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)

function Main(input) {
    const NA = input.split('\n');
    const N = parseInt(NA[0]);
    const A = NA[1].split(' ').map(n => parseInt(n));
    const B = A.map((n, i) => n-(i+1)).sort((a, b) => a-b);
    const b1 = B[parseInt(N/2)];
    const b2 = b1 + 1;
    const min1 = A.reduce((res, n, i) => res += Math.abs(n - (b1+i+1)), 0);
    const min2 = A.reduce((res, n, i) => res += Math.abs(n - (b2+i+1)), 0)
    
    if (min1 < min2) console.log(min1);
    else console.log(min2);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));