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>

int n;
int A[200000];

inline void swap(int *a, int *b){
  int z;
  z = *a;
  *a = *b;
  *b = z;
}

int kth(int *A, int n, int k){
  int ll, rr;
  ll = 0;
  rr = n;
  while(1){
    int i, l, r, pivot;
    swap(A+ll, A+(ll+rr)/2);
    pivot = A[ll];
    l = ll;
    r = rr;
    i = ll+1;
    while(i < r){
      if(A[i] < pivot) swap(A+l++, A+i++);
      else if(A[i] > pivot) swap(A+--r, A+i);
      else i++;
    } 
    if(k < l) rr = l;
    else if(k >= r) ll = r;
    else return pivot;
  }
}

int main(){
  int i, m;
  long long int r;
  scanf("%d", &n);
  for(i=0;i<n;i++){
    scanf("%d", A+i);
    A[i] -= i+1;
  }
  m = kth(A, n, n/2);
  r = 0;
  for(i=0;i<n;i++) r += abs(A[i] - m);
  printf("%lld\n", r);
  return 0;
}