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>

#define N_max 200000

int main(int argc, char const *argv[]) {
  int N;
  int A[N_max];
  int i, j;
  //入力
  scanf("%d", &N );
  for ( i = 0; i < N; i++) {
    scanf("%d", &A[i] );
  }
  //前処理
  long Sum = 0;
  for ( i = 0; i < N; i++) {
    A[i] = abs(A[i] - (i+1) );
    Sum += A[i];
  }
  //探索
  int B[N_max] = {0};
  int b = 0;
  long sum = 0;
  for ( i = 0; i < N_max; i++) {
    for ( j = 0; j < N; j++) {
      B[j] = abs(A[j] - b);
      sum += B[j];
    }
    if ( sum < Sum) {
      Sum = sum;
    }
    b++;
    sum = 0;
  }
  //出力
  printf("%ld\n", Sum );

  return 0;
}