Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

3
1 2 2
2 3 1

Sample Output 1

0
0
1

Sample Input 2

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

Sample Output 2

1
0
1
0
1

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]
use std::cmp::{max, min};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

use nyan::*;

fn main() {
    let stdin = std::io::stdin();
    let mut sc = Scanner::new(stdin.lock());

    let n: usize = sc.read();

    let mut t = vec![Vec::new(); n];
    for _ in 0..n - 1 {
        let u: usize = sc.read();
        let v: usize = sc.read();
        let w: usize = sc.read();
        t[u - 1].push((v - 1, w));
        t[v - 1].push((u - 1, w));
    }

    let mut c = vec![-1; n];
    c[0] = 0;

    fn d(t: &[Vec<(usize, usize)>], c: &mut [i32], u: usize) {
        for &(v, w) in t[u].iter() {
            if c[v] != -1 {
                continue;
            }
            c[v] = match (c[u], w % 2) {
                (0, 0) => 0,
                (1, 0) => 1,
                (0, 1) => 1,
                (1, 1) => 0,
                _ => -1,
            };
            d(t, c, v);
        }
    }

    d(&t, &mut c, 0);

    // println!("{:#?}", c);

    for i in c.iter() {
        println!("{}", i);
    }
}

#[allow(dead_code)]
mod nyan {
    use std::cmp::Ordering;
    use std::fmt::{Debug, Display};
    use std::io;
    use std::iter::FromIterator;
    use std::str::FromStr;

    // https://doc.rust-lang.org/1.39.0/src/core/num/mod.rs.html#4473-4523
    #[inline]
    pub fn is_ascii_whitespace(c: char) -> bool {
        match c {
            '\t' | '\n' | '\x0C' | '\r' | ' ' => true,
            _ => false,
        }
    }

    #[inline]
    pub fn is_ascii_linebreak(c: char) -> bool {
        match c {
            '\n' | '\r' => true,
            _ => false,
        }
    }

    pub struct Scanner<R: io::BufRead> {
        reader: R,
        buffer: String,
        cursor: usize,
    }

    impl<R: io::BufRead> Scanner<R> {
        pub fn new(reader: R) -> Scanner<R> {
            Scanner {
                reader: reader,
                buffer: String::with_capacity(32),
                cursor: 0,
            }
        }

        fn next<F: Fn(char) -> bool>(&mut self, f: F) -> io::Result<&str> {
            loop {
                if let Some(l) = self.buffer[self.cursor..].find(|c| !is_ascii_whitespace(c)) {
                    self.cursor += l;
                    break;
                }

                self.buffer.clear();
                self.cursor = 0;
                match self.reader.read_line(&mut self.buffer) {
                    Err(e) => return Err(e),
                    Ok(0) => return Err(io::Error::from(io::ErrorKind::UnexpectedEof)),
                    _ => (),
                }
            }

            let start = self.cursor;
            self.cursor = self.buffer[self.cursor..]
                .find(f)
                .map_or(self.buffer.len(), |l| start + l);
            Ok(&self.buffer[start..self.cursor])
        }

        fn next_word(&mut self) -> io::Result<&str> {
            self.next(|c| is_ascii_whitespace(c))
        }

        fn next_line(&mut self) -> io::Result<&str> {
            self.next(|c| c == '\n' || c == '\r')
        }

        pub fn read<T>(&mut self) -> T
        where
            T: FromStr,
            <T as FromStr>::Err: Debug,
        {
            self.next_word().unwrap().parse().unwrap()
        }

        pub fn read_vec<T, U>(&mut self, n: usize) -> T
        where
            T: FromIterator<U>,
            U: FromStr,
            <U as FromStr>::Err: Debug,
        {
            (0..n).map(|_| self.read()).collect()
        }

        pub fn read_vec2d<T, U, V>(&mut self, m: usize, n: usize) -> T
        where
            T: FromIterator<U>,
            U: FromIterator<V>,
            V: FromStr,
            <V as FromStr>::Err: Debug,
        {
            (0..m).map(|_| self.read_vec(n)).collect()
        }

        pub fn read_line<T: FromIterator<char>>(&mut self) -> T {
            self.next_line().unwrap().chars().collect()
        }

        pub fn read_lines<T, U>(&mut self, n: usize) -> T
        where
            T: FromIterator<U>,
            U: FromIterator<char>,
        {
            (0..n).map(|_| self.read_line()).collect()
        }
    }

    #[test]
    fn test_scanner_next_word() {
        let buf = io::Cursor::new(b"hello world\nfoo\n\n\n\nbar\n");
        let mut r = Scanner::new(buf);

        assert_eq!(r.next_word().unwrap(), "hello");
        assert_eq!(r.next_word().unwrap(), "world");
        assert_eq!(r.next_word().unwrap(), "foo");
        assert_eq!(r.next_word().unwrap(), "bar");
        assert!(r.next_word().is_err());
        assert!(r.next_word().is_err());
    }

    #[test]
    fn test_scanner_next_line() {
        let buf = io::Cursor::new(b"hello world\nfoo\n\n\n\nbar\n");
        let mut r = Scanner::new(buf);

        assert_eq!(r.next_line().unwrap(), "hello world");
        assert_eq!(r.next_line().unwrap(), "foo");
        assert_eq!(r.next_line().unwrap(), "bar");
        assert!(r.next_line().is_err());
        assert!(r.next_line().is_err());
    }

    #[test]
    fn test_scanner_no_linebreak() {
        let buf = io::Cursor::new(b"hello world");
        let mut r = Scanner::new(buf);

        assert_eq!(r.next_word().unwrap(), "hello");
        assert_eq!(r.next_word().unwrap(), "world");
        assert!(r.next_word().is_err());
        assert!(r.next_word().is_err());
    }

    pub fn print_vec<T: Display>(v: &[T]) {
        if v.is_empty() {
            return;
        }

        print!("{}", v[0]);
        for i in v.iter().skip(1) {
            print!(" {}", i);
        }
        println!();
    }

    // C++ like binary search functions (upper_bound, lower_bound, equal_range)
    pub trait BinarySearch<T> {
        fn lower_bound(&self, value: &T) -> usize;
        fn upper_bound(&self, value: &T) -> usize;
        fn equal_range(&self, value: &T) -> (usize, usize) {
            (self.lower_bound(value), self.upper_bound(value))
        }
    }

    impl<T: Ord> BinarySearch<T> for [T] {
        // https://en.cppreference.com/w/cpp/algorithm/lower_bound#Possible_implementation
        fn lower_bound(&self, value: &T) -> usize {
            let mut first = 0;
            let mut last = self.len();
            while last != first {
                let mid = (first + last) / 2;
                match self[mid].cmp(value) {
                    Ordering::Less => first = mid + 1,
                    _ => last = mid,
                }
            }
            first
        }

        // https://en.cppreference.com/w/cpp/algorithm/upper_bound#Possible_implementation
        fn upper_bound(&self, value: &T) -> usize {
            let mut first = 0;
            let mut last = self.len();
            while last != first {
                let mid = (first + last) / 2;
                match self[mid].cmp(value) {
                    Ordering::Greater => last = mid,
                    _ => first = mid + 1,
                }
            }
            first
        }
    }

    #[test]
    pub fn test_binary_search() {
        let data = vec![1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6];
        assert_eq!(data.lower_bound(&4), 7);
        assert_eq!(data.upper_bound(&4), 10);
    }

    // https://doc.rust-lang.org/std/cmp/struct.Reverse.html
    #[derive(PartialEq, Eq, Debug)]
    pub struct Rev<T>(pub T);

    impl<T: PartialOrd> PartialOrd for Rev<T> {
        fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
            other.0.partial_cmp(&self.0)
        }
    }

    impl<T: Ord> Ord for Rev<T> {
        fn cmp(&self, other: &Self) -> Ordering {
            other.0.cmp(&self.0)
        }
    }

    // Extended Euclidean algorithm
    // ax + by = gcd(x, y)
    pub fn extended_gcd(a: u64, b: u64) -> (u64, i64, i64) {
        if b == 0 {
            (a, 1, 0)
        } else {
            let (m, y, x) = extended_gcd(b, a % b);
            (m, x, y - (a / b) as i64 * x)
        }
    }

    pub fn gcd(a: u64, b: u64) -> u64 {
        if b == 0 {
            a
        } else {
            gcd(b, a % b)
        }
    }

    pub fn lcm(a: u64, b: u64) -> u64 {
        (a * b) / gcd(a, b)
    }

    // x^n (mod p)
    pub fn pow_mod(mut x: u64, mut n: u64, p: u64) -> u64 {
        let mut r = 1;
        while n > 0 {
            if n & 1 > 0 {
                r *= x;
                r %= p;
            }
            x *= x;
            x %= p;
            n >>= 1;
        }
        r
    }

    #[test]
    fn test_pow_mod() {
        assert_eq!(pow_mod(4, 13, 497), 445);
        assert_eq!(pow_mod(2, 90, 13), 12);
        assert_eq!(pow_mod(2, 99999999, 147), 134);
    }

    // a^{p-1} = 1 (mod p) (Fermat's little theorem)
    // a^{p - 2} * a = 1 → a^{-1} = a^{p-2}
    pub fn inv_mod(n: u64, p: u64) -> u64 {
        pow_mod(n, p - 2, p)
    }

    // s * (s + 1) * .. * t (mod p)
    pub fn prod_mod(s: u64, t: u64, p: u64) -> u64 {
        (s..t + 1).fold(1, |acc, x| acc * x % p)
    }

    // nCk (mod p)
    pub fn comb_mod(n: u64, k: u64, p: u64) -> u64 {
        // nCk = n! / (k! * (n - k)!)
        //     = ((n-k+1) * (n-k+2) * ... * n) * inv(k!)
        prod_mod(n - k + 1, n, p) * inv_mod(prod_mod(1, k, p), p) % p
    }

    #[inline]
    pub fn minmax<T: Ord>(a: T, b: T) -> (T, T) {
        if a < b {
            (a, b)
        } else {
            (b, a)
        }
    }

    #[test]
    fn test_minmax() {
        assert_eq!(minmax(1, 3), (1, 3));
        assert_eq!(minmax(3, 1), (1, 3));
    }

    #[inline]
    pub fn digits(x: u64, base: u64) -> u32 {
        (1..)
            .find(|&i| base.pow(i - 1) <= x && x < base.pow(i))
            .unwrap_or(0)
    }

    #[test]
    fn test_digits() {
        assert_eq!(digits(1234, 10), 4);
        assert_eq!(digits(1234567890, 10), 10);
        assert_eq!(digits(0xdeadbeef, 16), 8);
        assert_eq!(digits(0o123456, 8), 6);
        assert_eq!(digits(0b10101, 2), 5);
    }

    pub struct UnionFind {
        n: usize,
        root: Vec<usize>,
        rank: Vec<usize>,
        size: Vec<usize>,
    }

    impl UnionFind {
        pub fn new(n: usize) -> UnionFind {
            UnionFind {
                n: n,
                root: (0..n).collect(),
                rank: vec![0; n],
                size: vec![1; n],
            }
        }

        pub fn root(&mut self, x: usize) -> usize {
            let r = self.root[x];
            if r == x {
                r
            } else {
                self.root[x] = self.root(r);
                self.root[x]
            }
        }

        pub fn merge(&mut self, x: usize, y: usize) {
            let rx = self.root(x);
            let ry = self.root(y);
            if rx == ry {
                return;
            }

            if self.rank[rx] < self.rank[ry] {
                self.root[rx] = ry;
                self.size[ry] += self.size[rx];
            } else {
                self.root[ry] = rx;
                self.size[rx] += self.size[ry];
                if self.rank[rx] == self.rank[ry] {
                    self.rank[rx] += 1;
                }
            }
        }

        pub fn size(&mut self, x: usize) -> usize {
            let rx = self.root(x);
            self.size[rx]
        }
    }
}