Distinct colors in subtrees

Given an undirected connected tree with $N$ coloured nodes (colours denoted with integers $1$ to $N$), numbered from $1$ to $N$, and rooted at node $1$. Your task is to determine, for each node, the number of distinct colours present in its subtree. For example, a subtree rooted at a specific node might contain several nodes with duplicate colors. You must count only the unique colors present in