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2 초 256 MB 2 2 2 100.000%

문제

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 $a_e := a_e \oplus x$ ($\oplus$ 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

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

예제 입력 1

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

예제 출력 1

3

예제 입력 2

2
1 0 0

예제 출력 2

0

힌트

In Sample 1, 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 $x = 4$.