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 12.16.1) (judge verdict: Accepted)


function Main(input) {
  input=input.split("\n");
  if(input[input.length-1]===''){
    input.pop();
  }
  const N=input[0].split(' ')[0]-0;
  var array=input[1].split(' ').map((e,i)=>{
    return e-i-1;
  }).sort((a,b)=>{
    return a-b;
  });
  console.log(array.reduce((acc,cur)=>{
    return acc+Math.abs(cur-array[Math.floor(array.length/2)]);
  },0));

}

//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));

function permutation(n,k){
    var ret=[[]];
    var next;
    for(var i=0;i<k;i++){
        next=[];
        ret.forEach(e=>{
            for(var k=1;k<=n;k++){
                if(!e.includes(k)){
                    next.push(e.concat([k]));
                }
            }
        });
        ret=next.concat([]);
    }
    return ret;
}