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
$n = (int)trim(fgets(STDIN));
$a = explode(' ', trim(fgets(STDIN)));

for ($i = 0; $i < $n; $i++) {
    $a[$i] = (int)$a[$i];
}

$c = 0;
$c_i = 0;
$m = 0;
$m_i = 0;
for ($i = 0; $i < $n - 1; $i++) {
    if ($a[$i + 1] - $a[$i] === 1) {
        if ($c === 0) {
            $c_i = $i;
        }
        $c++;
    } else {
        $c = 0;
    }

    if ($c > $m) {
        $m = $c;
        $m_i = $c_i;
    }
}

if ($m_i > 0) {
    $b = $a[$m_i] - ($m_i + 1);
} else {
    $b = 0;
}

$ans = 0;
for ($i = 0; $i < $n; $i++) {
    $ans += abs($a[$i] - ($b + $i + 1));
}

echo $ans . PHP_EOL;