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: Time Limit Exceeded)

def f(a,b)
  a.map{|aa,idx|(aa-b).abs}.inject(:+) 
end

n=gets.to_i
a=gets.split.each_with_index.map{|s,i|s.to_i-i-1}

l=-10**18
r=10**18
sad=[f(a,l),f(a,r)].min
while l<=r
  m1=(2*l+r)/3
  temp1=f(a,m1)
  m2=(l+2*r)/3
  temp2=f(a,m2)
  if temp1<temp2
    sad=temp1 if sad>temp1
    r=m2-1
  else
    sad=temp2 if sad>temp2
    l=m1+1
  end
end
puts [sad,f(a,l),f(a,r)].min