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

inputFormat

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}

outputFormat

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

样例

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

3