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 <stdlib.h>
#include <stdio.h>
int compar(const int *val1,const int *val2){
    if(*val1 < *val2){
        return -1;
    }else if(*val1 == *val2){
        return 0;
    }else {
        return 1;
    }
}
int main()
{   int i,a[200000],bodd=0,beven=0,d,B[200000];
    scanf("%d",&d);
    for(i=0;i<d;i++){
        scanf("%d",&a[i]);
    }
    for(i=0;i<d;i++){
        B[i]=a[i]-i+1;
    }
    qsort(B,d,sizeof(int),
    (int(*)(const void *,const void *))compar);
    if(d%2==0){
        for(i=0;i<d;i++){
        beven += abs(B[i]-B[d/2-1]);
        bodd += abs(B[i]-B[d/2]);
    }
    if(beven<bodd){
        printf("%d",beven);
    }else{
        printf("%d",bodd);
    }
    
    }else{
        for(i=0;i<d;i++){
            beven+=abs(B[i]-B[(d+1)/2-1]);
        }
    printf("%d",beven);
    }
    return 0;
}