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 NEW(p,n){p=malloc((n)*sizeof(p[0]));if(p==NULL){printf("not enough memory\n");exit(1);};}
//pの型の変数n個の要素分のメモリを確保し、そのアドレスをpに代入するマクロ

#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define MIN(a, b) ((a) < (b) ? (a) : (b))

//昇順
int asc(const void* a, const void* b){
    return *(int*)a-*(int*)b;
}

int main(void){
    int N;
    scanf("%d",&N);

    //A[0]~A[N-1]にA_i-iの値を格納する
    int* A;
    NEW(A,N);
    for(int i=0;i<N;i++){
        scanf("%d",&A[i]);
        A[i]-=(i+1);
    }
    qsort(A,N,sizeof(int),asc);

    long ans=0;
    int b;
    if(N%2==0){
        b=(A[N/2]+A[N/2-1])/2;
        for(int i=0;i<N;i++) ans+=abs(A[i]-b);

        b++;
        long tmp=0;
        for(int i=0;i<N;i++) tmp+=abs(A[i]-b);

        ans=MIN(ans,tmp);
    }
    else{
        b=A[N/2];
        for(int i=0;i<N;i++) ans+=abs(A[i]-b);
    }

    printf("%ld\n",ans);

    return 0;
}