B"As a teacher, Riko Hakozaki often needs to help her students with problems from various subjects. Today, she is asked a programming task which goes as follows. You are given an undirected complete graph with n nodes, where some edges are pre-assigned with a positive weight while the rest aren't. You need to assign all unassigned edges with non-negative weights so that in the resulting fully-assigned complete graph the XOR sum of all weights would be equal to 0 . Define the ugliness of a fully-assigned complete graph the weight of its minimum spanning tree, where the weight of a spanning tree equals the sum of weights of its edges. You need to assign the weights so that the ugliness of the resulting graph is as small as possible. As a reminder, an undirected complete graph with n nodes contains all edges (u, v) with 1 <= u < v <= n ; such a graph has frac{n(n-1)}{2} edges. She is not sure how to solve this problem, so she asks you to solve it for her. The first line contains two integers n and m ( 2 <= n <= 2 cdot 10^5 , 0 <= m <= min(2 cdot 10^5, frac{n(n-1)}{2} - 1) ) -- the number of nodes and the number of pre-assigned edges. The inputs are given so that there is at least one unassigned edge. The i -th of the following m lines contains three integers u_i , v_i , and w_i ( 1 <= u_i, v_i <= n , u ne v , 1 <= w_i < 2^{30} ), representing the edge from u_i to v_i has been pre-assigned with the weight w_i . No edge appears in the input more than once. Print on one line one integer -- the minimum ugliness among all weight assignments with XOR sum equal to 0 . The following image showcases the first test case. The black weights are pre-assigned from the statement, the red weights are assigned by us, and the minimum spanning tree is denoted by the blue edges. "...