19273번 - XorTree 다국어

문제

You are given a tree with $N$ vertices. The vertices are numbered 0ドル$ through $N-1,ドル and the edges are numbered 1ドル$ through $N-1$. Edge $i$ connects vertex $x_i$ and $y_i,ドル 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,ドル then for each edge $e$ that belongs to the path, change $a_e$ by executing $a_e := a_e \oplus x$ ($\oplus$ denotes $XOR$).

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

입력

Input is given in the following format:

$N$

$x_1$ $y_1$ $a_1$

$x_2$ $y_2$ $a_2$

$\ldots$

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

출력

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

제한

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

힌트

In Sample 1, the objective can be achieved in three operations, as follows: first, choose the path connecting Vertex 1,ドル 2,ドル and $x = 1,ドル then, choose the path connecting Vertex 2,ドル 3,ドル and $x = 2$; lastly, choose the path connecting Vertex 0,ドル 4,ドル and $x = 4$.