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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

'use strict'

const main = (chunk => {
  const eachSad = (c, i) => c - i - 1
  const sad = (arr, diff, b) => arr.reduce((acc, c, i) => acc + Math.abs(diff[i] - b), 0)
  const diffs = arr => arr.map((e, i) => eachSad(e, i))
  const median = arr => arr[Math.floor(arr.length / 2)]

  let stack = []
  return (chunk) => {
    if (!stack.length) {
      stack.push(parseInt(chunk, 10)) // N
    } else if (stack.length === 1) {
      stack.push(chunk.split(' ').map(e => parseInt(e, 10))) // Array
      const diff = diffs(stack[1])
      const med = median(diff)
      const sadness = sad(stack[1], diff, med);
      console.log(sadness)
      stack = []
    }
  }
})()

process.stdin.setEncoding('utf-8')
process.stdin.on('data', chunk => main(chunk))