#include<bits/stdc++.h>
using namespace std;
int read(){
	int x=0,f=0;char ch=getchar();
	while(!isdigit(ch)){ch=getchar();}
	while(isdigit(ch)){x=x*10+ch-'0';ch=getchar();}
	return x;
}
const int N = 1e6;
int n,sum[1<<17],val[N],num[N],S,dp[1<<17];
int main()
{
	n = read();
	for(int i = 1;i < n;i++)
	{
		int a = read()+1,b = read()+1,w = read();
		val[a] ^= w;val[b] ^= w;
	}
	for(int i = 1;i <= n;i++) num[val[i]]++;
	int ans = 0;
	for(int i = 1;i < 16;i++)
	ans += num[i]/2,S |= ((num[i]&1)<<i-1);
	for(int i = 1;i < 1<<15;i++)
	{
		for(int j = 1;j < 16;j++)
		{
			sum[i] ^= j * ((i>>(j-1))&1);
			dp[i] += (i>>(j-1))&1;
		}
		dp[i]--;
	}
	dp[0] = 0;
	for(int i = 1;i < 1<<15;i++)
	{
		if(sum[i]) continue;
		for(int j = i;j;j=(j-1)&i)
		{
			if(sum[j]) continue;
			dp[i] = min(dp[i],dp[i^j]+dp[j]);
		}
	}
	cout<<ans+dp[S]<<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
#include<bits/stdc++.h>
using namespace std;
int read(){
	int x=0,f=0;char ch=getchar();
	while(!isdigit(ch)){ch=getchar();}
	while(isdigit(ch)){x=x*10+ch-'0';ch=getchar();}
	return x;
}
const int N = 1e6;
int n,sum[1<<17],val[N],num[N],S,dp[1<<17];
int main()
{
	n = read();
	for(int i = 1;i < n;i++)
	{
		int a = read()+1,b = read()+1,w = read();
		val[a] ^= w;val[b] ^= w;
	}
	for(int i = 1;i <= n;i++) num[val[i]]++;
	int ans = 0;
	for(int i = 1;i < 16;i++)
	ans += num[i]/2,S |= ((num[i]&1)<<i-1);
	for(int i = 1;i < 1<<15;i++)
	{
		for(int j = 1;j < 16;j++)
		{
			sum[i] ^= j * ((i>>(j-1))&1);
			dp[i] += (i>>(j-1))&1;
		}
		dp[i]--;
	}
	dp[0] = 0;
	for(int i = 1;i < 1<<15;i++)
	{
		if(sum[i]) continue;
		for(int j = i;j;j=(j-1)&i)
		{
			if(sum[j]) continue;
			dp[i] = min(dp[i],dp[i^j]+dp[j]);
		}
	}
	cout<<ans+dp[S]<<endl;
	return 0;
}
```