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: Time Limit Exceeded)

N = int(input())
data = list(map(int, input().split()))
for i in range(N):
    data[i] -= (i + 1)
ave = sum(data) / N
if ave > 0:
    key = int(ave + 1)
    key1 = int(ave)
else:
    key = int(ave - 1)
    key1 = int(ave)
data.sort()
sumdata = 0
sumdata1 = 0
sumdatax = 0
#for i in data:
 #   sumdata += abs(i - key)
  #  sumdata1 += abs(i - key1)
   # sumdatax += abs(i - ave)
cnt = 0
sumdataa = 0
key = data[0] - 1
for i in data:
    if key != i:
        key = i
        for j in data:
            sumdataa += abs(j - key)
        #print(sumdataa)
        if cnt == 0:
            minsum = sumdataa
        if sumdataa < minsum:
            minsum = sumdataa
    cnt += 1
    sumdataa = 0

#print(sumdatax)
#print(data)
#print(min([sumdata, sumdata1]))
print(minsum)