Question $27$

An unweighted undirected tree can be represented with $g$ nodes nodes numbered from $1$ to $g$ nodes and g$\_$edges $=$ g$\_$nodes $1$ edges where the $i^{th}$ edge connects nodes $g$ from$[$i$]$ and g$\_$to$[$i$].$ The tree is rooted at node $1.$

The task is to color the leaf nodes of the tree. Node $x$ is diversified if all the leaf nodes in its subtree have different colors.

Given $g$ nodes, $g_{-}$from, $g_{-}to,$ report an array of integers where the $i^{th}$ element represents the minimum number of different colors required to make the number of diversified nodes in the tree greater than or equal to $i.$

Note: A subtree of node, $x$ is defined as a