#include <cstdio>
#include <iostream>
using namespace std;
int read() {
	int w = 1,res = 0;
	char ch = getchar();
	while(ch < '0' || ch > '9') {
		if(ch == '-') w = -1;
		ch = getchar();
	}
	while(ch >= '0' && ch <= '9') res = res * 10 + ch - '0', ch = getchar();
	return w * res;
}
int w[200010], cnt[200010], res, st, d[66000], xr[66000], m = 1 << 15;
int main() {
	int n = read();
	for(int i = 1; i < n; i ++) {
		int u = read(), v = read(), val = read();
		w[u] = w[u] ^ val;
		w[v] = w[v] ^ val;
	}
	for(int i = 0; i < n; i ++) cnt[w[i]] ++;
	for(int i = 1; i <= 15; i ++) res += cnt[i] / 2, st = st | (cnt[i] & 1) << (i - 1);
	for(int i = 1; i < m; i ++) d[i] = d[i >> 1] + (i & 1);
	for(int i = 1; i < m; i ++) d[i] -= 1;
	for(int i = 1; i < m; i ++)
		for(int j = 0; j < 15; j ++) if((i >> j) & 1) xr[i] = xr[i] ^ (j + 1);
	for(int i = 1; i < m; i ++) {
		if(xr[i] != 0) continue;
		for(int j = (i - 1) & i; j; j = (j - 1) & i)
			if(xr[j] == 0) d[i] = min(d[i], d[j] + d[i ^ j]);
	}
	printf("%d", res + d[st]);
	return 0;
}
### Prompt

Create a solution in CPP for 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 <iostream>
using namespace std;
int read() {
	int w = 1,res = 0;
	char ch = getchar();
	while(ch < '0' || ch > '9') {
		if(ch == '-') w = -1;
		ch = getchar();
	}
	while(ch >= '0' && ch <= '9') res = res * 10 + ch - '0', ch = getchar();
	return w * res;
}
int w[200010], cnt[200010], res, st, d[66000], xr[66000], m = 1 << 15;
int main() {
	int n = read();
	for(int i = 1; i < n; i ++) {
		int u = read(), v = read(), val = read();
		w[u] = w[u] ^ val;
		w[v] = w[v] ^ val;
	}
	for(int i = 0; i < n; i ++) cnt[w[i]] ++;
	for(int i = 1; i <= 15; i ++) res += cnt[i] / 2, st = st | (cnt[i] & 1) << (i - 1);
	for(int i = 1; i < m; i ++) d[i] = d[i >> 1] + (i & 1);
	for(int i = 1; i < m; i ++) d[i] -= 1;
	for(int i = 1; i < m; i ++)
		for(int j = 0; j < 15; j ++) if((i >> j) & 1) xr[i] = xr[i] ^ (j + 1);
	for(int i = 1; i < m; i ++) {
		if(xr[i] != 0) continue;
		for(int j = (i - 1) & i; j; j = (j - 1) & i)
			if(xr[j] == 0) d[i] = min(d[i], d[j] + d[i ^ j]);
	}
	printf("%d", res + d[st]);
	return 0;
}
```