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 Perl (v5.18.2) (judge verdict: Wrong Answer)

#!/usr/bin/perl
#
use strict;
use warnings;

my $N = <>;
my @A = split(" ",<>);

my $n=1;
my @B =sort{$a<=>$b} map{ $_-$n++ }@A;
my $mid = scalar(@B);
my $B;
if($mid%2){
    $mid = ($mid-1)/2 - 1;
    $B = $B[$mid];
}else{
    $mid = $mid/2 - 1;
    $mid = $B[$mid]+$B[$mid+1];
    if($mid%2){
        $B = ($mid-1)/2;
    }else{
        $B = $mid/2;
    }
}
my $l=0;
for (my $i=1; $i<=$N; $i++){
    my $x = $A[$i-1];
    $l += abs($x-($B+$i));
}
print $l;