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>

#define NUM 200000

long absl(long a) {
    return a >= 0 ? a : - a;
}

void print_array(long *a, long size) {
    for(int i = 0; i < size; i++) {
        printf("%ld\n", a[i]);
    }
}

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


long median(long *a, long size) {
    long idx, idx2;
    qsort(a, size, sizeof(long), compare_int);
    if(size % 2 == 1) return a[size / 2];
    idx = size / 2;
    idx2 = (size / 2) - 1;
    return (a[idx] + a[idx2]) / 2;
}

int main() {
    long N;
    long m;
    long sum = 0;
    long a[NUM];
    char s[NUM];
    scanf("%ld\n", &N);
    for(int i = 0; i < N; i++) {
        scanf("%ld", &a[i]);
    }
    for(int i = 0; i < N; i++) {
        a[i] = a[i] - (i + 1);
    }
    m = median(a, N);
    for(int i = 0; i < N; i ++) {
        sum += absl(a[i] - m);
        a[i] = absl(a[i] - m);
    }
    printf("%ld\n", sum);
    return 0;
}