#include<bits/stdc++.h>
#define ll long long
#define fr(i,x,y) for(int i=(x);i<=(y);i++)
#define rf(i,x,y) for(int i=(x);i>=(y);i--)
#define frl(i,x,y) for(int i=(x);i<(y);i++)
using namespace std;
const int N=100005;
const int p=1e9+7;
int n,a[N];
int tot[16];

template<class T> void read(T &x){
	char ch=getchar();x=0;
	for(;ch<'0'||ch>'9';ch=getchar());
	for(;ch>='0'&&ch<='9';ch=getchar()) x=(x<<3)+(x<<1)+ch-'0';
}

void Add(int &x,int y){
	x+=y;
	while(x>=p) x-=p;
}

int f[1<<16],sum[1<<16];
int main(){
	read(n);
	int x,y,w;
	fr(i,2,n){
		read(x);read(y);read(w);
		x++;y++;
		a[x]^=w;a[y]^=w;
	}
	fr(i,1,n) tot[a[i]]++;
	int ans=0,all=0;
	fr(i,1,15) ans+=tot[i]/2,all^=(tot[i]&1)<<i;
	fr(i,1,all)
	 if ((i&all)==i){
	 	//if ((i&(-i))==i){ f[i]=1;continue; }
	 	sum[i]=0;
	 	fr(j,0,15) if (i&(1<<j)) sum[i]^=j,f[i]++;
	 	if (sum[i]) continue;
	 	f[i]--;
	 	for(int j=(i-1)&i;j;j=(j-1)&i)
	 	 if (sum[j]==0) f[i]=min(f[i],f[j]+f[i^j]);
	 }
	cout<<ans+f[all]<<endl;
	return 0;
}
### Prompt

Please create a solution in CPP to 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>
#define ll long long
#define fr(i,x,y) for(int i=(x);i<=(y);i++)
#define rf(i,x,y) for(int i=(x);i>=(y);i--)
#define frl(i,x,y) for(int i=(x);i<(y);i++)
using namespace std;
const int N=100005;
const int p=1e9+7;
int n,a[N];
int tot[16];

template<class T> void read(T &x){
	char ch=getchar();x=0;
	for(;ch<'0'||ch>'9';ch=getchar());
	for(;ch>='0'&&ch<='9';ch=getchar()) x=(x<<3)+(x<<1)+ch-'0';
}

void Add(int &x,int y){
	x+=y;
	while(x>=p) x-=p;
}

int f[1<<16],sum[1<<16];
int main(){
	read(n);
	int x,y,w;
	fr(i,2,n){
		read(x);read(y);read(w);
		x++;y++;
		a[x]^=w;a[y]^=w;
	}
	fr(i,1,n) tot[a[i]]++;
	int ans=0,all=0;
	fr(i,1,15) ans+=tot[i]/2,all^=(tot[i]&1)<<i;
	fr(i,1,all)
	 if ((i&all)==i){
	 	//if ((i&(-i))==i){ f[i]=1;continue; }
	 	sum[i]=0;
	 	fr(j,0,15) if (i&(1<<j)) sum[i]^=j,f[i]++;
	 	if (sum[i]) continue;
	 	f[i]--;
	 	for(int j=(i-1)&i;j;j=(j-1)&i)
	 	 if (sum[j]==0) f[i]=min(f[i],f[j]+f[i^j]);
	 }
	cout<<ans+f[all]<<endl;
	return 0;
}
```