#include <bits/stdc++.h>

using namespace std;

const int maxn = 100010,inf = 0x7ffffff;
int n,du[maxn],tong[1 << 16],ans,limit,f[1 << 16];

int prework(int sta)
{
    if (sta == 0)
        return 0;
    int res = 0,cnt = 0;
    for (int i = 0; i <= 15; i++)
        if (sta >> i & 1)
        {
            res ^= i;
            cnt++;
        }
    if (res == 0)
        return cnt - 1;
    else
        return inf;
}

int main()
{
    scanf("%d",&n);
    for (int i = 1; i < n; i++)
    {
        int x,y,z;
        scanf("%d%d%d",&x,&y,&z);
        x++;
        y++;
        du[x] ^= z;
        du[y] ^= z;
    }
    for (int i = 1; i <= n; i++)
        tong[du[i]]++;
    for (int i = 1; i <= 15; i++)
    {
        ans += tong[i] / 2;
        tong[i] %= 2;
        limit |= (tong[i] << i);
    }
    for (int i = 0; i <= limit; i++)
        f[i] = prework(i);
    for (int i = 0; i <= limit; i++)
        for (int j = i;j;j = (j - 1) & i)
            f[i] = min(f[i],f[j] + f[i ^ j]);
    printf("%d\n",f[limit] + 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 <bits/stdc++.h>

using namespace std;

const int maxn = 100010,inf = 0x7ffffff;
int n,du[maxn],tong[1 << 16],ans,limit,f[1 << 16];

int prework(int sta)
{
    if (sta == 0)
        return 0;
    int res = 0,cnt = 0;
    for (int i = 0; i <= 15; i++)
        if (sta >> i & 1)
        {
            res ^= i;
            cnt++;
        }
    if (res == 0)
        return cnt - 1;
    else
        return inf;
}

int main()
{
    scanf("%d",&n);
    for (int i = 1; i < n; i++)
    {
        int x,y,z;
        scanf("%d%d%d",&x,&y,&z);
        x++;
        y++;
        du[x] ^= z;
        du[y] ^= z;
    }
    for (int i = 1; i <= n; i++)
        tong[du[i]]++;
    for (int i = 1; i <= 15; i++)
    {
        ans += tong[i] / 2;
        tong[i] %= 2;
        limit |= (tong[i] << i);
    }
    for (int i = 0; i <= limit; i++)
        f[i] = prework(i);
    for (int i = 0; i <= limit; i++)
        for (int j = i;j;j = (j - 1) & i)
            f[i] = min(f[i],f[j] + f[i ^ j]);
    printf("%d\n",f[limit] + ans);

    return 0;
}

```