B"You are given a tree with n vertices and you are allowed to perform no more than 2n transformations on it. Transformation is defined by three vertices x, xe2 x80 x89y, xe2 x80 x89y' and consists of deleting edge (x, xe2 x80 x89y) and adding edge (x, xe2 x80 x89y'). Transformation x, xe2 x80 x89y, xe2 x80 x89y' could be performed if all the following conditions are satisfied: You should minimize the sum of squared distances between all pairs of vertices in a tree, which you could get after no more than 2n transformations and output any sequence of transformations leading initial tree to such state. Note that you don't need to minimize the number of operations. It is necessary to minimize only the sum of the squared distances. The first line of input contains integer n (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x892 xc2 xb7105) -- number of vertices in tree. The next n xe2 x80 x89- xe2 x80 x891 lines of input contains integers a and b (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89a, xe2 x80 x89b xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n, xe2 x80 x89a xe2 x80 x89 xe2 x89 xa0 xe2 x80 x89b) -- the descriptions of edges. It is guaranteed that the given edges form a tree. In the first line output integer k (0 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89k xe2 x80 x89 xe2 x89 xa4 xe2 x80 x892n) -- the number of transformations from your example, minimizing sum of squared distances between all pairs of vertices. In each of the next k lines output three integers x, xe2 x80 x89y, xe2 x80 x89y' -- indices of vertices from the corresponding transformation. Transformations with y xe2 x80 x89= xe2 x80 x89y' are allowed (even though they don't change tree) if transformation conditions are satisfied. If there are several possible answers, print any of them. This is a picture for the second sample. Added edges are dark, deleted edges are dotted. "...