Problem:
Score : 800 points

Problem Statement

Snuke Festival 2017 will be held in a tree with N vertices numbered 1,2, ...,N.
The i-th edge connects Vertex a_i and b_i, and has joyfulness c_i.

The staff is Snuke and N-1 black cats.
Snuke will set up the headquarters in some vertex, and from there he will deploy a cat to each of the other N-1 vertices.

For each vertex, calculate the niceness when the headquarters are set up in that vertex.
The niceness when the headquarters are set up in Vertex i is calculated as follows:

Let X=0.

For each integer j between 1 and N (inclusive) except i, do the following:

Add c to X, where c is the smallest joyfulness of an edge on the path from Vertex i to Vertex j.

The niceness is the final value of X.

Constraints

1 \leq N \leq 10^{5}

1 \leq a_i,b_i \leq N

1 \leq c_i \leq 10^{9}

The given graph is a tree.

All input values are integers.

Partial Scores

In the test set worth 200 points, N \leq 1000.

In the test set worth 200 points, c_i \leq 2.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1 c_1
:
a_{N-1} b_{N-1} c_{N-1}

Output

Print N lines. The i-th line must contain the niceness when the headquarters are set up in Vertex i.

Sample Input 1

3
1 2 10
2 3 20

Sample Output 1

20
30
30

The figure below shows the case when headquarters are set up in each of the vertices 1, 2 and 3.

The number on top of an edge denotes the joyfulness of the edge, and the number below an vertex denotes the smallest joyfulness of an edge on the path from the headquarters to that vertex.

Sample Input 2

15
6 3 2
13 3 1
1 13 2
7 1 2
8 1 1
2 8 2
2 12 2
5 2 2
2 11 2
10 2 2
10 9 1
9 14 2
4 14 1
11 15 2

Sample Output 2

16
20
15
14
20
15
16
20
15
20
20
20
16
15
20

Sample Input 3

19
19 14 48
11 19 23
17 14 30
7 11 15
2 19 15
2 18 21
19 10 43
12 11 25
3 11 4
5 19 50
4 11 19
9 12 29
14 13 3
14 6 12
14 15 14
5 1 6
8 18 13
7 16 14

Sample Output 3

103
237
71
263
370
193
231
207
299
358
295
299
54
368
220
220
319
237
370

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.Reader;
import java.util.Comparator;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInput in = new MyInput(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA {
        public void solve(int testNumber, MyInput in, PrintWriter out) {
            int n = in.nextInt();
            int[][] es = new int[n - 1][];
            for (int i = 0; i < n - 1; i++) {
                int a = in.nextInt() - 1;
                int b = in.nextInt() - 1;
                int c = in.nextInt();
                es[i] = new int[]{a, b, c};
            }
            Arrays.sort(es, Comparator.comparingInt(e -> -e[2]));
            UnionFind uf = new UnionFind(n);
            for (int[] e : es) {
                uf.union(e[0], e[1], e[2]);
            }
            for (int i = 0; i < n; i++) {
                out.println(uf.cost(i));
            }
        }

    }

    static class UnionFind {
        private int[] data;
        private int[] next;
        private int[] last;
        private long[] cost;
        private long[] cost2;

        public UnionFind(int size) {
            data = new int[size];
            next = new int[size];
            last = new int[size];
            cost = new long[size];
            cost2 = new long[size];
            clear();
        }

        public void clear() {
            Arrays.fill(data, -1);
            Arrays.fill(next, -1);
            Arrays.fill(cost, 0);
            for (int i = 0; i < last.length; i++) {
                last[i] = i;
            }
        }

        public int root(int x) {
            return data[x] < 0 ? x : (data[x] = root(data[x]));
        }

        public void union(int x, int y, long c) {
            if ((x = root(x)) != (y = root(y))) {
                if (data[y] < data[x]) {
                    final int t = x;
                    x = y;
                    y = t;
                }
                cost[y] += size(x) * c;
                cost[x] += size(y) * c;
                for (int i = y; i != -1; i = next[i]) {
                    cost2[i] += cost[y] - cost[x];
                }
                next[last[x]] = y;
                last[x] = last[y];
                data[x] += data[y];
                data[y] = x;
            }
        }

        public int size(int x) {
            return -data[root(x)];
        }

        public long cost(int x) {
            return cost[root(x)] + cost2[x];
        }

    }

    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }

        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }

        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new MyInput.EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }

        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++) ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }

        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (MyInput.EndOfFileRuntimeException e) {
            }
            return len;
        }

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }
}