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: Accepted)

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

namespace debug
{
    public static partial class Program
    {
        public static void Main()
        {
            var n = Console.ReadLine().ToLong();
            var ais = Console.ReadLine().ToLongArray().ToList();

            for (var i = 0; i < n; i++)
            {
                ais[i] -= i + 1;
            }

            ais.Sort();
            var b = ais[(int)(n / 2)];

            Console.WriteLine(ais.Sum(x => Math.Abs(x - b)));
        }
    }

    public static partial class Program
    {
        //テンプレここから
        private static long Gcd(long aaa, long bbb) => bbb == 0 ? aaa : Gcd(bbb, aaa % bbb);
        private static long Lcm(long aaa, long bbb) => aaa * bbb / Gcd(aaa, bbb);
        private static long ToLong(this double ddd) => (long) ddd;
        private static long ToLong(this string str) => long.Parse(str);
        private static long[] ToLong(this IEnumerable<string> strs) => strs.Select(x => x.ToLong()).ToArray();
        private static long[] ToLongArray(this string str, char opr = ' ') => str.Split(opr).ToLong();
        private static long Diff(long aaa, long bbb) => Math.Abs(Math.Max(aaa, bbb) - Math.Min(aaa, bbb));
        private static long Sign(this long iii) => Math.Sign(iii);
        private static bool IsEven(this long iii) => iii % 2 == 0;
        private static bool IsEven(this int iii) => iii % 2 == 0;

        private static readonly int[] Dx =
        {
            0, -1, 0, 1
        };

        private static readonly int[] Dy =
        {
            -1, 0, 1, 0
        };

        public const int Mod = 1000000007;
        public const string UpperAlphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
        public const string LowerAlphabet = "abcdefghijklmnopqrstuvwxyz";
        private static long ToLong(this char ccc) => ccc.ToString().ToLong();
        private static string Join(this IEnumerable<string> array, string sep = "") => string.Join(sep, array);
        private static string Join(this IEnumerable<char> array, string sep = "") => string.Join(sep, array);

        private static string JoinToStr(this IEnumerable<long> array, string sep = "") =>
            array.Select(xxx => xxx.ToString()).Join(sep);

        public static string JoinToStr(this IEnumerable<int> array, string sep = "") =>
            array.Select(xxx => xxx.ToString()).Join(sep);

        //テンプレここまで
    }
}