B'Vanya wants to minimize a tree. He can perform the following operation multiple times: choose a vertex v, and two disjoint (except for v) paths of equal length a0 xe2 x80 x89= xe2 x80 x89v, a1, ..., ak, and b0 xe2 x80 x89= xe2 x80 x89v, b1, ..., bk. Additionally, vertices a1, ..., ak, b1, ..., bk must not have any neighbours in the tree other than adjacent vertices of corresponding paths. After that, one of the paths may be merged into the other, that is, the vertices b1, ..., bk can be effectively erased: Help Vanya determine if it possible to make the tree into a path via a sequence of described operations, and if the answer is positive, also determine the shortest length of such path. The first line of input contains the number of vertices n (2 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x892 xc2 xb7105). Next n xe2 x80 x89- xe2 x80 x891 lines describe edges of the tree. Each of these lines contains two space-separated integers u and v (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89u, xe2 x80 x89v xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n, u xe2 x80 x89 xe2 x89 xa0 xe2 x80 x89v) -- indices of endpoints of the corresponding edge. It is guaranteed that the given graph is a tree. If it is impossible to obtain a path, print -1. Otherwise, print the minimum number of edges in a possible path. In the first sample case, a path of three edges is obtained after merging paths 2 xe2 x80 x89- xe2 x80 x891 xe2 x80 x89- xe2 x80 x896 and 2 xe2 x80 x89- xe2 x80 x894 xe2 x80 x89- xe2 x80 x895. It is impossible to perform any operation in the second sample case. For example, it is impossible to merge paths 1 xe2 x80 x89- xe2 x80 x893 xe2 x80 x89- xe2 x80 x894 and 1 xe2 x80 x89- xe2 x80 x895 xe2 x80 x89- xe2 x80 x896, since vertex 6 additionally has a neighbour 7 that is not present in the corresponding path. '...