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: Runtime Error)

line=input()
line=line.rstrip().split(" ")
list1=[]
for i in range(N):
    list1.append(int(line[i])-i-1)
#print(list1)

list2=[]
list3=[]
for j in range(2):
    for k in range(N):
        list2.append(abs(list1[k]-1-j))
        
    list3.append(sum(list2))
    list2=[]
#print(list3)

if list3[0]==list3[1]:
    print(list3[0])
elif list3[0]<list3[1]:
    list2=[]
    list3=[]
    count=100000000000000000
    for l in range(1000000000):
        for m in range(N):
            list2.append(abs(list1[m]-1+l))
        if count>=sum(list2):
            count=sum(list2)
            #print(list2)
            list2=[]
            l=l+10
        else:
            count=100000000000000000
            for n in range(l,l+11):
                for o in range(N):
                    list2.append(abs(list1[o]-1+(n-10)))
                if count>=sum(list2):
                    count=sum(list2)
                    list2=[]
                else:
                    print(count)
                    break
                    
            
        
else: 
    list2=[]
    list3=[]
    count=100000000000000000
    for l in range(1000000000):
        for m in range(N):
            list2.append(abs(list1[m]-1-l))
        if count>=sum(list2):
            count=sum(list2)
            list2=[]
            l=l+10
        else:
            count=100000000000000000
            for n in range(l,l+11):
                for o in range(N):
                    list2.append(abs(list1[o]-1+(n-10)))
                if count>=sum(list2):
                    count=sum(list2)
                    list2=[]
                else:
                    print(count)
                    break