Walking Around

You are given a weighted tree with $N$ vertices, numbered from $1$ to $N$. The edges are numbered from $1$ to $N - 1$, where edge $i$ connects two vertices $U_i$ and $V_i$ and has a non-negative integer weight $W_i$.

A path in the tree is a sequence of distinct vertices $(u_0, u_1, \dots, u_m)$ for some $m \ge 1$, such that every pair of adjacent vertices $(u_j, u_{j+1})$ for $0 \le j < m$ is connected by an edge of the tree. The score of the path $(u_0, \dots, u_m)$ is the bitwise XOR of the weights of all edges on the path, that is $\text{XOR}(w_0, w_1, \dots, w_{m-1})$, where $w_j$ is the weight of the edge connecting $u_j$ and $u_{j+1}$.

Find the minimum and the maximum score among all paths in the tree.

The first line contains an integer $N$ ($2 \le N \le 100\,000$), the number of vertices. Each of the next $N - 1$ lines contains three integers $U_i$, $V_i$, and $W_i$ ($1 \le U_i < V_i \le N$; $0 \le W_i \le 10^9$), describing edge $i$.

Print the minimum and the maximum score separated by a space, on a single line.