Problem:
Height of a Tree

Given a tree T with non-negative weight, find the height of each node of the tree. For each node, the height is the distance to the most distant leaf from the node.

Input

n
s1 t1 w1
s2 t2 w2
:
sn-1 tn-1 wn-1

The first line consists of an integer n which represents the number of nodes in the tree. Every node has a unique ID from 0 to n-1 respectively.

In the following n-1 lines, edges of the tree are given.

si and ti represent end-points of the i-th edge (undirected) and wi represents the weight (distance) of the i-th edge.

Output

The output consists of n lines. Print the height of each node 0, 1, 2, ..., n-1 in order.

Constraints

1 ≤ n ≤ 10,000

0 ≤ wi ≤ 1,000

Sample Input 1

4
0 1 2
1 2 1
1 3 3

Sample Output 1

5
3
4
5

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using SB = System.Text.StringBuilder;
//using System.Threading.Tasks;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
using System.Numerics;
using static System.Math;
using pair = Pair<int, int>;
 
class Program
{
    static void Main()
    {
        SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    readonly Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    readonly int dom = 998244353;
    bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (b.CompareTo(a) < 0) { a = b; return true; } return false; }
 
    void solve()
    {
        int N = cin.nextint;
        var T = new WeightedTree();
        var G = T.Input(N, 0);
        long[] A, B, C;
        var p = T.BFS(G, 0, out A);
        var q = T.BFS(G, p, out B);
        T.BFS(G, q, out C);
        for (int i = 0; i < N; i++)
        {
            WriteLine(Max(B[i], C[i]));
        }
 
    }
}
 
class WeightedTree
{
    public List<Edge>[] Input(int n, int indexed = 1)
    {
        Scanner cin = new Scanner();
        var ret = new List<Edge>[n];
        for (int i = 0; i < ret.Length; i++) ret[i] = new List<Edge>();
        for (int i = 0; i < n - 1; i++)
        {
            int a = cin.nextint - indexed;
            int b = cin.nextint - indexed;
            var c = cin.nextlong;
            ret[a].Add(new Edge(a, b, c));
            ret[b].Add(new Edge(b, a, c));
        }
        return ret;
    }
    public int BFS(List<Edge>[] T, int s, out long[] dist, IEnumerable<int> multi = null)
    {
        int n = T.Length;
        dist = new long[n];
        for (int i = 0; i < dist.Length; i++) dist[i] = -1;
 
        var Q = new Queue<int>();
        if (multi == null) { Q.Enqueue(s); dist[s] = 0; }
        else foreach (var v in multi) { Q.Enqueue(v); dist[v] = 0; }
 
        while (Q.Count > 0)
        {
            var u = Q.Dequeue();
            foreach (var v in T[u])
            {
                if (dist[v.to] >= 0) continue;
                dist[v.to] = dist[u] + v.cost;
                Q.Enqueue(v.to);
            }
        }
        int far = s;
        long max = long.MinValue;
        for (int i = 0; i < dist.Length; i++)
        {
            if (max < dist[i])
            {
                max = dist[i];
                far = i;
            }
        }
        return far;
    }
    public long Diameter(List<Edge>[] T)
    {
        long[] dist;
        var far = BFS(T, BFS(T, 0, out dist), out dist);
        return dist[far];
    }
}
 
class Edge : IComparable<Edge>
{
    public int from, to, id; public long cost;
    public Edge(int from, int to, long cost, int id = -1)
    {
        this.from = from;
        this.to = to;
        this.cost = cost;
        this.id = id;
    }
    public int CompareTo(Edge e) => cost.CompareTo(e.cost);
    public override string ToString() => $"{from} {to} {cost}";
}
 
static class Ex
{
    public static void join<T>(this IEnumerable<T> values, string sep = " ") => WriteLine(string.Join(sep, values));
    public static string concat<T>(this IEnumerable<T> values) => string.Concat(values);
    public static string reverse(this string s) { var t = s.ToCharArray(); Array.Reverse(t); return t.concat(); }
 
    public static int lower_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) < 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
    public static int upper_bound<T>(this IList<T> arr, T val) where T : IComparable<T>
    {
        int low = 0, high = arr.Count;
        int mid;
        while (low < high)
        {
            mid = ((high - low) >> 1) + low;
            if (arr[mid].CompareTo(val) <= 0) low = mid + 1;
            else high = mid;
        }
        return low;
    }
}
 
class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f; public U s;
    public Pair(T f, U s) { this.f = f; this.s = s; }
    public int CompareTo(Pair<T, U> a) => f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    public override string ToString() => $"{f} {s}";
}
 
class Scanner
{
    string[] s; int i;
    readonly char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan => ReadLine().Split();
    public int[] scanint => Array.ConvertAll(scan, int.Parse);
    public long[] scanlong => Array.ConvertAll(scan, long.Parse);
    public double[] scandouble => Array.ConvertAll(scan, double.Parse);
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint => int.Parse(next);
    public long nextlong => long.Parse(next);
    public double nextdouble => double.Parse(next);
}