#include <cstdio>
#include <algorithm>
#include <vector>
#define file(x) freopen(#x".in", "r", stdin), freopen(#x".out", "w", stdout)

const int maxn(2e5 + 10);
int n, val[maxn], f[maxn], cnt[20], ans, S, sum[maxn];

int main()
{
	scanf("%d", &n);
	for (int i = 1, a, b, c; i < n; i++)
		scanf("%d%d%d", &a, &b, &c), val[a] ^= c, val[b] ^= c;
	for (int i = 0; i < n; i++) ++cnt[val[i]];
	for (int i = 1; i <= 15; i++) ans += (cnt[i] >> 1), S |= (cnt[i] & 1) << (i - 1);
	for (int i = 1; i < (1 << 15); i++) f[i] = f[i >> 1] + (i & 1);
	for (int i = 1; i < (1 << 15); i++) --f[i];
	for (int i = 1; i < (1 << 15); i++)
		for (int j = 0; j < 15; j++) if (i & (1 << j)) sum[i] ^= (j + 1);
	for (int i = 1; i < (1 << 15); i++) if (!sum[i])
		for (int j = (i - 1) & i; j; j = (j - 1) & i)
			if (!sum[j]) f[i] = std::min(f[i], f[j] + f[i ^ j]);
	printf("%d\n", ans + f[S]);
	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 <cstdio>
#include <algorithm>
#include <vector>
#define file(x) freopen(#x".in", "r", stdin), freopen(#x".out", "w", stdout)

const int maxn(2e5 + 10);
int n, val[maxn], f[maxn], cnt[20], ans, S, sum[maxn];

int main()
{
	scanf("%d", &n);
	for (int i = 1, a, b, c; i < n; i++)
		scanf("%d%d%d", &a, &b, &c), val[a] ^= c, val[b] ^= c;
	for (int i = 0; i < n; i++) ++cnt[val[i]];
	for (int i = 1; i <= 15; i++) ans += (cnt[i] >> 1), S |= (cnt[i] & 1) << (i - 1);
	for (int i = 1; i < (1 << 15); i++) f[i] = f[i >> 1] + (i & 1);
	for (int i = 1; i < (1 << 15); i++) --f[i];
	for (int i = 1; i < (1 << 15); i++)
		for (int j = 0; j < 15; j++) if (i & (1 << j)) sum[i] ^= (j + 1);
	for (int i = 1; i < (1 << 15); i++) if (!sum[i])
		for (int j = (i - 1) & i; j; j = (j - 1) & i)
			if (!sum[j]) f[i] = std::min(f[i], f[j] + f[i ^ j]);
	printf("%d\n", ans + f[S]);
	return 0;
}

```