#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cstring>

const int maxn = 1e5 + 20;
const int maxs = (1 << 16) + 7;

int n;
int val[maxn], cnt[16], ans;
int dp[maxs];

template<class TAT>void checkmin(TAT &x,const TAT &y)
{
	if(y < x) x = y;
}
int dfs(int x)
{
	if(dp[x] != -1) return dp[x];
	
	dp[x] = maxs;
	
	for(int i = 0; i < 16; i++)
		for(int j = 0; j < 16; j++)
			if(i != j && ((x >> i) & 1) && ((x >> j) & 1))
			{
				int tmp = x ^ (1 << i) ^ (1 << j);
				int modify = i ^ j;
				
				checkmin(dp[x], dfs(tmp ^ (1 << modify)) + 1 + ((tmp >> modify) & 1));
			}
	
	return dp[x];
}
int main()
{
	scanf("%d", &n);
	for(int i = 1, x, y, a; i < n; i++)
	{
		scanf("%d%d%d", &x, &y, &a);
		++x, ++y;
		val[x] ^= a, val[y] ^= a;
	}
	
	for(int i = 1; i <= n; i++)
	{
		if(val[i])
		{
			ans += cnt[val[i]];
			cnt[val[i]] ^= 1;
		}
	}
	
	int now = 0;
	
	for(int i = 0; i < 16; i++) now |= (1 << i) * cnt[i];
	
	memset(dp, -1, sizeof(dp));
	dp[0] = 0;
	ans += dfs(now);
	
	printf("%d\n", ans);
	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 <cstdlib>
#include <algorithm>
#include <cstring>

const int maxn = 1e5 + 20;
const int maxs = (1 << 16) + 7;

int n;
int val[maxn], cnt[16], ans;
int dp[maxs];

template<class TAT>void checkmin(TAT &x,const TAT &y)
{
	if(y < x) x = y;
}
int dfs(int x)
{
	if(dp[x] != -1) return dp[x];
	
	dp[x] = maxs;
	
	for(int i = 0; i < 16; i++)
		for(int j = 0; j < 16; j++)
			if(i != j && ((x >> i) & 1) && ((x >> j) & 1))
			{
				int tmp = x ^ (1 << i) ^ (1 << j);
				int modify = i ^ j;
				
				checkmin(dp[x], dfs(tmp ^ (1 << modify)) + 1 + ((tmp >> modify) & 1));
			}
	
	return dp[x];
}
int main()
{
	scanf("%d", &n);
	for(int i = 1, x, y, a; i < n; i++)
	{
		scanf("%d%d%d", &x, &y, &a);
		++x, ++y;
		val[x] ^= a, val[y] ^= a;
	}
	
	for(int i = 1; i <= n; i++)
	{
		if(val[i])
		{
			ans += cnt[val[i]];
			cnt[val[i]] ^= 1;
		}
	}
	
	int now = 0;
	
	for(int i = 0; i < 16; i++) now |= (1 << i) * cnt[i];
	
	memset(dp, -1, sizeof(dp));
	dp[0] = 0;
	ans += dfs(now);
	
	printf("%d\n", ans);
	return 0;
}
```