#include<bits/stdc++.h>
using namespace std;
#define N 200010
int n,va[N],c[N],ans,s,f[N],ss[N],nm[N];
int main(){
	cin>>n;
	for(int i=1;i<N;i++)
		nm[i]=nm[i-(i&-i)]+1;
	for(int i=1;i<N;i++)nm[i]--;
	for(int i=1;i<n;i++){
		int x,y,z;
		cin>>x>>y>>z;
		va[x]^=z;
		va[y]^=z;
	}
	for(int i=0;i<n;i++)
		c[va[i]]++;
	for(int i=1;i<=15;i++){
		ans+=c[i]/2;
		if(c[i]%2==1)s|=(1<<(i-1));
	}
	for(int i=1;i<(1<<15);i++)
		for(int j=0;j<15;j++)
			if(i&(1<<j))ss[i]^=(j+1);
	for(int i=1;i<(1<<15);i++)
		if(!ss[i])
			for(int j=i;j;j=(j-1)&i)
				if(!ss[j]&&!ss[i-j])
					nm[i]=min(nm[i],nm[i-j]+nm[j]);
	cout<<ans+nm[s];
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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.

Examples

Input

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


Output

3


Input

2
1 0 0


Output

0

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
#define N 200010
int n,va[N],c[N],ans,s,f[N],ss[N],nm[N];
int main(){
	cin>>n;
	for(int i=1;i<N;i++)
		nm[i]=nm[i-(i&-i)]+1;
	for(int i=1;i<N;i++)nm[i]--;
	for(int i=1;i<n;i++){
		int x,y,z;
		cin>>x>>y>>z;
		va[x]^=z;
		va[y]^=z;
	}
	for(int i=0;i<n;i++)
		c[va[i]]++;
	for(int i=1;i<=15;i++){
		ans+=c[i]/2;
		if(c[i]%2==1)s|=(1<<(i-1));
	}
	for(int i=1;i<(1<<15);i++)
		for(int j=0;j<15;j++)
			if(i&(1<<j))ss[i]^=(j+1);
	for(int i=1;i<(1<<15);i++)
		if(!ss[i])
			for(int j=i;j;j=(j-1)&i)
				if(!ss[j]&&!ss[i-j])
					nm[i]=min(nm[i],nm[i-j]+nm[j]);
	cout<<ans+nm[s];
}
```