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题目链接
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 n 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 0 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 n n nodes contains all edges ( u , v ) (u, v) (u,v) with 1 ≤ u < v ≤ n 1 \le u < v \le n 1≤u<v≤n; such a graph has n ( n ? 1 ) 2 \frac{n(n-1)}{2} 2n(n?1)? edges.
She is not sure how to solve this problem, so she asks you to solve it for her.
Input
The first line contains two integers n n n and m m m ( 2 ≤ n ≤ 2 ? 1 0 5 2 \le n \le 2 \cdot 10^5 2≤n≤2?105, 0 ≤ m ≤ min ? ( 2 ? 1 0 5 , n ( n ? 1 ) 2 ? 1 ) 0 \le m \le \min(2 \cdot 10^5, \frac{n(n-1)}{2} - 1) 0≤m≤min(2?105,2n(n?1)??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 i i-th of the following m m m lines contains three integers u i u_i ui?, v i v_i vi?, and w i w_i wi? ( 1 ≤ u i , v i ≤ n 1 \le u_i, v_i \le n 1≤ui?,vi?≤n, u ≠ v u \ne v u?=v, 1 ≤ w i < 2 30 1 \le w_i < 2^{30} 1≤wi?<230), representing the edge from u i u_i ui? to v i v_i vi? has been pre-assigned with the weight w i w_i wi?. No edge appears in the input more than once.
Output
Print on one line one integer — the minimum ugliness among all weight assignments with XOR sum equal to 0 0 0.
Examples
input
4 4
2 1 14
1 4 14
3 2 15
4 3 8
output
15
input
6 6
3 6 4
2 4 1
4 5 7
3 4 10
3 5 1
5 2 15
output
0
input
5 6
2 3 11
5 3 7
1 4 10
2 4 14
4 3 8
2 5 6
output
6
Note
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.
显然,一定存在一种最优解,使得加入的边有一条为
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i
=
1
m
w
i
\bigoplus \limits_{i=1}^mw_i
i=1?m?w