#include <cstdio>
#include <cctype>
#include <algorithm>

const int N = 1e5 + 7;

inline int read() {
	char ch = getchar(); int r = 0, w = 1;
	while(!isdigit(ch)) {if(ch == '-') w = -1; ch = getchar();}
	while(isdigit(ch)) {r = r * 10 + ch - '0', ch = getchar();}
	return r * w;
}

int n;
int tot, w[N], cnt[32], p[20], dp[1 << 16], ans;

inline int calc(int x) {
	int now = 0, res = 0, sz = 0;
	while(x) {
		if(x & 1) res ^= p[now], sz++;
		x >>= 1;
		now++;
	}
	return res ? sz : sz - 1;
}

int main() {
	n = read();
	for(register int i = 1; i < n; i++) {
		int x = read() + 1, y = read() + 1, z = read();
		w[x] ^= z, w[y] ^= z;
	}
	for(register int i = 1; i <= n; i++)
		cnt[w[i]]++;
	for(register int i = 1; i <= 31; i++) {
		ans += cnt[i] / 2;
		if(cnt[i] & 1)
			p[tot++] = i;
	}
	for(register int S = 1; S < 1 << tot; S++) {
		dp[S] = calc(S);
		for(register int T = S; T; T = (T - 1) & S) {
			dp[S] = std::min(dp[S], dp[T] + dp[S ^ T]);
		}
	}
	if(tot) printf("%d\n", ans + dp[(1 << (tot - 1)) - 1]);
	else printf("%d\n", ans);
	return 0;
}
### Prompt

Generate 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 <cctype>
#include <algorithm>

const int N = 1e5 + 7;

inline int read() {
	char ch = getchar(); int r = 0, w = 1;
	while(!isdigit(ch)) {if(ch == '-') w = -1; ch = getchar();}
	while(isdigit(ch)) {r = r * 10 + ch - '0', ch = getchar();}
	return r * w;
}

int n;
int tot, w[N], cnt[32], p[20], dp[1 << 16], ans;

inline int calc(int x) {
	int now = 0, res = 0, sz = 0;
	while(x) {
		if(x & 1) res ^= p[now], sz++;
		x >>= 1;
		now++;
	}
	return res ? sz : sz - 1;
}

int main() {
	n = read();
	for(register int i = 1; i < n; i++) {
		int x = read() + 1, y = read() + 1, z = read();
		w[x] ^= z, w[y] ^= z;
	}
	for(register int i = 1; i <= n; i++)
		cnt[w[i]]++;
	for(register int i = 1; i <= 31; i++) {
		ans += cnt[i] / 2;
		if(cnt[i] & 1)
			p[tot++] = i;
	}
	for(register int S = 1; S < 1 << tot; S++) {
		dp[S] = calc(S);
		for(register int T = S; T; T = (T - 1) & S) {
			dp[S] = std::min(dp[S], dp[T] + dp[S ^ T]);
		}
	}
	if(tot) printf("%d\n", ans + dp[(1 << (tot - 1)) - 1]);
	else printf("%d\n", ans);
	return 0;
}
```