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 ← a_e ⊕ 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.

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.

Constraints

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

Sample Input 1

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

Sample Output 1

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.

Sample Input 2

2
1 0 0

Sample Output 2

0

见题面 Input 部分

见题面 Output 部分