You are given a connected undirected graph which has even numbers of nodes. A connected graph is a graph in which all nodes are connected directly or indirectly by edges. Your task is to find a spanning tree whose median value of edges' costs is minimum. A spanning tree of a graph means that a tree which contains all nodes of the graph. \InputFile The input consists of multiple datasets. The format of each dataset is as follows. \textbf{n m} \textbf{s_1 t_1 c_1} \textbf{...} \textbf{s_m t_m c_m} The fi rst line contains an even number \textbf{n} (\textbf{2} ≤ \textbf{n} ≤ \textbf{1000}) and an integer \textbf{m} (\textbf{n-1} ≤ \textbf{m} ≤ \textbf{10000}). \textbf{n} is the nubmer of nodes and \textbf{m} is the number of edges in the graph. Then \textbf{m} lines follow, each of which contains \textbf{s_i} (\textbf{1} ≤ \textbf{s_i} ≤ \textbf{n}), \textbf{t_i} (\textbf{1} ≤ \textbf{s_i} ≤ \textbf{n}, \textbf{t_i} ≠ \textbf{s_i}) and \textbf{c_i} (\textbf{1} ≤ \textbf{c_i} ≤ \textbf{1000}). This means there is an edge between the nodes \textbf{s_i} and \textbf{t_i} and its cost is \textbf{c_i}. There is no more than one edge which connects \textbf{s_i} and \textbf{t_i}. The input terminates when \textbf{n = 0} and \textbf{m = 0}. Your program must not output anything for this case. \OutputFile Print the median value in a line for each dataset.