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: Accepted)

'use strict';
const inputRaw = require("fs").readFileSync("/dev/stdin", "utf8").trim().split("\n");
const INPUT_LIST_LENGTH_INDEX = 0;
const INPUT_LIST_INDEX = 1;
const INPUT_LIST_DELIMITER = " ";
const inputListLength = parseInt(inputRaw[INPUT_LIST_LENGTH_INDEX]);
const inputList = inputRaw[INPUT_LIST_INDEX].split(INPUT_LIST_DELIMITER);

const process = (inputList, inputListLength) => {
  // pattern: min(b) in (sum(A-b)) === median of sorted A

  // sum(A - (b + i)) === sum ((A - i) - b)
  // convert list to A-i
  for (let i=0;i<inputListLength;i++) {
    inputList[i] = parseInt(inputList[i])-i;
  }

  inputList.sort((prev,next) => prev-next);

  const median = inputList[Math.floor(inputListLength/2)];

  return inputList.reduce((acc, currentItem) => acc + Math.abs(currentItem-median), 0);
}

console.log(process(inputList, inputListLength));