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: Accepted)

#include <bits/stdc++.h>

#if MYDEBUG
#include "lib/cp_debug.hpp"
#else
#define DBG(...) ;
#endif

using LL = long long;
constexpr LL LINF = 334ll << 53;
constexpr int INF = 15 << 26;
constexpr LL MOD = 1E9 + 7;

namespace Problem {
using namespace std;

class Solver {
 public:
  int n;
  vector<LL> a, b;

  Solver(LL n) : n(n), a(n){};

  void solve() {
    for (int i = 0; i < n; ++i) {
      cin >> a[i];
    }
    b = a;
    for (int i = 0; i < n; ++i) {
      b[i] -= i + 1;
    }
    sort(b.begin(), b.end());
    LL m = b[n / 2];
    DBG(m)
    LL ans = 0;
    for (int i = 0; i < n; ++i) {
      ans += abs(a[i] - m - i - 1);
    }
    cout << ans << endl;
  }
};
}  // namespace Problem

int main() {
  std::cin.tie(0);
  std::ios_base::sync_with_stdio(false);
  long long n = 0;
  std::cin >> n;

  Problem::Solver sol(n);
  sol.solve();
  return 0;
}