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;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp90 {
    class Program {
        static long N;
        static long[] A;

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

            var A_new = new long[N];

            for (int i = 0; i < N; i++) {
                A_new[i] = A[i] + i + 1;
            }

            Array.Sort(A_new);

            var minMaxList = new List<long>();

            

            for (int i = 0; i < N; i++) {
                minMaxList.Add(A[i] - (i + 1));
            }
            long min = minMaxList.Min();
            long max = minMaxList.Max();

            //答え(正確にはb)はminとmaxの間にある！！→二分探索！

            //Console.WriteLine("min : " + min);
            //Console.WriteLine("max : " + max);

            long ans = Calculate(max);

            for (long i = min; i <= max; i++) {
                ans = Math.Min(ans, Calculate(i));
            }

            Console.WriteLine(ans);
        }

        //static bool CheckRightOrLeft(int min_, int max_) {
        //    int middle = (min_ + max_) / 2;




        //}

        //悲しさを計算する
        static long Calculate(long b_) {
            long value = 0;
            for (int i = 0; i < N; i++) {
                value += Math.Abs(A[i] - (b_ + i + 1));
            }

            return value;
        }
    }
}