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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
import java.lang.*;
//import java.util.Scanner;
//import java.io.InputStream;
//import java.io.IOException;
//import java.util.NoSuchElementException;
//import java.io.PrintWriter;
//import java.lang.Math;
//import java.io.BufferedReader;
//import java.io.InputStreamReader;
//import java.util.StringTokenizer;

public class Main
{
	public static void main(String[] args)
	{
		StringBuilder sb = new StringBuilder();
		
//		Scanner sc = new Scanner(System.in);
		FastScanner sc = new FastScanner();
		Util39 util = new Util39();
//		int n = sc.nextInt();
//		String s = sc.next();
//		int a[] = new int[3];
//		for (int ii = 0; ii < 3; ii++) a[ii] = sc.nextInt();
		
		
		
		int N = sc.nextInt();
		int a[] = new int[N];
		for (int ii = 0; ii < N; ii++)
		{
			a[ii] = sc.nextInt();
		}
		
		int sad1 = 0;
		int NN = N;
		int AA = 0;
		for (int i = 0; i < N; i++)
		{
			int s = Math.abs(a[i] - (i + 1));
			sad1 += s;
			NN += i;
			AA += a[i];
		}
		int b = (AA - NN) / N;
		int flg = -1;
		while (true)
		{
		System.out.println(b);
			int sad2 = 0;
			for (int j = 0; j < N; j++)
			{
				int ss = Math.abs(a[j] - (j + 1 + b));
				sad2 += ss;
			}
			if (sad2 <= sad1)
			{
				sad1 = sad2;
			}
			else if (flg == -1)
			{
				b++;
				flg = 1;
			}
			else
			{
				break;
			}
			b = b + flg;
		}
		
		
		sb.append(sad1);
		
		
		
//		System.out.println(sb.toString());
		PrintWriter out = new PrintWriter(System.out);
		out.println(sb.toString());
		out.flush();
	}
}

class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}

class Util39 {
	public int pow(int a, int b)
	{
		int r = 1;
		for (int i = 0; i < b; i++) r *= a;
		return r;
	}
}