
        $total_cnt_abs = 0;
      }
    }
  }
  echo $ans;