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 <algorithm>
#include <iostream>
using namespace std;

long long a[200001], n;

long long sadness(long long b) {
	long long ret=0;
	for (long long i=1; i<=n; i++) {
		ret+=abs(a[i]-(b+i));
	}
	return ret;
}

int main() {
	cin>>n;
	for (long long i=1; i<=n; i++) {
		cin>>a[i];
	}
	// for (long long i=0; i<=n; i++) {
		// cout<<sadness(i)<<endl;
	// }
	long long R = 200000000;
	long long L = -200000000;
	while (R-L>1) {
		// cout<<"R: "<<R<<endl;
		// cout<<"L: "<<L<<endl;
		// cout<<endl;
		long long M1 = L+(R-L)/3;
		long long M2 = L+2*(R-L)/3;
		if (sadness(M1)<sadness(M2)) {
			// cout<<"no need for n>"<<M2<<endl;
			R = M2-1;
		} else if (sadness(M1)>sadness(M2)) {
			// cout<<"no need for n<"<<M1<<endl;
			L = M1+1;
		} else {
			// cout<<"no need for n>"<<M2<<endl;
			// cout<<"no need for n<"<<M1<<endl;
			L = M1+1;
			R = M2-1;
		}
	}
	// cout<<R<<": "<<sadness(R)<<endl;
	// cout<<L<<": "<<sadness(L)<<endl;
	cout<<min(sadness(L),sadness(R))<<endl;
}