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:
import sys
sys.setrecursionlimit(100000)

N = int(input())
d = {}
e = [[] for _ in range(N)]
dd = [-1]*N
for _ in range(N-1):
    u, v, w = list(map(int, input().split()))
    e[u-1].append(v-1)
    e[v-1].append(u-1)
    d[(u-1,v-1)]= d[(v-1,u-1)] = w

def dfs(i, _d):
    dd[i] = _d
    for c in e[i]:
        if dd[c]!=-1: continue
        dfs(c, _d+d[(i,c)])

dfs(0,0)
for _dd in dd:
    print(_dd%2)