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)

#include <iostream>
#include <string>
#include <algorithm>
#include <cmath>
#include <cstdio>
#include <numeric>
#include <vector>
#include <queue>
#include <map>
typedef unsigned long long ull;
typedef long long ll;
#define MAX 200005
using namespace std;

//すべてマイナスになった時点で終わり
ull gloomM(ll x[], ll s, int n) {
  ull max=0;
  //すべてマイナスだったらfalse
  bool flag=false;
  for(int i=1;i<=n;i++) {
    x[i] -= s;
    if(x[i] >= 0) {
      max += x[i];
      flag=true;
    }
    else max += -x[i];
  }
  if(flag) return min(gloomM(x,s+1,n), max);
  else return max;
}
//すべてプラスになった時点で終わり
ull gloomP(ll x[], ll s, int n) {
  ull max=0;
  //すべてプラスだったらfalse
  bool flag=false;
  for(int i=1;i<=n;i++) {
    x[i] += s;
    if(x[i] >= 0) max += x[i];
    else {
      max += -x[i];
      flag=true;
    }
  }
  if(flag) return min(gloomP(x,s+1,n), max);
  else return max;
}

int main() {
  ll A[MAX];
  int n;
  cin >> n;
  for(int i=1;i<=n;i++) {
    cin >> A[i];
    A[i] -= i;
  }
  ull p =gloomP(A,0,n);
  ull m =gloomM(A,0,n);
  ull ans = (p<m)?p:m;
  cout << ans << endl;
  return 0;
}