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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static int process(TestCase testCase) {
        int N = testCase.N;
        List<Integer> A = testCase.A;

        List<Integer> differences = new ArrayList<>();
        List<Integer> negative = new ArrayList<>();
        List<Integer> positive = new ArrayList<>();
        int zeroCount = 0;

        for (int i = 0; i < N; ++i) {
            int target = (i + 1);
            final int diff = target - A.get(i);
            differences.add(diff);

            if (diff == 0) {
                zeroCount++;
            } else if (diff < 0) {
                negative.add(diff);
            } else {
                positive.add(diff);
            }
        }

        differences.sort(Integer::compareTo);

        int mid = N / 2;
        final int midDiff = differences.get(mid);

        return differences.stream().map(i -> Math.abs(i - midDiff)).mapToInt(i -> i).sum();
//
//        final int midPlusOneDiff = differences.get(mid + 1);
//        if (noChangeNeeded(N, positive, negative, midDiff, midPlusOneDiff)) {
//            return getAbsSum(negative) + getAbsSum(positive);
//        } else {
//            return getResult(zeroCount, negative, positive, midDiff);
//        }
    }

    private static int getResult(int zeroCount, List<Integer> negative, List<Integer> positive, int midDiff) {
        int negativeSum = Math.abs(sum(negative) - midDiff * negative.size());
        int positiveSum = Math.abs(sum(positive) - midDiff * positive.size());
        int zeroSum = Math.abs(zeroCount * midDiff);
        return negativeSum + zeroSum + positiveSum;
    }

    private static boolean noChangeNeeded(int N, List<Integer> positive, List<Integer> negative, int midDiff, int midPlusOneDiff) {
        final boolean isMidDiffZero = midDiff == 0;
        final boolean isForEvenMidPlusOneDiffZero = (N % 2 == 0) && midPlusOneDiff == 0;
        final boolean isSameNumPosAndNeg = positive.size() == negative.size();

        return isMidDiffZero || isForEvenMidPlusOneDiffZero || isSameNumPosAndNeg;
    }

    private static int getAbsSum(List<Integer> list) {
        return Math.abs(sum(list));
    }

    private static int sum(List<Integer> list) {
        return list.stream().mapToInt(i -> i).sum();
    }

    // Util func

    public static void main(String[] args) {
        TestCase testCase = readFromInput();

        final int result = process(testCase);

        output(result);
    }

    private static TestCase readFromInput() {
        Scanner sc = new Scanner(System.in);

        int N = sc.nextInt();

        List<Integer> A = new ArrayList<>();
        for (int i = 0; i < N; ++i) {
            A.add(sc.nextInt());
        }

        sc.close();
        return new TestCase(N, A);
    }

    private static void output(int result) {
        System.out.println(result);
    }

    public static class TestCase {
        final int N;
        final List<Integer> A;

        public TestCase(int N, List<Integer> A) {
            this.N = N;
            this.A = A;
        }
    }

}