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)

#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<cmath>

using namespace std;

typedef long long ll;

#define FOR(i,n) for(int (i)=0;(i)<(n);(i)++)
#define FOR1(i,n) for(int (i)=1;(i)<(n);(i)++)
#define eFOR(i,n) for(int (i)=0;(i)<=(n);(i)++)
#define eFOR1(i,n) for(int (i)=1;(i)<=(n);(i)++)
#define SORT(i) sort((i).begin(),(i).end())
#define INF 1000000000

int main() {

	int n, ans = 0;
	cin >> n;
	vector<int> A(n), B(n);
	FOR(i, n) {
		cin >> A[i];
		B[i] = A[i] - i;
	}
	SORT(B);
	int b1 = B[n / 2 - 1], b2 = B[n / 2], ans1 = 0, ans2 = 0;

	FOR(i, n) {
		ans1 += abs(B[i] - b1);
		ans2 += abs(B[i] - b2);
	}

	cout << min(ans1, ans2) << endl;

	return 0;
}