Problem 3 You are given a connected weighted undirected graph without any loops and multiple edges. Let us remind you that a graph's spanning tree is defined as an acyclic connected sub graph of the given graph that includes all of the graph's vertexes. The weight of a tree is defined as the sum of weights of the edges that the given tree contains. The minimum spanning tree (MST) of a graph is defined as the graph's spanning tree having the minimum possible weight. For any connected graph obviously exists the minimum spanning tree, but in the general case, a graph's minimum spanning tree is not unique. Your task is to determine the following for each edge of the given graph: whether it is either included in any MST, or included at least in one MST, or not included in any MST Input The first line contains two integers n and m (25n310-15m 5 min(109, n.))) the number of the graph's vertexes and edges, correspondingly. Then follow m lines, each of them contains three integers - the description of the graph's edges as "abw" (14.b.sh. I sw.s10,a #b), where a, and b, are the numbers of vertexes connected by the 1-th edge, w, is the edge's weight. It is guaranteed that the graph is connected and doesn't contain loops or multiple edges. Output Print mn lines the answers for all edges. If the i-th edge is included in any MST, print any, it the i-th edge is included at least in one MST, print at least one" if the i-th edge isn't included in any MST, print "none". Print the answers for the edges in the order in which the edges are specified in the input Examples Input 45 1 2 101 13 100 232 242 341 Output#1 none any at least one at least one any input#2 33 121 231 132 Outputs any any none input13 33 121 231 131 Output at least one at least one at least one Note In the second sample the MST is unique for the given graph it contains two first edges In the third sample any two edges form the MST for the given graph. That means that each edge is included at least in one MST