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You are given a tree of $$n$$ nodes, some of the nodes contain numbers and others don't. Your task is to compute the number of ways to complete the labeling of the tree rooted at $$1$$, such that the following condition is satisfied "for any subtree $$x$$ all elements of the subtree must divide its root".
Input:
First line contains a single integer $$n$$, denoting the number of nodes in the tree.
Next Line contains $$n$$ integers, each number describes the content of a node in order (e.g: first number describes
content of node 1, second describes content of node 2, ... etc). If a number is $$0$$, it means that the content is unknown.
Next $$n-1$$ lines contain each two numbers $$(u, v)$$, meaning that there is an edge between node $$u$$ and node $$v $$.
Output:
Ouput a single integer denoting the number of ways to fill the tree without breaking the constraint modulo $$10^9+7$$;
Constraints:
The possible labelling are: