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 <algorithm>
#include<string>
#include <bitset>
#include <vector>
#include <functional>
#include <climits>
#include <iomanip>
using namespace std;
int main()
{

	//int a = 0, b = 0, c = 0, d = 0, e = 0, f = 0, g = 0, h = 0, ans = 0;
	 long a = 0, b = 0, c = 0, d = 0, e = 0, f = 0, g = 0, h = 0, i = 0, j = 0, k = 0, l = 0, ans = 0;
	//cout << LONG_MAX << endl;
	//string s[1001];
	//long long n, A[1000000000];
	//string s;
	 long n;
	cin >> n;
	 long A[200002];

	for (a = 1; a <= n; a++)
	{
		cin >> A[a];
		A[a] -= a + 1;
	}
	sort(A+1, A + n+1);
	/*for (a = 1; a <= n; a++)
	{
		cout << A[a] << endl;
	}*/
	if (n%2==1)
	{
		b = ((double)n  / 2) + 0.5000001;
		//cout << b << endl;
		//cout << 1111111111111111111 << endl;
		b=A[b];
	}
	else
	{
		b = A[n/2]+ A[(n / 2)+1];
		b =((double)b/2)+0.5;
	}
	//cout << A[n/2] << endl;

	for (a = 1; a <= n; a++)
	{
		d += abs(A[a] - b);
	}
	cout << d << endl;
	return 0;
}