#include<bits/stdc++.h>

using namespace std ;

#define N 200007

int n , num[20] , val[N] ;
int C[N] , Cnt[N] ;

int main()
{
    scanf("%d" , &n ) ;
    for(int i = 1 ; i <= n - 1 ; i++ ){ int u , v , w ; scanf("%d%d%d" , &u , &v , &w ) ; val[u] ^= w , val[v] ^= w ;  }
    for(int i = 0 ; i <= n - 1 ; i++ ) num[val[i]]++ ;
    int ans = 0 , ed = 0 ;
    for(int i = 1 ; i < ( 1 << 15 ) ; i++ ){
        for(int j = 0 ; j < 15 ; j++ ) if( ( i >> j ) & 1 ) C[i] = C[i] ^ ( j + 1 ) ;
    }
    for(int i = 1 ; i <= 15 ; i++ ) ans += num[i] / 2 ;
    for(int i = 1 ; i <= 15 ; i++ ) if( num[i] & 1 ) ed |= ( 1 << ( i - 1 ) ) ;
    for(int i = 1 ; i < ( 1 << 15 ) ; i++ ) Cnt[i] = Cnt[i >> 1] + ( i & 1 ) ;
    for(int i = 1 ; i < ( 1 << 15 ) ; i++ ){
        Cnt[i]-- ;
        if( C[i] ) continue ;
        for(int k = ( i - 1 ) & i ; k ; k = ( k - 1 ) & i ){
            if( C[k] == 0 ) Cnt[i] = min( Cnt[i ^ k] + Cnt[k] , Cnt[i] ) ;
        }
    }
    printf("%d\n" , ans + Cnt[ed] ) ;
    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<bits/stdc++.h>

using namespace std ;

#define N 200007

int n , num[20] , val[N] ;
int C[N] , Cnt[N] ;

int main()
{
    scanf("%d" , &n ) ;
    for(int i = 1 ; i <= n - 1 ; i++ ){ int u , v , w ; scanf("%d%d%d" , &u , &v , &w ) ; val[u] ^= w , val[v] ^= w ;  }
    for(int i = 0 ; i <= n - 1 ; i++ ) num[val[i]]++ ;
    int ans = 0 , ed = 0 ;
    for(int i = 1 ; i < ( 1 << 15 ) ; i++ ){
        for(int j = 0 ; j < 15 ; j++ ) if( ( i >> j ) & 1 ) C[i] = C[i] ^ ( j + 1 ) ;
    }
    for(int i = 1 ; i <= 15 ; i++ ) ans += num[i] / 2 ;
    for(int i = 1 ; i <= 15 ; i++ ) if( num[i] & 1 ) ed |= ( 1 << ( i - 1 ) ) ;
    for(int i = 1 ; i < ( 1 << 15 ) ; i++ ) Cnt[i] = Cnt[i >> 1] + ( i & 1 ) ;
    for(int i = 1 ; i < ( 1 << 15 ) ; i++ ){
        Cnt[i]-- ;
        if( C[i] ) continue ;
        for(int k = ( i - 1 ) & i ; k ; k = ( k - 1 ) & i ){
            if( C[k] == 0 ) Cnt[i] = min( Cnt[i ^ k] + Cnt[k] , Cnt[i] ) ;
        }
    }
    printf("%d\n" , ans + Cnt[ed] ) ;
    return 0 ;
}
```