B"Christmas was knocking on the door, and our protagonist, Bob, was preparing a spectacular present for his long-time second best friend Charlie. As chocolate boxes are lame, he decided to decorate a tree instead. Bob's tree can be represented as an undirected connected graph with n nodes (numbered 1 to n ) and n-1 edges. Initially, Bob placed a decoration with label i on node i , for each 1 <= i <= n . However, as such a simple arrangement is lame, he decided to shuffle the decorations a bit. Formally, Bob did the following steps: After finishing, Bob seemed satisfied with the arrangement, so he went to sleep. The next morning, Bob wakes up only to find out that his beautiful arrangement has been ruined! Last night, Bob's younger brother Bobo dropped some of the decorations on the floor while he was playing with the tree. Fortunately, no decorations were lost, so Bob can repair the tree in no time. However, he completely forgets how the tree looked like yesterday. Therefore, given the labels of the decorations still on the tree, Bob wants to know the number of possible configurations of the tree. As the result can be quite large, Bob will be happy if you can output the result modulo 1000000007 ( 10^9+7 ). Note that, it is possible that there exists no possible configurations. The first line contains a single integer n ( 2 <= q n <= q 500 ,000 ) -- the number of nodes. Each of the next n - 1 lines contains two integers u and v ( 1 <= q u, v <= q n ), denoting that there is an edge connecting two nodes u and v . It is guaranteed that the given edges form a tree. The last line contains n integers a_1, a_2, ldots, a_n ( 0 <= a_i <= n ). For each i , a_i = 0 means that the decoration of node i has been dropped on the floor. Otherwise, a_i is the label of the decoration of node i . It is guaranteed that no label appears mo"...