#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int MAXS = 1 << 16;
const int MAXN = 1e5 + 5;
int dp[MAXS] , n , S , a[MAXN];
int DP(int now) {
	if(now == 0) return 0;
	if(dp[now] != -1) return dp[now];
	dp[now] = 1e9;
	for (int i = 0; i < 15; ++i) {
		if(!(now & (1 << i))) continue;
		for (int j = i + 1; j < 15; ++j) {
			if(!(now & (1 << j))) continue;
			int nnow = now ^ (1 << i) ^ (1 << j) ^ (1 << (((i+1) ^ (j+1)) - 1));
			int f;
			if(((now ^ (1 << i) ^ (1 << j)) & (1 << (((i+1) ^ (j+1)) - 1)))) f = 1;
			else f = 0;
			dp[now] = min(dp[now] , DP(nnow) + 1 + f);
		}
	}
	return dp[now];	
}
int main() {
	scanf("%d" , &n);
	for (int i = 1; i < n; ++i) {
		int u , v , w;
		scanf("%d %d %d" , &u , &v , &w);
		a[u] ^= w;
		a[v] ^= w;
	}
	int ans = 0;
	for (int i = 0; i < n; ++i) {
		if(!a[i]) continue;
		if(S & (1 << (a[i] - 1))) ans ++;
		S ^= (1 << (a[i] - 1));
	} 
	memset(dp , -1 , sizeof dp);
	dp[0] = 0;
	ans += DP(S);
	printf("%d" , ans);
	return 0;
}
### Prompt

In Cpp, your task is to solve 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 <cstring>
#include <algorithm>
using namespace std;
const int MAXS = 1 << 16;
const int MAXN = 1e5 + 5;
int dp[MAXS] , n , S , a[MAXN];
int DP(int now) {
	if(now == 0) return 0;
	if(dp[now] != -1) return dp[now];
	dp[now] = 1e9;
	for (int i = 0; i < 15; ++i) {
		if(!(now & (1 << i))) continue;
		for (int j = i + 1; j < 15; ++j) {
			if(!(now & (1 << j))) continue;
			int nnow = now ^ (1 << i) ^ (1 << j) ^ (1 << (((i+1) ^ (j+1)) - 1));
			int f;
			if(((now ^ (1 << i) ^ (1 << j)) & (1 << (((i+1) ^ (j+1)) - 1)))) f = 1;
			else f = 0;
			dp[now] = min(dp[now] , DP(nnow) + 1 + f);
		}
	}
	return dp[now];	
}
int main() {
	scanf("%d" , &n);
	for (int i = 1; i < n; ++i) {
		int u , v , w;
		scanf("%d %d %d" , &u , &v , &w);
		a[u] ^= w;
		a[v] ^= w;
	}
	int ans = 0;
	for (int i = 0; i < n; ++i) {
		if(!a[i]) continue;
		if(S & (1 << (a[i] - 1))) ans ++;
		S ^= (1 << (a[i] - 1));
	} 
	memset(dp , -1 , sizeof dp);
	dp[0] = 0;
	ans += DP(S);
	printf("%d" , ans);
	return 0;
}
```