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 (Clang 3.8.0) (judge verdict: Wrong Answer)

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

typedef int value_type; /* ソートするキーの型 */

/* x, y, z の中間値を返す */
value_type med3(value_type x, value_type y, value_type z) {
    if (x < y) {
        if (y < z) return y; else if (z < x) return x; else return z;
    } else {
        if (z < y) return y; else if (x < z) return x; else return z;
    }
}

/* クイックソート
 * a     : ソートする配列
 * left  : ソートするデータの開始位置
 * right : ソートするデータの終了位置
 */
void quicksort(value_type a[], int left, int right) {
    if (left < right) {
        int i = left, j = right;
        value_type tmp, pivot = med3(a[i], a[i + (j - i) / 2], a[j]); /* (i+j)/2 ではオーバーフローしてしまう */
        while (1) { /* a[] を pivot 以上と以下の集まりに分割する */
            while (a[i] < pivot) i++; /* a[i] >= pivot となる位置を検索 */
            while (pivot < a[j]) j--; /* a[j] <= pivot となる位置を検索 */
            if (i >= j) break;
            tmp = a[i]; a[i] = a[j]; a[j] = tmp; /* a[i], a[j] を交換 */
            i++; j--;
        }
        quicksort(a, left, i - 1);  /* 分割した左を再帰的にソート */
        quicksort(a, j + 1, right); /* 分割した右を再帰的にソート */
    }
}

int main(void){

  int N;
  scanf("%d\n", &N);

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

  for(int i=0; i<N; i++){
    A[i] -= i+1;
  }

  quicksort(A,0,N-1);

  int mid = A[N/2];
  int ans=0;

  for(int i=0; i<=N/2; i++){
    ans += mid - A[i];
  }
  for(int i=N/2+1; i<N; i++){
    ans += A[i] - mid;
  }

  printf("%d\n", ans);
  return 0;
}