Problem: 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

Solution (in PYTHON3):

Solution:
from collections import deque

n = int(input())
g = tuple(set() for _ in range(n))
for _ in range(n - 1):
    u, v, w = map(int, input().split())
    u -= 1
    v -= 1
    g[u].add((v, w))
    g[v].add((u, w))

d = [-1] * n
d[0] = 0

q = deque()
q.append(0)

while q:
    v = q.popleft()
    for u, w in g[v]:
        if d[u] != -1:
            continue
        d[u] = (d[v] + w) % 2
        q.append(u)

print(*d, sep='\n')