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 <sstream>
#include <string>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <vector>
using namespace std;

#ifndef INF
#define INF 1000000
#endif

long long sadness(int* a, int n, long long b){
	long long ret = 0;
	for(int i = 0; i < n; i++){
		ret += abs(a[i]-b);
	}
	return ret;
}

int main(){
	int n, tmp;
	long long sum = 0LL;
	long long b, b_sub, ret;
	cin >> n;
	int a[n];
	for(int i = 0; i < n; i++){
		cin >> tmp;
		a[i] = tmp - (i+1);
		sum += a[i];
	}
	b = sum / n;
	b_sub = b - 1;
	ret = min( sadness(a,n,b),sadness(a,n,b_sub) );
	cout << ret << endl;
	return 0;
}