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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

/*  -*- coding: utf-8 -*-
 *
 * a.cc: C: Linear Approximation
 */

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<iostream>
#include<string>
#include<vector>
#include<map>
#include<set>
#include<stack>
#include<list>
#include<queue>
#include<deque>
#include<algorithm>
#include<numeric>
#include<utility>
#include<complex>
#include<functional>
 
using namespace std;

/* constant */

const int MAX_N = 200000;
const long long LINF = 1LL << 62;

/* typedef */

typedef long long ll;
typedef vector<int> vi;
typedef queue<int> qi;
typedef pair<int,int> pii;

/* global variables */

int as[MAX_N];

/* subroutines */

/* main */

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

  ll asum = 0;
  for (int i = 0; i < n; i++) {
    scanf("%d", &as[i]);
    as[i] -= i;
    asum += as[i];
  }
  int b = asum / n;
  //printf("asum=%lld, b=%d\n", asum, b);

  ll mind = LINF;
  for (int c = b - 1; c <= b + 1; c++) {
    ll d = 0;
    for (int i = 0; i < n; i++) d += abs(as[i] - c);
    if (mind > d) mind = d;
  }

  printf("%lld\n", mind);
  return 0;
}