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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
            Console.Read();
        }

        public void Solve(ConsoleInput cin)
        {
            //var D = cin.ReadInt;
            var N = cin.ReadInt;
            //var M = cin.ReadInt;//buy
            long[] A = new long[N];
            A = cin.ReadLongArray(N);
            long x = 0;
            //    int y = 0;
            x = A.Max() - A.Min();



            //long[] a = new long[N];
            //long count =0;
            //long[] x = new long[N];
            //long[] y = new long[N];
            //long[] z = new long[N];
            //long A,B,C; 

            for (int i = 0; i < N; i++)
            {
                A[i] -= (i + 1);
            }
            long sum = 0;
            long sum2 = 1;
            double result = Math.Pow(10, 9);
            //long sum3 =0;
            //long b = A.Max();
            long s =0, t =0;
            for (int i = 0; i < N; i++)
            {
                s += System.Math.Abs(A[i] - A.Max());
                t += System.Math.Abs(A[i] - A.Min());
            }
            //sum3 = Math.Max(sum, sum2);
            if (s <= t) {
                for (long b = A.Max(); b >= A.Min(); b--)
                {
                    //    //while (a[i] % 2 == 0) { a[i] /= 2;count++; }
                    //    //x[i] = cin.ReadLong;
                    for (int i = 0; i < N; i++)
                    {
                        sum += System.Math.Abs(A[i] - b);

                    }
                    //Console.WriteLine(b + "," + sum);
                    if (b == A.Max())
                    {
                        if (sum < result) { result = sum; }
                        sum2 = sum;
                        sum = 0;

                    }
                    else
                    {
                        if (sum > sum2) { break; }
                        else
                        {
                            if (sum < result) { result = sum; }
                            sum2 = sum;
                            sum = 0;
                        }
                    }
                }

            }
            else
            {
                for (long b = A.Min(); b <= A.Max(); b++)
                {
                    //    //while (a[i] % 2 == 0) { a[i] /= 2;count++; }
                    //    //x[i] = cin.ReadLong;
                    for (int i = 0; i < N; i++)
                    {
                        sum += System.Math.Abs(A[i] - b);

                    }
                    //Console.WriteLine(b + "," + sum);
                    if (b == A.Min())
                    {
                        if (sum < result) { result = sum; }
                        sum2 = sum;
                        sum = 0;

                    }
                    else
                    {
                        if (sum > sum2) { break; }
                        else
                        {
                            if (sum < result) { result = sum; }
                            sum2 = sum;
                            sum = 0;
                        }
                    }
                }
            }
            //var A=0;
            //if (N % 2 == 0)
            //{
            //    A = N;
            //}
            //else
            //{
            //    A = N * 2;
            //}



            Console.WriteLine(result);
            Console.Read();

        }
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }
        ///
        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }
}