#include <cstdio>
#include <algorithm>
#include <cstring>
#include <vector>

typedef long long ll;
const int N = 1e5 + 9;

int n, a[N], t[N];
ll f[N << 2], INF;

void addmin(ll &x, ll y) {
	x = std::min(x, y);
}

ll dfs(int st) {
	if (st == 0) return 0;
	if (f[st] != INF) return f[st];
	for (int i = 0; i < 16; ++i) if ((st >> i) & 1)
		for (int j = 0; j < 16; ++j) if (((st >> j) & 1) && i != j) {
			int st_ = st ^ (1 << (i ^ j)) ^ (1 << i) ^ (1 << j);
			if (st >> (i ^ j) & 1)
				addmin(f[st], dfs(st_) + 2);
			else
				addmin(f[st], dfs(st_) + 1);
		}
	return f[st];
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i < n; ++i) {
		int u, v, w;
		scanf("%d %d %d", &u, &v, &w);
		++u, ++v;
		a[u] ^= w, a[v] ^= w;
	}
	ll ans = 0;
	int st = 0;
	for (int i = 1; i <= n; ++i) t[a[i]]++;
	for (int i = 1; i < 16; ++i) {
		ans += t[i] / 2;
		st |= (1 << i) * (t[i] & 1);
	}
//	printf("%d\n", st);
	memset(f, 0x3f, sizeof f);
	INF = f[0];
	f[0] = 0;
	printf("%lld\n", dfs(st) + ans);
	return 0;
}
### 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 <algorithm>
#include <cstring>
#include <vector>

typedef long long ll;
const int N = 1e5 + 9;

int n, a[N], t[N];
ll f[N << 2], INF;

void addmin(ll &x, ll y) {
	x = std::min(x, y);
}

ll dfs(int st) {
	if (st == 0) return 0;
	if (f[st] != INF) return f[st];
	for (int i = 0; i < 16; ++i) if ((st >> i) & 1)
		for (int j = 0; j < 16; ++j) if (((st >> j) & 1) && i != j) {
			int st_ = st ^ (1 << (i ^ j)) ^ (1 << i) ^ (1 << j);
			if (st >> (i ^ j) & 1)
				addmin(f[st], dfs(st_) + 2);
			else
				addmin(f[st], dfs(st_) + 1);
		}
	return f[st];
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i < n; ++i) {
		int u, v, w;
		scanf("%d %d %d", &u, &v, &w);
		++u, ++v;
		a[u] ^= w, a[v] ^= w;
	}
	ll ans = 0;
	int st = 0;
	for (int i = 1; i <= n; ++i) t[a[i]]++;
	for (int i = 1; i < 16; ++i) {
		ans += t[i] / 2;
		st |= (1 << i) * (t[i] & 1);
	}
//	printf("%d\n", st);
	memset(f, 0x3f, sizeof f);
	INF = f[0];
	f[0] = 0;
	printf("%lld\n", dfs(st) + ans);
	return 0;
}
```