Micro is having a tree which is having $$N$$ 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 functions $$f(X)$$ 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 $$1 \le i \le N$$.
First line consists of a single integer denoting $$N$$.
Following $$N-1$$ lines consists of two space separated integers $$X$$ and $$Y$$ denoting there is an edge between nodes $$X$$ and $$Y$$.
Print the required answer.
$$1 \le N \le 16$$
$$1 \le X, Y \le N$$