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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"os"
	"fmt"
	"bufio"
	"strconv"
	"strings"
)

func abs(n int) int {
	if n < 0 {
		return -n
	} else {
		return n
	}
}

func main() {
	var sc = bufio.NewScanner(os.Stdin)	
	sc.Scan()
	N, _ := strconv.Atoi(sc.Text())
	sc.Scan()
	A := strings.Split(sc.Text(), " ")

	min := 1000000000
	for b := N - 1000; b < N + 1000; b++ {
		sum := 0
		for i, str := range A {
			tmp, _ := strconv.Atoi(str)
			sum += abs(tmp - (b + (i + 1)))
		}
		if min > sum {
			min = sum
		}
	}
	fmt.Println(min)
}