Hello There

I came across this problem on spoj

we're given a tree and we have to find two paths that don't share vertices and which sum of their length is maximum

no i got an idea where we compute the longest path for each subtree rooted with vertex u and there answer is the max sum for each node where for each node we sum the longest path in the subtree rooted with u and the longest path in the entire tree minus the sub tree rooted with u

the latter was a bit confusing for me and i couldn't come up with the solution

any advises or hints about how to compute the longest path in the tree minus the subtree rooted with u for each vertex u would be greatly appreciated