Score : $1000$ points

Problem Statement

You are given a tree with $N$ vertices. The vertices are numbered $0$ through $N-1$, and the edges are numbered $1$ through $N-1$. Edge $i$ connects Vertex $x_i$ and $y_i$, and has a value $a_i$. You can perform the following operation any number of times:

• Choose a simple path and a non-negative integer $x$, then for each edge $e$ that belongs to the path, change $a_e$ by executing $a_e \gets a_e \oplus x$ (⊕ denotes XOR).

Your objective is to have $a_e = 0$ for all edges $e$. Find the minimum number of operations required to achieve it.

Constraints

• $2 \leq N \leq 10^5$
• $0 \leq x_i,y_i \leq N-1$
• $0 \leq a_i \leq 15$
• The given graph is a tree.
• All input values are integers.

Input

Input is given from Standard Input in the following format:

$N$

$x_1$ $y_1$ $a_1$

$x_2$ $y_2$ $a_2$

$:$

$x_{N-1}$ $y_{N-1}$ $a_{N-1}$

Output

Find the minimum number of operations required to achieve the objective.

5
0 1 1
0 2 3
0 3 6
3 4 4

3

The objective can be achieved in three operations, as follows:

• First, choose the path connecting Vertex $1, 2$, and $x = 1$.
• Then, choose the path connecting Vertex $2, 3$, and $x = 2$.
• Lastly, choose the path connecting Vertex $0, 4$, and $x = 4$.

2
1 0 0

0