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 <bits/stdc++.h>
#include <iostream>
#include <iomanip>
#include <ios> 
#include <vector>
#include <string>
#include <algorithm>
//#include <functional>
#include <queue>
//#include <stack>
//#include <set>
#include <cmath>
//#include <bitset>
#include <map>
using namespace std;
typedef long long ll;

ll judge(int N,ll *A, ll b){
  ll ans=0;
  for(int i=0; i<N; i++){
    ans += abs(A[i] - b);
  }
  return ans;
}



int main() {
  int N;
  cin >> N;
  ll A[N];
  for(int i=0; i<N; i++){
    cin >> A[i];
    A[i] -= (i+1);
  }
  sort(A, A+N);

  ll lb = A[0];
  ll rb = A[N-1];
  /*  if(N >1){
    ll ans = min(judge(N,A,A[N/2]),min(judge(N,A,A[N/2+1]), judge(N,A,A[N/2-1])));
    cout << ans << endl;
  }
  else
    cout << 0 << endl;
  return 0;
  */
  if(N==1){
    cout << 0 << endl;
  }
  else{
  while ((rb - lb) >1){
    ll m = (rb + lb)/2;
    if(judge(N,A,lb) >= judge(N,A,m)){
      lb = m;
    }
    else{
      rb = m;
    }
  }

  
  cout << min(judge(N,A,rb), judge(N,A,lb)) << endl;
  }

}