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 <stdlib.h>

int sadness(int N, int * a, long int b){
    //abs(A1−(b+1))+abs(A2−(b+2))+...+abs(AN−(b+N))を計算する
    int i,sadness=0;
    for(i=0;i<N;i++){
        sadness += abs(a[i]-b);
    }
    return sadness;
}

int main(){
    int N,i;
    scanf("%d", &N);
    int * A = malloc(sizeof(int)*N);
    int * a = malloc(sizeof(int)*N);
    long int b = 0;
    for(i=0;i<N;i++){
        scanf("%d", &A[i]);
        a[i] = A[i] - i - 1;
        b += a[i];
    }

    if(b%N==0){
        b /= N;
    } else {
        b /= N;
        int sad_1 = sadness(N,a,b);
        if(sad_1 > sadness(N,a,b-1))
            b -= 1;
        if(sad_1 > sadness(N,a,b+1))
            b += 1;
    }

    printf("%d", sadness(N,a,b));
    return 0;
}