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: Wrong Answer)

<?php
// WA
// 単純に中央値求めればいいらしいんだけど
$n = (int)trim(fgets(STDIN));
$input = explode(' ', trim(fgets(STDIN)));
$array = [];
$res_min = 0;
for ($i=0; $i < $n; $i++) { 
	$v = (int)$input[$i];
	$array[] = $v-$i-1;
	$res_min += abs($v-$i-1);
}

$right = 1000000000 * (int)($n * ($n+1) / 2);
$left = -$right;

while ($left < $right) {
	$mid = (int)floor(($left+$right)/2);
	$res = calc($mid);
	// echo 'left:' . $left . ' right:' . $right . PHP_EOL;
	// echo 'res: ' .$res['abs_sum'] . PHP_EOL;
	if ($res_min === null) {
		$res_min = $res['abs_sum'];
	}else{
		$res_min = min($res_min, $res['abs_sum']);
	}
	if ($res_min === 0) {
		break;
	}
	if ($res['sum'] > 0) {
		$left = $mid+1;
	}else{
		$right = $mid;
	}
}
echo $res_min;

function calc($b){
	global $array;
	global $n;
	$sum = 0;
	$abs_sum = 0;
	for ($i=0; $i < $n; $i++) { 
		$abs_sum += abs($array[$i] - $b);
		$sum += $array[$i] - $b;
	}
	return [
		'abs_sum' => $abs_sum,
		'sum' => $sum,
	];
}