CF165D Beard Graph

Let's define a non-oriented connected graph of $ n $ vertices and $ n-1 $ edges as a beard, if all of its vertices except, perhaps, one, have the degree of 2 or 1 (that is, there exists no more than one vertex, whose degree is more than two). Let us remind you that the degree of a vertex is the number of edges that connect to it. Let each edge be either black or white. Initially all edges are black. You are given the description of the beard graph. Your task is to analyze requests of the following types: - paint the edge number $ i $ black. The edge number $ i $ is the edge that has this number in the description. It is guaranteed that by the moment of this request the $ i $ -th edge is white - paint the edge number $ i $ white. It is guaranteed that by the moment of this request the $ i $ -th edge is black - find the length of the shortest path going only along the black edges between vertices $ a $ and $ b $ or indicate that no such path exists between them (a path's length is the number of edges in it) The vertices are numbered with integers from $ 1 $ to $ n $ , and the edges are numbered with integers from $ 1 $ to $ n-1 $ .

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In the first sample vertices $ 1 $ and $ 2 $ are connected with edge number $ 1 $ , and vertices $ 2 $ and $ 3 $ are connected with edge number $ 2 $ . Before the repainting edge number $ 2 $ each vertex is reachable from each one along the black edges. Specifically, the shortest path between $ 1 $ and $ 3 $ goes along both edges. If we paint edge number $ 2 $ white, vertex $ 3 $ will end up cut off from other vertices, that is, no path exists from it to any other vertex along the black edges.