#class Node:
#  def __init__(self, value, next=None):
#    self.val = value
#    self.next = next
class Solution:
  def reorder(self, head):
    
    def find_mid(head):
      slow, fast = head, head 
      while slow and fast:
        if fast:
          if fast.next:
            fast = fast.next.next
          else:
            return slow
        else:
          return slow
        slow = slow.next
      return slow
    
    def reverse(node):
      prev = None
      while node:
        next_node = node.next
        node.next = prev
        prev = node
        node = next_node
      return prev 

    # Find the middle and last points then reverse linked list from the middle to the end
    start = head
    mid = find_mid(head)
    last = reverse(mid)

    # Construct the new linked list by linking start->last->start->last ... 
    new_head = start
    while last != mid:
      next_start = start.next
      next_last = last.next

      start.next = last
      last.next = next_start

      start = next_start
      last = next_last
    return new_head