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 Python (3.4.3) (judge verdict: Wrong Answer)

# import bisect
# from collections import Counter, deque
# import copy
# from fractions import gcd
# from functools import reduce
# from itertools import accumulate, permutations, combinations, combinations_with_replacement, groupby, product
# import math
import numpy as np
import sys
sys.setrecursionlimit(10 ** 5 + 10)
# input = sys.stdin.readline

def resolve():
    N=int(input())
    A=np.array(list(map(int,input().split())))

    B=np.array([i for i in range(1,N+1)])

    A=A-B


    val1 = 0
    val2=0
    for i in A:
        val1 += abs(i - 1)
        val2+=abs(i+1)
    if val1<val2:

        minval = 10 ** 50
        temp = 10**50
        for j in range(abs(sum(A))):
            val=0
            for i in A:
                val+=abs(i-j)
            if val>=temp:
                break
            else:
                temp=val
                minval=min(minval,val)

    else:

        minval = 10 ** 50
        temp = 10**50
        for j in range(abs(sum(A))):
            val=0
            for i in A:
                val+=abs(i+j)
            if val>=temp:
                break
            else:
                temp=val
                minval=min(minval,val)
    print(minval)
resolve()