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)

// サンプル4がなければ解けなかった
// b=0としたら順に(1-1)+(1-2)+(1-3)+(1-4)+(2-5)+(3-6)+(4-7)で
// 0 -1 -2 -3 -3 -3 -3 となりこの最も多い-3をbで潰せばいけるのでは? -> いけました
// -> なんか実装がうまくいかない感じで8WA

package main

import (
	"fmt"
	"sort"
)

type KV struct {
	Key, Value int
}

type KVS []KV

func (kvs KVS) Len() int {
	return len(kvs)
}

func (kvs KVS) Swap(i, j int) {
	kvs[i], kvs[j] = kvs[j], kvs[i]
}

func (kvs KVS) Less(i, j int) bool {
	if kvs[i].Value == kvs[j].Value {
		return kvs[i].Key < kvs[j].Key
	}
	return kvs[i].Value > kvs[j].Value
}

func main() {
	var N int
	fmt.Scan(&N)
	T := make(map[int]int)
	A := make([]int, N)
	for i := 0; i < N; i++ {
		var V int
		fmt.Scan(&V)
		x := V - (i + 1)
		T[x]++
		A[i] = V
	}
	kvss := make(KVS, len(T))
	idx := 0
	for k, v := range T {
		kvss[idx] = KV{Key: k, Value: v}
		idx++
	}
	sort.Sort(kvss)
	maxK := kvss[0].Key
	ans := 0
	for i := 0; i < N; i++ {
		ans += abs(A[i] - (maxK + i + 1))
	}
	fmt.Println(ans)
}

func abs(x int) int {
	if x < 0 {
		x *= -1
	}
	return x
}