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.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)1e9 + 7;
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var N = Sarray()[0];
            var A = Slist();
            for (var i = 0; i < N; ++i)
                A[i] -= i + 1;
            A.Sort();
            var min = A.Min();
            var max = A.Max();
            var rui = new long[N + 1];
            for (var i = 1; i <= N; ++i)
                rui[i] = rui[i - 1] + A[i - 1];
            var ans = long.MaxValue;
            while (min <= max)
            {
                var mid = min + (max - min) / 2;
                var kouho = Calc(mid, rui, A);
                var kouhou = Calc(mid + 1, rui, A);
                ans = Min(ans, kouho);

                if (kouho <= kouhou)
                    max = mid - 1;
                else
                    min = mid + 1;
            }
            WriteLine(ans);
            //Out.Flush();
        }
        class lb<T> : IComparer<T> where T : IComparable<T>
        {
            public int Compare(T x, T y) => 0 <= x.CompareTo(y) ? 1 : -1;
        }
        static long Calc(long mid, long[] rui, List<long> A)
        {
            var idx = ~A.BinarySearch(mid, new lb<long>());
            var N = A.Count;
            var r = rui[N] - rui[idx] - mid * (N - idx);
            var l = mid * idx - rui[idx];
            return r + l;
        }
    }
}