#include<bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < n; i++)
using namespace std;
int qmax(int a, int b){
	return (a > b) ? a : b;
}

int n;
int val[100100];
int cnt[20];
int res;
int target_mask;
bool good[33333];
int dp[33333];

int main(){
	scanf("%d", &n);
	rep(i, n-1){
		int a, b, c;
		scanf("%d %d %d", &a, &b, &c);
		a--, b--;
		val[a] ^= c;
		val[b] ^= c;
	}
	rep(i, n) if(val[i]) cnt[val[i]]++;
	res = 0;
	int bp = 0;
	rep(i, 16){
		res += (cnt[i] / 2);
		if(i){
			bp += (cnt[i] & 1);
			target_mask |= ((cnt[i] & 1) << (i-1));
		}
	}
	rep(mask, 1<<15){
		int XORsum = 0;
		rep(i, 15){
			int now = i+1;
			if(mask & (1 << i)) XORsum ^= now;
		}
		if(XORsum == 0) good[mask] = 1;
	}
	memset(dp, 0, sizeof(dp));
	rep(mask, 1<<15){
		int mask2 = mask;
		while(mask2 > 0){
			if(good[mask2]) dp[mask] = qmax(dp[mask], dp[mask ^ mask2] + 1);
			mask2 = (mask2 - 1) & mask;
		}
	}
	cout << res + bp - dp[target_mask] << endl;
	return 0;
}
### Prompt

Your task is to create 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<bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < n; i++)
using namespace std;
int qmax(int a, int b){
	return (a > b) ? a : b;
}

int n;
int val[100100];
int cnt[20];
int res;
int target_mask;
bool good[33333];
int dp[33333];

int main(){
	scanf("%d", &n);
	rep(i, n-1){
		int a, b, c;
		scanf("%d %d %d", &a, &b, &c);
		a--, b--;
		val[a] ^= c;
		val[b] ^= c;
	}
	rep(i, n) if(val[i]) cnt[val[i]]++;
	res = 0;
	int bp = 0;
	rep(i, 16){
		res += (cnt[i] / 2);
		if(i){
			bp += (cnt[i] & 1);
			target_mask |= ((cnt[i] & 1) << (i-1));
		}
	}
	rep(mask, 1<<15){
		int XORsum = 0;
		rep(i, 15){
			int now = i+1;
			if(mask & (1 << i)) XORsum ^= now;
		}
		if(XORsum == 0) good[mask] = 1;
	}
	memset(dp, 0, sizeof(dp));
	rep(mask, 1<<15){
		int mask2 = mask;
		while(mask2 > 0){
			if(good[mask2]) dp[mask] = qmax(dp[mask], dp[mask ^ mask2] + 1);
			mask2 = (mask2 - 1) & mask;
		}
	}
	cout << res + bp - dp[target_mask] << endl;
	return 0;
}
```