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 Lua (5.3.2) (judge verdict: Accepted)

function median(list)
  table.sort(list)
  local center = math.floor(#list / 2)
  if #list % 2 == 0 then
    return (list[center] + list[center + 1]) / 2
  else
    return list[center + 1]
  end
end

function sad(A, b)
  local acc = 0
  for i, v in ipairs(A) do
    acc = acc + math.abs(v - (b + i))
  end
  return acc
end

local N = tonumber(io.read())
local A = {}
for n in io.read():gmatch('%d+') do
  table.insert(A, tonumber(n))
end

local B = {}
for i, v in ipairs(A) do
  table.insert(B, (v - i))
end

io.write(sad(A, median(B)))