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)

function sadness(b, A){
  var result = 0;
  for(var i=0;i<A.length;i++){
    result += Math.abs(A[i]-(b+i+1))
  }
  return result;
}

function main(input){
  const lines = input.split('\n');
  const N = parseInt(lines[0]);
  const As = lines[1].split(' ').map(x => parseInt(x));

  const median_index = Math.floor(N/2);
  var sorted_A_diffs = [];
  for(var i=0;i<As.length;i++){
    sorted_A_diffs.push(As[i]-(i+1));
  }
  sorted_A_diffs.sort(function(a,b){return a-b;})

  //console.log(N);
  //console.log(As);
  //console.log(A_diffs);
  //console.log([sadness(b, As), sadness(b+1, As)]);
  var result = 0;
  if(N%2==0){
    var b = Math.floor((sorted_A_diffs[median_index] + sorted_A_diffs[median_index+1])/2);
    result = sadness(b, As);
  }else{
    var b = sorted_A_diffs[median_index];
    result = sadness(b, As);
  }

  console.log(result);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));