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*
n,*t=map(int,open(0).read().split())
e=[[]for _ in range(n)]
for v,w,c in zip(t[::3],t[1::3],t[2::3]):
  e[v-1].append((w-1,c))
  e[w-1].append((v-1,c))
q=deque([(0,0)])
f=[0]+[-1]*~-n
while q:
  v,c=q.pop()
  for w,d in e[v]:
    if-1<f[w]:continue
    d=(c+d)%2
    f[w]=d
    q.append((w,d))
print(*f,sep='\n')