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';

// given vector A
// S = summation of (Ai - (b+i))^2 as i goes from 1 to N
// find dS/db = 0 (minimize), (Ai - (b+i)) = 0
// summation (Ai) - summation (b+i) = 0
// summation (Ai) = summation (b+i)
// summation A(i) = n*b
// b = summation A(i)/n
// sqrt everything to return to original form

const summation = intList => intList.reduce((acc, curr) => acc+parseInt(curr), 0);

const input = require("fs").readFileSync("/dev/stdin", "utf8").split("\n");
/// const input = "5\n2 2 3 5 5".split("\n");
const count = parseInt(input[0]);
const inputList = input[1].split(" ");

console.log(Math.round(Math.sqrt(summation(inputList)/count)));