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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;

namespace C
{
    class Program
    {
        static int SunukeRec(int[] tmp, int max, int min) {
            while (max != min) {
                int pivot = min + (max - min + 1) / 2;
                int frontSunuke = Sunuke(tmp, pivot + (max - pivot + 1) / 2);
                int backSunuke = Sunuke(tmp, min + (pivot - min + 1) / 2);
                if (backSunuke < frontSunuke) {
                    max = pivot;
                }
                else {
                    min = pivot;
                }
            }
            return max;
        }
        
        static int Sunuke(int[] tmp, int b) {
            int ans = 0;
            foreach (int t in tmp) {
                ans += Math.Abs(t - b);
            }
            return ans;
        }

        static void Main(string[] args) {
            int N = int.Parse(Console.ReadLine());
            int[] A = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

            int[] tmp = new int[N];
            int max = int.MinValue;
            int min = int.MaxValue;
            for(int i = 0; i < N; ++i) {
                tmp[i] = A[i] - (i + 1);
                if (tmp[i] < min) min = tmp[i];
                if (tmp[i] > max) max = tmp[i];
            }

            Console.WriteLine(Sunuke(tmp, SunukeRec(tmp, max, min)));

        }
    }
}