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";
function Main(input) {
    let cin = new Inputer(input);
    let N = cin.getInt();
    let A = cin.getIntArray(N);
    let B = A.map((v, i) => v - i - 1);
    B.sort((a,b) => a- b);
   let c = Math.floor(N / 2);
    let b = B[c];
    let ans = A.reduce((ac, v, i) => ac + Math.abs(v - (b + i + 1)),  0);
console.log(ans);
}
class Inputer{constructor(t){if(typeof t=='undefined')throw new Error('引数（stdin）を省略できません！');this.cnt=0;this.items=t.split(/\n|\s/)}getInt(){return this.items[this.cnt++]-0}getIntArray(t){if(typeof t=='undefined')throw new Error('引数（1以上）を省略できません！');if(t<1)throw new Error('引数は1以上であること！');let r=new Array(t);for(let e=0;e<t;e++)r[e]=this.getInt();return r}getStr(){return this.items[this.cnt++]}getStrArray(t){if(typeof t=='undefined')throw new Error('引数（1以上）を省略できません！');if(t<1)throw new Error('引数は1以上であること！');let r=new Array(t);for(let e=0;e<t;e++)r[e]=this.getStr();return r}}
if (typeof window == "undefined") Main(require("fs").readFileSync("/dev/stdin", "utf8"));