Problem:
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

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

class Main{
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int N = scan.nextInt();
        int bit[] = new int[N];
        for(int i=0;i<N-1;++i){
            int x = scan.nextInt();
            int y = scan.nextInt();
            int a = scan.nextInt();
            bit[x]^=a;
            bit[y]^=a;
        }
        int count[] = new int[1<<4];
        for(int i=0;i<N;++i)count[bit[i]]++;
        int ans =0;
        for(int i=1;i<(1<<4);++i){
            ans+=count[i]/2;
            count[i]%=2;
        }
        int num=0;
        for(int i=1;i<(1<<4);++i){
            if(count[i]>0){
                num^=i;
                count[i]--;
                if(num==i)continue;
                ++ans;
                if(count[num]>0){
                    ++ans;
                    num=0;
                    count[num]--;
                }
            }
        }
        System.out.println(ans);
    }
}