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 <vector>
#include <cmath>
#include <algorithm>
#include <numeric>

#define rep(i, n) for(int i=0;i<(int)(n);i++)
#define pb(a) push_back(a)
#define MAX(a, b) ((a < b)?b:a)
#define MIN(a, b) ((a > b)?b:a)

typedef long long int ll;

using namespace std;

int n;
vector<int> a;
int sum_a;

ll snuke_pm(int b)
{
	ll sum_a = 0;

	rep(i, n)
	{
		sum_a += abs(a[i] - (b));
	}

	return sum_a;
}

int main()
{
	cin >> n;

	sum_a = 0;
	a.reserve(n);
	rep(i, n)
	{
		int value;
		cin >> value;
		a.pb(value - i - 1);
	}
	auto ave = std::accumulate(std::begin(a), std::end(a), 0.0) / a.size();

	ll min = 999999999999999;

	//for(int i = a[0]; i <= a[n - 1] / 2; i++)
	//{
	//	ll sum = snuke_pm(i);
	//	if ( min > sum ) min = sum;
	//}

	cout << MIN(MIN(snuke_pm((int)ave), snuke_pm((int)ave + 1)), snuke_pm((int)ave - 1)) << endl;

	return 0;
}