Micro and Tree

Micro has a tree with $n$ nodes. Micro can perform some operations on the tree. In one operation he can select a node and remove it along with the entire subtree rooted at it, from its current position and attach it as child of some other node. He defines a function $f(x)$ on the tree, as the minimum number of operations needed to be done to make a straight chain of nodes out of the given tree, when the tree is rooted at node $x$. Now Micro wants to find out the minimum of all the $f(i)$ where 1 \leq i \leq n.