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)

use v5.18;
use warnings;
use List::Util qw ( sum );
sub read_line { chomp(my $str = <STDIN>); $str }
sub splited_read_line { split / /, read_line }

sub uniq {
  my %uniqer;
  for my $num (@_) {
    $uniqer{$num} = 0;
  }
  keys %uniqer;
}

my $n = read_line;
my @nums = splited_read_line;
my @abss = do {
  my $i = 1;
  map { $_ - $i++ } @nums;
};

# 最頻値
my %counter;
for my $num (@abss) {
  $counter{$num}++;
}
my $is_same_all = uniq(values %counter) == 1 ? 1 : 0;
my $var = do {
  if ($is_same_all) {
    (sort { $a <=> $b } map { abs $_ } keys %counter)[0];
  }
  else {
    (sort { $counter{$a} <=> $counter{$b} } keys %counter)[-1];
  }
};

my $i = 1;
say sum map { abs($_ - ($var + $i++)) } @nums;