#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;

const int N = 200010;

int n, res, m;
int w[N], d[N], cnt[20], sxr[N];

int main()
{
    scanf("%d", &n);

    for (int i = 1; i < n; i++) 
    {
        int a, b, c;
        scanf("%d%d%d", &a, &b, &c); 
        w[a] ^= c;
        w[b] ^= c; 
    }

    for (int i = 0; i < n; i++)  cnt[w[i]]++; 

    for (int i = 1; i <= 15; i++)
    {
        res += cnt[i] / 2;
        m |= (cnt[i] & 1) << (i - 1);
    }

    for (int i = 1; i < (1 << 15); i++) d[i] = d[i >> 1] + (i & 1);
    for (int i = 1; i < (1 << 15); i++) d[i] -= 1;
    for (int i = 1; i < (1 << 15); i++)
    {
        for (int j = 0; j < 15; j++)
        {
            if ((i >> j) & 1)sxr[i] ^= (j + 1);
        }
    }
    
    for (int i = 1; i < (1 << 15); i++)
    {
        if (sxr[i] != 0)continue;
        for (int k = (i - 1) & i; k; k = (k - 1) & i)
        {
            if (sxr[k] == 0)d[i] = min(d[i], d[k] + d[i ^ k]);
        }
    }

    printf("%d", res + d[m]);
}
### 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<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;

const int N = 200010;

int n, res, m;
int w[N], d[N], cnt[20], sxr[N];

int main()
{
    scanf("%d", &n);

    for (int i = 1; i < n; i++) 
    {
        int a, b, c;
        scanf("%d%d%d", &a, &b, &c); 
        w[a] ^= c;
        w[b] ^= c; 
    }

    for (int i = 0; i < n; i++)  cnt[w[i]]++; 

    for (int i = 1; i <= 15; i++)
    {
        res += cnt[i] / 2;
        m |= (cnt[i] & 1) << (i - 1);
    }

    for (int i = 1; i < (1 << 15); i++) d[i] = d[i >> 1] + (i & 1);
    for (int i = 1; i < (1 << 15); i++) d[i] -= 1;
    for (int i = 1; i < (1 << 15); i++)
    {
        for (int j = 0; j < 15; j++)
        {
            if ((i >> j) & 1)sxr[i] ^= (j + 1);
        }
    }
    
    for (int i = 1; i < (1 << 15); i++)
    {
        if (sxr[i] != 0)continue;
        for (int k = (i - 1) & i; k; k = (k - 1) & i)
        {
            if (sxr[k] == 0)d[i] = min(d[i], d[k] + d[i ^ k]);
        }
    }

    printf("%d", res + d[m]);
}
```