Even Relation

We have a tree with N vertices numbered 1 to N. The i-th edge in the tree connects Vertex u_i and Vertex v_i, and its length is w_i. Your objective is to paint each vertex in the tree white or black (it is fine to paint all vertices the same color) so that the following condition is satisfied:

• For any two vertices painted in the same color, the distance between them is an even number.

Find a coloring of the vertices that satisfies the condition and print it. It can be proved that at least one such coloring exists under the constraints of this problem.

Constraints

• All values in input are integers.
• 1 \leq N \leq 10^5
• 1 \leq u_i < v_i \leq N
• 1 \leq w_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N u_1 v_1 w_1 u_2 v_2 w_2 . . . u_{N - 1} v_{N - 1} w_{N - 1}

Output

Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain 0 if Vertex i is painted white and 1 if it is painted black.

If there are multiple colorings that satisfy the condition, any of them will be accepted.

Examples

Input

3 1 2 2 2 3 1

Output

0 0 1

Input

5 2 5 2 2 3 10 1 3 8 3 4 2

Output

1 0 1 0 1

inputFormat

input are integers.

• 1 \leq N \leq 10^5
• 1 \leq u_i < v_i \leq N
• 1 \leq w_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N u_1 v_1 w_1 u_2 v_2 w_2 . . . u_{N - 1} v_{N - 1} w_{N - 1}

outputFormat

Output

Print a coloring of the vertices that satisfies the condition, in N lines. The i-th line should contain 0 if Vertex i is painted white and 1 if it is painted black.

If there are multiple colorings that satisfy the condition, any of them will be accepted.

Examples

Input

3 1 2 2 2 3 1

Output

0 0 1

Input

5 2 5 2 2 3 10 1 3 8 3 4 2

Output

1 0 1 0 1

样例

5
2 5 2
2 3 10
1 3 8
3 4 2

1
0
1
0
1

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