#include <bits/stdc++.h>
 
using namespace std;
 
const int maxn = 100100;
const int maxj = 17;
 
int n,res,mask,nn,a[maxn],cnt[maxn],dp[(int)1<<maxj],good[(int)1<<maxj];
 
int main() {
  //  freopen("in.txt","r",stdin);
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin>>n;
    for (int i=1;i<n;i++) {
        int x,y,z;
        cin>>x>>y>>z;
        a[x]^=z;
        a[y]^=z;
    }
    for (int i=0;i<n;i++) cnt[a[i]]++;
    for (int i=1;i<=maxj;i++) {
        res+=cnt[i]/2;
        cnt[i]%=2;
    }
    for (int i=1;i<=maxj;i++)
        if (cnt[i]!=0) {
            mask|=(1<<i);
            nn++;
        }
    for (int tt=0;tt<(1<<maxj);tt++) {
        int x=0;
        for (int i=0;i<maxj;i++)
            if (tt&(1<<i)) x^=i;
        good[tt] = (x==0);
    }
    for (int tt=0;tt<(1<<maxj);tt++) {
        if (tt&1) continue;
        int u=tt;
        while (u>0) {
            if (good[u]) dp[tt] = max(dp[tt],dp[tt^u] + 1);
            u = (u-1)&tt;
        }
    }
    cout<<res+nn-dp[mask];
}
### Prompt

Please formulate 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 <bits/stdc++.h>
 
using namespace std;
 
const int maxn = 100100;
const int maxj = 17;
 
int n,res,mask,nn,a[maxn],cnt[maxn],dp[(int)1<<maxj],good[(int)1<<maxj];
 
int main() {
  //  freopen("in.txt","r",stdin);
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin>>n;
    for (int i=1;i<n;i++) {
        int x,y,z;
        cin>>x>>y>>z;
        a[x]^=z;
        a[y]^=z;
    }
    for (int i=0;i<n;i++) cnt[a[i]]++;
    for (int i=1;i<=maxj;i++) {
        res+=cnt[i]/2;
        cnt[i]%=2;
    }
    for (int i=1;i<=maxj;i++)
        if (cnt[i]!=0) {
            mask|=(1<<i);
            nn++;
        }
    for (int tt=0;tt<(1<<maxj);tt++) {
        int x=0;
        for (int i=0;i<maxj;i++)
            if (tt&(1<<i)) x^=i;
        good[tt] = (x==0);
    }
    for (int tt=0;tt<(1<<maxj);tt++) {
        if (tt&1) continue;
        int u=tt;
        while (u>0) {
            if (good[u]) dp[tt] = max(dp[tt],dp[tt^u] + 1);
            u = (u-1)&tt;
        }
    }
    cout<<res+nn-dp[mask];
}
```