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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		string str = Console.ReadLine();
		int N = int.Parse(str);
		string[] str2 = Console.ReadLine().Split();
		int[] A = new int[N];
		int sum = 0;
		int suma = 0;
		int min = 999999999;
		int max = -999999999;
		int ans = 999999999;
		for(var i=0;i<N;i++){
			A[i] = int.Parse(str2[i]);
			min = Math.Min(A[i] - (i+1),min);
			max = Math.Max(A[i] - (i+1),max);
		}
		int ia = min;
		int mina = 999999999;
		while(ia<=max){
			sum = 0;
			mina = 99999999;
			for(var j=0;j<N;j++){
				sum += Math.Abs(A[j] - (j+1) - ia);
				mina = Math.Min((A[j] - (j+1) - ia),mina);
			}
			ans = Math.Min(ans,sum);
			if(mina > 1){
				ia += mina;
			} else {
				ia += 1;
			}
		}
		Console.WriteLine(ans);
	}
}