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: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

int compare_int(const void *a, const void *b)
{
    return *(int*)a - *(int*)b;
}


int main()
{
    int N;
    scanf("%d",&N);
    int i,j,A[N],B[N],min=1000000000;
    for(i=0;i<N;i++){
        scanf("%d",&A[i]);
        B[i] = A[i] - (i+1);
        if( min > B[i] ){
            min = B[i];
        }
    }

    long long int sad=0;
    int b,bmin,tmp;

    qsort(B,N,sizeof(int),compare_int);

    for(i=1;i<=N;i++){
        if( i >=  N - i ){
            b = B[i-1];
            break;
        }
    }
    for(i=0;i<N;i++){
        sad += abs(B[i] - b);
    }


    printf("%lld\n",sad);


    return 0;
}