p03442 AtCoder Petrozavodsk Contest 001 - XOR Tree
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
```python
from collections import Counter
from functools import reduce
from itertools import combinations
from operator import xor

n = int(input())
nodes = [0] * n
for _ in range(n - 1):
    x, y, a = map(int, input().split())
    nodes[x] ^= a
    nodes[y] ^= a

c = Counter(nodes)
ans = 0
remains = set()
for i, v in c.items():
    if i == 0:
        continue
    ans += v // 2
    if v % 2:
        remains.add(i)

for r in (3, 4, 5):
    while True:
        for ns in combinations(remains, r):
            if reduce(xor, ns) == 0:
                remains.difference_update(ns)
                ans += r - 1
                break
        else:
            break
print(ans)

```