Problem:
Score : 1000 points

Problem Statement

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.

Sample Input 1

5
0 1 1
0 2 3
0 3 6
3 4 4

Sample Output 1

3

The objective can be achieved in three operations, as follows:

First, choose the path connecting Vertex 1, 2, and x = 1.

Then, choose the path connecting Vertex 2, 3, and x = 2.

Lastly, choose the path connecting Vertex 0, 4, and x = 4.

Sample Input 2

2
1 0 0

Sample Output 2

0

Solution in Python (3.4.3) (judge verdict: Runtime Error)

N = int(input())
B = [0]*N
for i in range(N-1):
    x, y, a = map(int, input().split())
    B[x] ^= a
    B[y] ^= a
D = {}
for b in B:
    D[b] = D.get(b, 0) + 1
D[0] = 0
ans = 0
first = 0
for b in D:
    ans += D[b]//2
    if D[b]%2:
        first |= 1 << b

A = [0]*(1 << 15)
for i in range(1, 1<<15):
    bit = i & -i
    l = len(bin(bit))-3
    A[i] = A[i ^ bit] ^ l

memo = {0: 0}
def dfs(state):
    if state in memo:
        return memo[state]
    cur = state
    res = 10**9+7
    while cur:
        if A[cur] == 0:
            res = min(res, dfs(state ^ cur) + bin(cur).count('1')-1)
        cur -= 1
        cur &= state
    memo[state] = res
    return res
ans += dfs(first)
print(ans)