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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map.Entry;

import java.util.PriorityQueue;
import java.util.Scanner;

class Main {
    static final int MOD = 1000000007;
    static final int INF = 1 << 30;
    static final int ALF = 26;

    Main() {
        Scanner sc = new Scanner(System.in);
        long ans = 0;
        int N = sc.nextInt();
        long[] A = new long[N];
        for (int i = 0; i < N; i++) {
            A[i] = sc.nextLong();
        }
        long left = -10000000000l;
        long right = 10000000000l;
        // long preans = -1;
        while (true) {
            // long lv = calc(A, left);
            // long rv = calc(A, right);
            long m1 = (left*2+right)/3;
            long m2 = (left+right*2)/3;
            // System.err.println("m1 "+m1);
            // System.err.println("m2 "+m2);
            // long mv = calc(A, mid);
            
            long mv1 = calc(A, m1);
            long mv2 = calc(A, m2);

            if(mv1<mv2){
                right = m2;
            }else{
                left = m1;
            }

            if(m2-m1<=1){
                ans = Math.min(mv1, mv2);
                break;
            }
        }
        System.out.println(ans);
    }

    long calc(long[] A, long val) {
        long ret = 0;
        for (int i = 0; i < A.length; i++) {
            ret += Math.abs(A[i] - val - i);
        }
        return ret;
    }

    public static void main(String[] args) {
        new Main();
    }
}