## 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*:

⊕ 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

## Note:

The xor-longest path is 0->1->2, which has length 7 (=3 ⊕ 4)