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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int Abs(int A,int b,int number);

int main(int argc, const char * argv[]) {
    
    int N = 0;
    int result = 1000000000;
    int x = 0;
    int b = 0;
    scanf("%d",&N);
    
    int A[N];
    
    for (int i = 0; i < N; i++) {
        scanf("%d",&A[i]);
    }
    
    
    
    //bをどうするべきか
    for (int j = -11000; j < 11000; j++) {
        x = 0;
        b = j;
        for (int i = 0; i < N; i++) {
            x = x + Abs(A[i],b,i+1);
        }
        if (result > x) {
            result = x;
        }
    }
    
    printf("%d",result);
    
    return 0;
}

int Abs(int A,int b,int number){
    int result = 0;
    
    result = (A - (b + number));
    
    if (result < 0) {
        result = result * -1;
    }
    
    return result;
}