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 ← 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.

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.

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.


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