Embedding a Tree (Challenge)

You are given a tree with N nodes. You should embed this tree in a 2-D plane such that each node of the tree is located at a point with integer coordinates. Let's denote the coordinates of the i-th node by pi = (xi, yi). An edge between nodes u and v corresponds to a line segment between points pu and pv. Formally, the mapping of the nodes to points should satisfy the following property: No two