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 Ruby (2.3.3) (judge verdict: Accepted)

class UnionFind
    attr_reader :set_size, :rank
    def initialize(n)
        @par = Array.new(n)
        n.times{ |i| @par[i] = i }
        @rank = Array.new(n, 0)
        @set_size = Array.new(n, 1)
        @diff_weight = Array.new(n, 0)
    end

    def find(x)
        if @par[x] == x
            x
        else
            r = find(@par[x])
            @diff_weight[x] += @diff_weight[@par[x]]
            @par[x] = r
        end
    end

    def unite(x, y, w)
        w += weight(x)
        w -= weight(y)
        x = find(x)
        y = find(y)
        return if x == y

        if @rank[x] < @rank[y]
            @par[x] = y
            @set_size[y] += @set_size[x]
            @diff_weight[x] = -w;
        else
            @par[y] = x
            @set_size[x] += @set_size[y]
            @diff_weight[y] = w;
            @rank[x] += 1 if @rank[x] == @rank[y]
        end
    end

    def weight(x)
        find(x)
        @diff_weight[x]
    end

    def diff(x, y)
        weight(y) - weight(x)
    end

    def same?(x, y)
        find(x) == find(y)
    end
end


N = gets.to_i
edges = []
(N-1).times do |i|
    a, b, c = gets.split.map(&:to_i)
    edges.push([a-1, b-1, c])
end
edges.sort_by!{|arr| -arr[2]}

uf = UnionFind.new(N)
sum = Array.new(N, 0)

edges.each do |a, b, c|
    next if uf.same?(a, b)
    ap = uf.find(a)
    bp = uf.find(b)
    sum[ap] += uf.set_size[bp] * c
    sum[bp] += uf.set_size[ap] * c
    uf.unite(ap, bp, sum[bp] - sum[ap])
end

base = sum[uf.find(0)]

N.times do |i|
    puts uf.weight(i) + base
end