//by (111110101)2
#include<iostream>
#include<sstream>
#include<fstream>
#include<string>
#include<vector>
#include<deque>
#include<queue>
#include<stack>
#include<set>
#include<map>
#include<algorithm>
#include<functional>
#include<utility>
#include<bitset>
#include<cmath>
#include<cstdlib>
#include<ctime>
#include<cstdio>
using namespace std;
int n,dp[1<<17],nm[101010],sum,cnt[22],ans,mk;
bool gd[1<<17];
int main()
{
	for(int i=0;i<(1<<16);i++)
	{
		sum=0;
		for(int j=0;j<16;j++)
		{
			if((i>>j)&1)
			{
				sum^=j;
			}
		}
		if(sum==0)
		{
			gd[i]=true;
		}
	}
	cin>>n;
	for(int i=0;i<n-1;i++)
	{
		int a,b,c;
		cin>>a>>b>>c;
		a--;
		b--;
		nm[a]^=c;
		nm[b]^=c;
	}
	for(int i=0;i<n;i++)
	{
		if(nm[i])
		{
			cnt[nm[i]]++;
		}
	}
	for(int i=0;i<21;i++)
	{
		ans+=cnt[i]/2;
		cnt[i]%=2;
		if(cnt[i])
		{
			ans++;
			mk|=(1<<i);
		}
	}
	for(int i=0;i<=mk;i++)
	{
		for(int j=i;j;j=(j-1)&i)
		{
			if(gd[j])
			{
				dp[i]=max(dp[i],dp[i^j]+1);
			}
		}
	}
	cout<<ans-dp[mk]<<endl;
	return 0;
}
### Prompt

Create a solution in Cpp for the following problem:

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
//by (111110101)2
#include<iostream>
#include<sstream>
#include<fstream>
#include<string>
#include<vector>
#include<deque>
#include<queue>
#include<stack>
#include<set>
#include<map>
#include<algorithm>
#include<functional>
#include<utility>
#include<bitset>
#include<cmath>
#include<cstdlib>
#include<ctime>
#include<cstdio>
using namespace std;
int n,dp[1<<17],nm[101010],sum,cnt[22],ans,mk;
bool gd[1<<17];
int main()
{
	for(int i=0;i<(1<<16);i++)
	{
		sum=0;
		for(int j=0;j<16;j++)
		{
			if((i>>j)&1)
			{
				sum^=j;
			}
		}
		if(sum==0)
		{
			gd[i]=true;
		}
	}
	cin>>n;
	for(int i=0;i<n-1;i++)
	{
		int a,b,c;
		cin>>a>>b>>c;
		a--;
		b--;
		nm[a]^=c;
		nm[b]^=c;
	}
	for(int i=0;i<n;i++)
	{
		if(nm[i])
		{
			cnt[nm[i]]++;
		}
	}
	for(int i=0;i<21;i++)
	{
		ans+=cnt[i]/2;
		cnt[i]%=2;
		if(cnt[i])
		{
			ans++;
			mk|=(1<<i);
		}
	}
	for(int i=0;i<=mk;i++)
	{
		for(int j=i;j;j=(j-1)&i)
		{
			if(gd[j])
			{
				dp[i]=max(dp[i],dp[i^j]+1);
			}
		}
	}
	cout<<ans-dp[mk]<<endl;
	return 0;
}
```