#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int N=100005;
int val[N],cnt[N],sxr[1<<17];
int a[17];
int dp[1<<17];
inline int read(){
	int x=0;char e=getchar();
	for (;e<'0'||e>'9';e=getchar());
	for (;e>='0'&&e<='9';e=getchar()) x=(x<<1)+(x<<3)+(e^48);
	return x;
}
inline int Min(int a,int b){
	return a<b?a:b;
}
int main (){
	int n=read();
	for (int i=1;i<n;i++){
		int u=read()+1,v=read()+1,w=read();
		val[u]^=w,val[v]^=w;
	}
	for (int i=1;i<=n;i++) cnt[val[i]]++;
	int ans=0,to=0;
	for (int i=1;i<16;i++){
		ans+=(cnt[i]>>1);
		if (cnt[i]&1) to|=(1<<i);
	}
	for (int i=0;i<(1<<16);i++)
		for (int j=0;j<16;j++)
			if (i&(1<<j)) sxr[i]^=j;
	for(int i=0;i<(1<<16);i++) dp[i]=dp[i>>1]+(i&1);
    for(int i=1;i<(1<<16);i++) dp[i]--;
	for (int i=0;i<(1<<16);i++){
        if (sxr[i]) continue;
        for (int k=(i-1)&i;k;k=(k-1)&i)
            if (!sxr[k]) dp[i]=Min(dp[i],dp[k]+dp[i^k]);
	}
	printf ("%d",dp[to]+ans);
	return 0;
}
### Prompt

Your challenge is to write a Cpp solution 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 <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int N=100005;
int val[N],cnt[N],sxr[1<<17];
int a[17];
int dp[1<<17];
inline int read(){
	int x=0;char e=getchar();
	for (;e<'0'||e>'9';e=getchar());
	for (;e>='0'&&e<='9';e=getchar()) x=(x<<1)+(x<<3)+(e^48);
	return x;
}
inline int Min(int a,int b){
	return a<b?a:b;
}
int main (){
	int n=read();
	for (int i=1;i<n;i++){
		int u=read()+1,v=read()+1,w=read();
		val[u]^=w,val[v]^=w;
	}
	for (int i=1;i<=n;i++) cnt[val[i]]++;
	int ans=0,to=0;
	for (int i=1;i<16;i++){
		ans+=(cnt[i]>>1);
		if (cnt[i]&1) to|=(1<<i);
	}
	for (int i=0;i<(1<<16);i++)
		for (int j=0;j<16;j++)
			if (i&(1<<j)) sxr[i]^=j;
	for(int i=0;i<(1<<16);i++) dp[i]=dp[i>>1]+(i&1);
    for(int i=1;i<(1<<16);i++) dp[i]--;
	for (int i=0;i<(1<<16);i++){
        if (sxr[i]) continue;
        for (int k=(i-1)&i;k;k=(k-1)&i)
            if (!sxr[k]) dp[i]=Min(dp[i],dp[k]+dp[i^k]);
	}
	printf ("%d",dp[to]+ans);
	return 0;
}
```