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.io.*;
import java.math.*;
import java.util.*;

public class Main {
    private static boolean debug = false;
    private static boolean elapsed = false;

    private static PrintWriter _out = new PrintWriter(System.out);
    private static PrintWriter _err = new PrintWriter(System.err);

    private void solve(Scanner sc) {
        int N = sc.nextInt();
        int[] A = new int[N];
        Map<Integer, Integer> map = new HashMap<>();
        for (int i = 0; i < N; ++i) {
            A[i] = sc.nextInt() - (i + 1);
            Integer tmp = map.get(A[i]);
            if (tmp == null) {
                map.put(A[i], 1);
            } else {
                map.put(A[i], tmp + 1);
            }
        }
        int max = 0;
        int maxCnt = 0;
        int minCnt = Integer.MAX_VALUE;
        Set<Integer> bSet = new HashSet<>();
        for (Map.Entry<Integer, Integer> entry : map.entrySet()) {
            if (entry.getValue() > maxCnt) {
                bSet.clear();
                bSet.add(entry.getKey());
                maxCnt = entry.getValue();
            } else if (entry.getValue() == maxCnt) {
                bSet.add(entry.getKey());
            }
            if (entry.getValue() < minCnt) {
                minCnt = entry.getValue();
            }
        }
        long ans = Long.MAX_VALUE;
        if (false && maxCnt == minCnt) {
            ans = 0;
            for (int i = 0; i < N; ++i) {
                ans += Math.abs(A[i]);
            }
        } else {
            for (int b : bSet) {
                long tmp = 0;
                for (int i = 0; i < N; ++i) {
                    tmp += Math.abs(A[i] - b);
                }
                if (tmp < ans) {
                    ans = tmp;
                }
            }
        }
        _out.println(ans);
    }
    private static BigInteger C(long n, long r) {
        BigInteger res = BigInteger.ONE;
        for (long i = n; i > n - r; --i) {
            res = res.multiply(BigInteger.valueOf(i));
        }
        for (long i = r; i > 1; --i) {
            res = res.divide(BigInteger.valueOf(i));
        }
        return res;
    }
    private static BigInteger P(long n, long r) {
        BigInteger res = BigInteger.ONE;
        for (long i = n; i > n - r; --i) {
            res = res.multiply(BigInteger.valueOf(i));
        }
        return res;
    }
    /*
     * 10^10 > Integer.MAX_VALUE = 2147483647 > 10^9
     * 10^19 > Long.MAX_VALUE = 9223372036854775807L > 10^18
     */
    public static void main(String[] args) {
        long S = System.currentTimeMillis();

        Scanner sc = new Scanner(System.in);
        new Main().solve(sc);
        _out.flush();

        long G = System.currentTimeMillis();
        if (elapsed) {
            _err.println((G - S) + "ms");
        }
        _err.flush();
    }
}