Paheli and Bhoojo are Appro’s long lost friends . The Last time Appro met them was in class 10th science class. Appro sees them after 6 years today but they are very angry with her , so they punish her and ask her to calculate strength of the tree in their backyard.
Strength of a tree is defined as maximum sum of number of divisors of subset of nodes of a tree but there is one condition , if a node is included in this set, none of its children can be a part.
Please help Appro with this.
Note: The tree is rooted at 1.
The first line of input contains single integer $$N$$ denoting the number of nodes in the tree.
Next $$N-1$$ lines contains 2 space separated integers $$A$$ and $$B$$ denoting that there is an edge from node $$A$$ to node $$B$$.
Print the required answer.
$$ 1\le N \le 10^6 $$
$$ 1\le A,B \le N $$