You need to find a binary tree of size n that satisfies a given set of c constraints. Suppose that the nodes of the unknown binary tree are labeled using a pre-order traversal starting with 1. For the i-th constraint you are given two labels, ai and bi and a direction, left or right. In case of left direction, bi is an element of the subtree rooted at ai's left child. Similarly in the case of right direction bi is an element of the subtree rooted at ai's right child.
Output
Output will be on a single line.
Any binary tree that satisfies the constraints will be accepted. The tree's nodes should be printed out as
n space separated labels representing an
in-order traversal, using the
pre-order numbers as labels of vertices.
If there are no trees that satisfy the constraints, print "
IMPOSSIBLE" (without quotes).
Note
Consider the first sample test. We need to find a tree with 3 nodes that satisfies the following two constraints. The node labeled 2 with pre-order traversal should be in the left subtree of the node labeled 1 with pre-order traversal; the node labeled 3 with pre-order traversal should be in the right subtree of the node labeled 1. There is only one tree with three nodes that satisfies these constraints and its in-order traversal is
(2,1,3).
Pre-order is the "root — left subtree — right subtree" order.
In-order is the "left subtree — root — right subtree" order.
For other information regarding
in-order and
pre-order, see
http://en.wikipedia.org/wiki/Tree_traversal.