Linear Approximation

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.

Examples

Input

5 2 2 3 5 5

Output

2

Input

9 1 2 3 4 5 6 7 8 9

Output

0

Input

6 6 5 4 3 2 1

Output

18

Input

7 1 1 1 1 2 3 4

Output

6

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N

outputFormat

Output

Print the minimum possible sadness of Snuke.

Examples

Input

5 2 2 3 5 5

Output

2

Input

9 1 2 3 4 5 6 7 8 9

Output

0

Input

6 6 5 4 3 2 1

Output

18

Input

7 1 1 1 1 2 3 4

Output

6

样例

5
2 2 3 5 5

2