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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <stdint.h>
#include <string.h>
#include <wchar.h>

#define MIN(a, b) (a < b ? a : b)
#define MAX(a, b) (a > b ? a : b)
#define ABSS(a, b) ((a) > (b) ? (a) - (b) : (b) - (a))

int64_t A[200000];

int main(void) {
	int64_t N;

	scanf("%"PRId64"\n", &N);
	for (uint32_t idx = 0; idx < N; idx++) {
		scanf(idx != N - 1 ? "%"PRId64" " : "%"PRId64, &(A[idx]));
	}

	int64_t sum = 0;

	for (int64_t i = 0; i < N; i++) {
		sum += A[i] - (i + 1);
	}
	const int64_t b = sum >= 0 ? sum / N : -(-sum / N);
	const int64_t b2 = sum >= 0 ? b + 1 : b - 1;

	int64_t absSum = 0;
	for (int64_t i = 0; i < N; i++) {
		absSum += ABSS(A[i], i + 1 + b);
	}

	int64_t absSum2 = 0;
	for (int64_t i = 0; i < N; i++) {
		absSum2 += ABSS(A[i], i + 1 + b2);
	}

	printf("%"PRId64, absSum < absSum2 ? absSum : absSum2);

	return 0;
}