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: Accepted)

#include <iostream>
#include <string>
#include <cstring>
#include <algorithm>
#include <functional>
#include <cmath>
#include <set>
#include <queue>
#include <vector>
#include <climits>
#include <sstream>
#include <iomanip>
#include <map>
using namespace std;

int main()
{
	long long N;
	cin >> N;
	vector<long long> A(N);
	for (auto i = 1; i <= N; ++i)
	{
		cin >> A[i - 1];
		A[i - 1] -= i;
	}

	sort(A.begin(), A.end());

	auto result = 0ll;
	for (auto i = 1; i < N; ++i)
	{
		result += A[i] - A[0];
	}

	auto sum = result;
	for (auto i = 1; i < N; ++i)
	{
		auto diff = A[i] - A[i - 1];
		sum += diff * i;
		sum -= diff * (N - i);
		result = min(result, sum);
	}

	cout << result << endl;

	return 0;
}