#include <algorithm>
#include <iostream>
#include <vector>

bool test(const int x, const int y) { return x & 1 << y; }

int main() {
  int n;
  std::cin >> n;
  std::vector<int> v(n, 0);
  for (int i = 0; i != n - 1; i += 1) {
    int x, y, a;
    std::cin >> x >> y >> a;
    v[x] ^= a;
    v[y] ^= a;
  }
  int ans = n;
  int b = 0;
  for (const int e : v) {
    if (e == 0) {
      ans -= 1;
      continue;
    }
    if (test(b, e))
      ans -= 1;
    b ^= 1 << e;
  }
  std::vector<int> dp(b + 1, -1);
  dp[b] = 0;
  for (int s = b; s != 0; s -= 1) {
    if (dp[s] == -1)
      continue;
    int i = 16;
    while (i != 0) {
      i -= 1;
      if (test(s, i))
        break;
    }
    for (int j = 0; j != i; j += 1) {
      if (!test(s, j))
        continue;
      const int k = i ^ j;
      if (k > j)
        continue;
      int &d = dp[s ^ 1 << i ^ 1 << j ^ 1 << k];
      if (test(s, k))
        d = std::max(d, dp[s] + 1);
      else
        d = std::max(d, dp[s]);
    }
  }
  std::cout << ans - dp[0] << std::endl;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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 <algorithm>
#include <iostream>
#include <vector>

bool test(const int x, const int y) { return x & 1 << y; }

int main() {
  int n;
  std::cin >> n;
  std::vector<int> v(n, 0);
  for (int i = 0; i != n - 1; i += 1) {
    int x, y, a;
    std::cin >> x >> y >> a;
    v[x] ^= a;
    v[y] ^= a;
  }
  int ans = n;
  int b = 0;
  for (const int e : v) {
    if (e == 0) {
      ans -= 1;
      continue;
    }
    if (test(b, e))
      ans -= 1;
    b ^= 1 << e;
  }
  std::vector<int> dp(b + 1, -1);
  dp[b] = 0;
  for (int s = b; s != 0; s -= 1) {
    if (dp[s] == -1)
      continue;
    int i = 16;
    while (i != 0) {
      i -= 1;
      if (test(s, i))
        break;
    }
    for (int j = 0; j != i; j += 1) {
      if (!test(s, j))
        continue;
      const int k = i ^ j;
      if (k > j)
        continue;
      int &d = dp[s ^ 1 << i ^ 1 << j ^ 1 << k];
      if (test(s, k))
        d = std::max(d, dp[s] + 1);
      else
        d = std::max(d, dp[s]);
    }
  }
  std::cout << ans - dp[0] << std::endl;
}
```