#include<stdio.h>
void ckmin(int&x,const int&y)
{
	x=x<y?x:y;
}
int n,m,a[100005],f[1<<15],ans;
int main()
{
	scanf("%d",&n);
	for(int i=1,x,y,z;i<n;i++)
	{
		scanf("%d%d%d",&x,&y,&z);
		a[x]^=z;a[y]^=z;
	}
	for(int i=0;i<n;i++)
		if(a[i]--)
			ans+=m>>a[i]&1,m^=1<<a[i];
	for(int s=1;s<=m;++s)
	{
		int x=0;
		for(int j=0;j<16;++j)if(s>>j&1)x^=j+1;
		if(x)f[s]=1e9;
		else{
			f[s]=__builtin_popcount(s)-1;
			for(int t=(s-1)&s;t;t=(t-1)&s)ckmin(f[s],f[t]+f[s^t]);
		}
	}
	printf("%d",ans+f[m]);
	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<stdio.h>
void ckmin(int&x,const int&y)
{
	x=x<y?x:y;
}
int n,m,a[100005],f[1<<15],ans;
int main()
{
	scanf("%d",&n);
	for(int i=1,x,y,z;i<n;i++)
	{
		scanf("%d%d%d",&x,&y,&z);
		a[x]^=z;a[y]^=z;
	}
	for(int i=0;i<n;i++)
		if(a[i]--)
			ans+=m>>a[i]&1,m^=1<<a[i];
	for(int s=1;s<=m;++s)
	{
		int x=0;
		for(int j=0;j<16;++j)if(s>>j&1)x^=j+1;
		if(x)f[s]=1e9;
		else{
			f[s]=__builtin_popcount(s)-1;
			for(int t=(s-1)&s;t;t=(t-1)&s)ckmin(f[s],f[t]+f[s^t]);
		}
	}
	printf("%d",ans+f[m]);
	return 0;
}

```