#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
using namespace std;
const int N = 205100;

template <typename T>
void read(T &x) {
    x = 0; char c = getchar();
    while (!isdigit(c)) c=getchar();
    for (;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+(c^48);
}

int x, y, n, res, st;
int d[N], sum[N], u[N], cnt[N];
inline int to(int x) {return 1 << x;}
int main() {
    read(n);
    for (int i = 1;i < n; i++) {
        int x, y, a; read(x), read(y), read(a);
        u[x] ^= a, u[y] ^= a;
    }
    for (int i = 0;i < n; i++) cnt[u[i]]++;
    int all = to(15);
    for (int i = 1;i < all; i++) d[i] = d[i>>1] + (i & 1);
    for (int i = 1;i < all; i++) d[i]--;
    for (int i = 1;i <= 15; i++) res += cnt[i] / 2, st |= (cnt[i] & 1) << (i-1);
    for (int i = 1;i < all; i++) 
        for (int j = 0;j < 15; j++) 
            if (i & to(j)) sum[i] ^= (j + 1);
    for (int i = 1;i < all; i++) {
        if (sum[i] != 0) continue;
        for (int j = (i - 1) & i; j; j = (j - 1) & i) 
            if (sum[j] == 0) d[i] = min(d[i], d[j] + d[i ^ j]);
    }
    cout << res + d[st] << endl;
    return 0;
}

### Prompt

Generate 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 <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
using namespace std;
const int N = 205100;

template <typename T>
void read(T &x) {
    x = 0; char c = getchar();
    while (!isdigit(c)) c=getchar();
    for (;isdigit(c);c=getchar()) x=(x<<3)+(x<<1)+(c^48);
}

int x, y, n, res, st;
int d[N], sum[N], u[N], cnt[N];
inline int to(int x) {return 1 << x;}
int main() {
    read(n);
    for (int i = 1;i < n; i++) {
        int x, y, a; read(x), read(y), read(a);
        u[x] ^= a, u[y] ^= a;
    }
    for (int i = 0;i < n; i++) cnt[u[i]]++;
    int all = to(15);
    for (int i = 1;i < all; i++) d[i] = d[i>>1] + (i & 1);
    for (int i = 1;i < all; i++) d[i]--;
    for (int i = 1;i <= 15; i++) res += cnt[i] / 2, st |= (cnt[i] & 1) << (i-1);
    for (int i = 1;i < all; i++) 
        for (int j = 0;j < 15; j++) 
            if (i & to(j)) sum[i] ^= (j + 1);
    for (int i = 1;i < all; i++) {
        if (sum[i] != 0) continue;
        for (int j = (i - 1) & i; j; j = (j - 1) & i) 
            if (sum[j] == 0) d[i] = min(d[i], d[j] + d[i ^ j]);
    }
    cout << res + d[st] << endl;
    return 0;
}

```