Reorder the list

Problem

Reorder a linked list L0, L1, ..., Ln into L0, Ln, L1, Ln-1, L2, Ln-2, and so on, by changing links only. Print the result.

Example 1

Input

1 2 3 4 5

Output

1 5 2 4 3

Example 2

Input

1 2 3 4

Output

1 4 2 3

Try the problem first. Open one hint at a time.

Hint 1

Find the middle, cut the list in two and reverse the second half.

Hint 2

Then weave the two halves together one node at a time.

Write your Python code, run it on the examples and submit it to hidden tests.