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>
#include <math.h>

int main(void){
    int s,i,j,tmp,r,b,l,a;
    r = 0;
    b = 0;
    scanf("%d",&s);
    int data[s];
    for(i = 0;i < s;i++){
        scanf("%d",&data[i]);
    }
    for(i = 0;i < s-1;i++){
        if(data[i] > data[i+1]){
          tmp = data[i+1];
          data[i+1] = data[i];
          data[i] = tmp;  
        }
    }
    for(i = 0;i <= data[0];i++){
        //printf("r = ");
        for(j = 1;j <= s;j++){
            l = data[j-1] - (i + j);
            r += abs(l);
            //printf("%d - (%d + %d) +",data[j-1],i,j);
        }
        printf("\n");
        if(i == 0)b = r+1;
        //printf("r = %d : b = %d\n",r,b); 
        if(b >= r){
            b = r;
            r = 0;
            a = i;
            //printf("a change\n");
        }else {
            break;
        }
    }
    for(i = data[s-1];;i++){
        for(j = 1;j <= s;j++){
           r += abs(data[j-1] - (i + j)); 
        }
        if(b >= r){
            b = r;
            r = 0;
            a = i;
        }else break;
    }
    printf("%d",b);
    return 0;
}