Weird Paths in a tree

You are given a tree. Each node of the tree is assigned a distinct value. A path in the tree is considered weird if the values in the path increase and decrease alternatively. For example: Consider a straight chain of nodes 1→3→2→4→5 with value assigned to any node i being i itself. Then the path 3→2→4, 1→3→2, etc. are weird whereas 1→3→2→4→5 is not weird because 2→4 and 4→5 are both increasing.