Description
In an edge-weighted tree, the xor-length of a path p is defined as the xor sum of the weights of edges on p:
{xor}length(p)=\oplus{e \in p}w(e)
⊕ is the xor operator.
We say a path the xor-longest path if it has the largest xor-length. Given an edge-weighted tree with n nodes, can you find the xor-longest path?
Input
The input contains several test cases. The first line of each test case contains an integer n(1<=n<=100000), The following n-1 lines each contains three integers u(0 <= u < n),v(0 <= v < n),w(0 <= w < 2^31), which means there is an edge between node u and v of length w.
Output
For each test case output the xor-length of the xor-longest path.
Sample Input
4
0 1 3
1 2 4
1 3 6
Sample Output
7