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 Ruby (2.3.3) (judge verdict: Accepted)

n = gets.to_i
a = gets.split.map &:to_i

c = []
max = 1000000000
min = -100000
a.each_with_index do |ai, i|
    ci = a[i] - i - 1
    c[i] = ci
    max = [max, ci].max
    min = [min, ci].min
end

best = nil
target = min + 1
dif = max - min
while true
    sum1 = 0
    plus = 0
    minus = 0
    c.each do |ci|
        sum1 += (ci - target).abs
        plus += (ci - (target + 1)).abs
        minus += (ci - (target - 1)).abs
    end
    if sum1 > plus
        dif /= 2
        dif = 1 if dif == 0
        target += dif
    elsif sum1 > minus
        dif /= 2
        dif = 1 if dif == 0
        target -= dif
    else
        puts sum1
        exit
    end
end