#include "bits/stdc++.h"
using namespace std;
const long long mod = 1000000007;
const int maxn = 100100;
int deg[maxn], cnt[16];
int dp[1<<16], xo[1<<16];
int main(){
    int n;
    cin >> n;
    for(int e = 0; e < n - 1; e++){
        int u, v, w;
        cin >> u >> v >> w;
        deg[u] ^= w;
        deg[v] ^= w;
    }
    for(int e = 0; e < n; e++){
        cnt[deg[e]]++;
    }
    int ans = cnt[0];
    for(int e = 1; e < 16; e++){
        ans += cnt[e] / 2;
        cnt[e] %= 2;
    }
    for(int e = 1; e < 1<<16; e++){
        xo[e] = 0;
        for(int f = 0; f < 16; f++)
            if(e & (1<<f)) xo[e] ^= f;
    }
    dp[0] = 0;
    for(int e = 1; e < 1<<16; e++){
        for(int f = e; f > 0; f = (f - 1) & e){
            if(xo[f] == 0) dp[e] = max(dp[e], dp[f] + 1);
        }
    }
    int msk = 0;
    for(int e = 1; e < 16; e++)
        if(cnt[e]) msk |= (1<<e);
    ans += dp[msk];
    cout << n - ans << endl;
	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 "bits/stdc++.h"
using namespace std;
const long long mod = 1000000007;
const int maxn = 100100;
int deg[maxn], cnt[16];
int dp[1<<16], xo[1<<16];
int main(){
    int n;
    cin >> n;
    for(int e = 0; e < n - 1; e++){
        int u, v, w;
        cin >> u >> v >> w;
        deg[u] ^= w;
        deg[v] ^= w;
    }
    for(int e = 0; e < n; e++){
        cnt[deg[e]]++;
    }
    int ans = cnt[0];
    for(int e = 1; e < 16; e++){
        ans += cnt[e] / 2;
        cnt[e] %= 2;
    }
    for(int e = 1; e < 1<<16; e++){
        xo[e] = 0;
        for(int f = 0; f < 16; f++)
            if(e & (1<<f)) xo[e] ^= f;
    }
    dp[0] = 0;
    for(int e = 1; e < 1<<16; e++){
        for(int f = e; f > 0; f = (f - 1) & e){
            if(xo[f] == 0) dp[e] = max(dp[e], dp[f] + 1);
        }
    }
    int msk = 0;
    for(int e = 1; e < 16; e++)
        if(cnt[e]) msk |= (1<<e);
    ans += dp[msk];
    cout << n - ans << endl;
	return 0;
}

```