**Time limit:**1.00 s**Memory limit:**512 MB

You are given a 3 \times 3 grid containing the numbers 1,2,\dots,9. Your task is to perform a sequence of moves so that the grid will look like this:

1 2 3 4 5 6 7 8 9

On each move, you can swap the numbers in any two adjacent squares (horizontally or vertically). What is the minimum number of moves required?

# Input

The input has three lines, and each of them has three integers.

# Output

Print one integer: the minimum number of moves.

# Example

Input:

2 1 3 7 5 9 8 4 6

Output:

4