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: Runtime Error)

#include<iostream>
using namespace std;

int main(){
	int N;
	int i;
	int var_a[20000];
	int app[20000];
	int b;
	int sum_except_b =0;
	int answer = 0;
	
	double Db,Decimal_b;
	
	
	cin >> N;
	
	
	for(i=0;i<N;i++)
	{
		cin >> var_a[i];
		
	
		app[i] = var_a[i]-(i+1);
		
		if(app[i] < 0)
		{
			app[i] = -1 * app[i];
		}
		
		sum_except_b += app[i];
	}
	
	
	
	Db = (double)(sum_except_b/N);
	Decimal_b =  Db - (int)Db;
	
	if(Decimal_b >= 0.5)
	{
		b=(int)(Db+1.0);
	}else{
		b = (int)Db;
	}
	
		cout << b << endl;
	
		for(i=0;i<N;i++)
	{	
		app[i] = var_a[i]-(b+i+1);
		
		if(app[i] < 0)
		{
			app[i] = -1 * app[i];
		}
		
		answer += app[i];
	}
	
	cout << answer << endl;
	
	return 0;
}