#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<unordered_set>
#include<unordered_map>
using namespace std;
typedef long long ll;
#define mod 1000000007
#define mad(a,b) a=(a+b)%mod;
#define chmax(a,b) a=max(a,b);
#define N 100010
ll cnt[16],t[N];
ll f[(1<<16)][16];
int main(){
  ll n; cin>>n;
  for(int i=0;i<n;i++)t[i]=0;
  for(int i=0;i<n-1;i++){
      ll a,b,c;cin>>a>>b>>c;
      t[a]^=c;
      t[b]^=c;
  }
  for(int i=0;i<16;i++)cnt[i]=0;
  for(int i=0;i<n;i++)cnt[t[i]]++;
  ll ans=cnt[0]; cnt[0]=0;
  for(int i=1;i<16;i++){
      ans+=(cnt[i]/2);
      cnt[i]%=2;
      //cout<<i<<":"<<cnt[i]<<endl;
  }
  ll ma=0;
  for(int i=0;i<(1<<16);i++)for(int j=0;j<16;j++)f[i][j]=0;
  f[0][0]=0;
  for(int i=0;i<(1<<16);i++)for(int j=0;j<16;j++){
      ma=max(ma,f[i][j]);
      for(int k=0;k<16;k++)if(((i>>k)&1)==0&&cnt[k]>0){
	  chmax(f[i+(1<<k)][j^k],f[i][j]+(j==k));
      }
  }
  ans+=ma;
  cout<<n-ans<<endl;
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<unordered_set>
#include<unordered_map>
using namespace std;
typedef long long ll;
#define mod 1000000007
#define mad(a,b) a=(a+b)%mod;
#define chmax(a,b) a=max(a,b);
#define N 100010
ll cnt[16],t[N];
ll f[(1<<16)][16];
int main(){
  ll n; cin>>n;
  for(int i=0;i<n;i++)t[i]=0;
  for(int i=0;i<n-1;i++){
      ll a,b,c;cin>>a>>b>>c;
      t[a]^=c;
      t[b]^=c;
  }
  for(int i=0;i<16;i++)cnt[i]=0;
  for(int i=0;i<n;i++)cnt[t[i]]++;
  ll ans=cnt[0]; cnt[0]=0;
  for(int i=1;i<16;i++){
      ans+=(cnt[i]/2);
      cnt[i]%=2;
      //cout<<i<<":"<<cnt[i]<<endl;
  }
  ll ma=0;
  for(int i=0;i<(1<<16);i++)for(int j=0;j<16;j++)f[i][j]=0;
  f[0][0]=0;
  for(int i=0;i<(1<<16);i++)for(int j=0;j<16;j++){
      ma=max(ma,f[i][j]);
      for(int k=0;k<16;k++)if(((i>>k)&1)==0&&cnt[k]>0){
	  chmax(f[i+(1<<k)][j^k],f[i][j]+(j==k));
      }
  }
  ans+=ma;
  cout<<n-ans<<endl;
  return 0;
}

```