Watchtower Coverage

**Problem.** A rooted tree of n watchtowers (root 1). Line 1: n. Then n-1 lines: parent of v. For EVERY node print the maximum number of edges from it down to any node in its own subtree, one per line in node order 1..n. **Constraints:** 1 <= n <= 200000; the tree may be a bamboo. **R versus W.** The graded wrong solution prints the global tree height for every node.