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: Wrong Answer)

@n = gets.to_i
as = gets.strip.split.map(&:to_i)
max_a = as.max

l = 1
r = 1e9

as2 = (1..@n).map { |i| as[i - 1] - i }.sort

cumsum = []
for a in as2
    last = cumsum.empty? ? 0 : cumsum.last
    cumsum << last + a
end

# an - b の符号の変わり目を二分探索
def search(as2, b)
    lb = 0
    rb = as2.size
    while rb - lb > 1 do
        center = (lb + rb) / 2
        if as2[center] - b >= 0
            rb = center
        else
            lb = center
        end
    end
    return lb
end

def sorrow(cumsum, as2, b)
    n1 = search(as2, b)
    s = -2 * cumsum[n1] + cumsum[@n - 1] + (2 * n1 - @n) * b
end

puts (0..max_a).map { |b| sorrow(cumsum, as2, b) }.min