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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#define _USE_MATH_DEFINES
#include <cmath>
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <stdio.h>
#define rep(i,n) for(int i=0;i<(int)n;i++)
using namespace std;
int main() {
	int n, sum = 0, B, ans = 0;
	int A[200000];
	cin >> n;
	rep(i, n) {
		cin >> A[i];
		A[i]= A[i] - i - 1;
	}

	sort(A, A + n);

	if (n % 2 == 0) {
		B = (A[n / 2 - 1] + A[n / 2]);
	}
	else if (n % 2 == 1) {
		B = A[n / 2];
	}
	rep(i, n) {
		ans += abs(A[i] - B);
	}
	cout << ans << endl;
	return 0;
}