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";

process.stdin.resume();
process.stdin.setEncoding('utf8');

var g_input = '';
process.stdin.on('data', function(chunk) {
    g_input += chunk;
});

process.stdin.on('end', function() {
    Main(g_input.split(/\r?\n/));
});

function Main(input) {

    const n = parseInt(input[0], 10);
    const a = input[1].split(' ').map(function(value) { return parseInt(value, 10); });
    const aMinusI = a
    .map(function(value, index) {
        return value - (index + 1);
    })
    .sort(function (a, b) {
        if (a < b) {
            return -1;
        }
        else if (a > b) {
            return 1;
        }
        else {
            return 0;
        }
    });

    const b = aMinusI[Math.floor(n / 2)];

    const ans = aMinusI
    .map(function(value) {
        return Math.abs(value - b);
    })
    .reduce(function(prev, current) {
        return Math.abs(prev + current);
    });

    console.log(ans);

    return 0;
}