Problem - Lomsat gelral

You are given a tree where each node has a color (an integer). For each node v, find the sum of all colors that appear most frequently in v's subtree. Example: if the subtree has colors {$1$, $1$, $2$, $3$, $3$, $3$}, the most frequent color is $3$ (appears $3$ times), so the answer for that node is $3$.

If there is a tie, sum all tied colors. There are up to $100$,$000$ nodes. The standard approach is small-to-large merging (DSU on tree), which runs in $O(n \log n)$ total time.