#include<bits/stdc++.h>
using namespace std ;
#define rep( i, s, t ) for( register int i = s; i <= t; ++ i )
#define re register
#define D(i) ( 1 << (i) )
int gi() {
	char cc = getchar() ; int cn = 0, flus = 1 ;
	while( cc < '0' || cc > '9' ) {  if( cc == '-' ) flus = - flus ; cc = getchar() ; }
	while( cc >= '0' && cc <= '9' )  cn = cn * 10 + cc - '0', cc = getchar() ;
	return cn * flus ;
}
const int N = 1e5 + 5 ;
const int M = 16 ;
int n, ans, w[N], cnt[M], dp[1 << M], R[1 << M] ;
signed main()
{
	n = gi() ; int x, y, z, Sta ; 
	rep( i, 2, n ) x = gi() + 1,  y = gi() + 1, 
	z = gi(), w[x] ^= z, w[y] ^= z ; 
	rep( i, 1, n ) ++ cnt[w[i]] ;
	rep( i, 1, 15 ) ans += cnt[i] / 2, Sta |= ( ( cnt[i] & 1 ) << ( i - 1 ) ) ;
	int maxm = ( 1 << 15 ) - 1 ;
	rep( i, 1, maxm ) {
		rep( j, 1, 15 ) if( D(j - 1) & i ) R[i] ^= j, ++ dp[i] ;
		-- dp[i] ;
	}
	rep( i, 1, maxm ) {
		if( R[i] != 0 ) continue ;
		for( re int j = i; j; j = ( j - 1 ) & i )
		if( R[j] == 0 ) dp[i] = min( dp[i], dp[j] + dp[i ^ j] ) ;
	}
	printf("%d\n", ans + dp[Sta] ) ;
	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 ;
#define rep( i, s, t ) for( register int i = s; i <= t; ++ i )
#define re register
#define D(i) ( 1 << (i) )
int gi() {
	char cc = getchar() ; int cn = 0, flus = 1 ;
	while( cc < '0' || cc > '9' ) {  if( cc == '-' ) flus = - flus ; cc = getchar() ; }
	while( cc >= '0' && cc <= '9' )  cn = cn * 10 + cc - '0', cc = getchar() ;
	return cn * flus ;
}
const int N = 1e5 + 5 ;
const int M = 16 ;
int n, ans, w[N], cnt[M], dp[1 << M], R[1 << M] ;
signed main()
{
	n = gi() ; int x, y, z, Sta ; 
	rep( i, 2, n ) x = gi() + 1,  y = gi() + 1, 
	z = gi(), w[x] ^= z, w[y] ^= z ; 
	rep( i, 1, n ) ++ cnt[w[i]] ;
	rep( i, 1, 15 ) ans += cnt[i] / 2, Sta |= ( ( cnt[i] & 1 ) << ( i - 1 ) ) ;
	int maxm = ( 1 << 15 ) - 1 ;
	rep( i, 1, maxm ) {
		rep( j, 1, 15 ) if( D(j - 1) & i ) R[i] ^= j, ++ dp[i] ;
		-- dp[i] ;
	}
	rep( i, 1, maxm ) {
		if( R[i] != 0 ) continue ;
		for( re int j = i; j; j = ( j - 1 ) & i )
		if( R[j] == 0 ) dp[i] = min( dp[i], dp[j] + dp[i ^ j] ) ;
	}
	printf("%d\n", ans + dp[Sta] ) ;
	return 0 ;
}

```