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 Kotlin (1.0.0) (judge verdict: Accepted)

// Reads multiple ints in a line, separate by a space.
// It works even if the actual number of ints is smaller than n.
// WARNING: This function does not work for -2^31.
// NOTE: This function does not handle error cases.
fun fastReadInts(n: Int): IntArray {
  val xs = IntArray(n)
  val s = readLine()!!
  var currentValue = 0
  var isNegative = false
  var currentIndex = 0
  for (c in s) {
    if (c == ' ') {
      xs[currentIndex] = currentValue * if (isNegative) -1 else 1
      currentValue = 0
      isNegative = false
      currentIndex++
    } else if (c == '-') {
      isNegative = true
    } else {
      currentValue *= 10
      currentValue += c - '0'
    }
  }
  xs[currentIndex] = currentValue * if (isNegative) -1 else 1
  return xs
}

// Implements Union-Find Set.
// Manages integers of [0, n).
class UFSet(n: Int) {
  private var ranks = IntArray(n, { 1 })
  private var prevs = IntArray(n, { it })

  // Returns a root of a tree which x belongs to.
  // The argument x needs to be in [0, n).
  fun find(x: Int): Int {
    if (x != prevs[x]) prevs[x] = find(prevs[x])
    return prevs[x]
  }

  // Merges a set which x belongs to and a set which y belongs to.
  // The argument x and y need to be in [0, n).
  fun union(x: Int, y: Int) {
    val xRoot = find(x)
    val yRoot = find(y)
    when {
      ranks[xRoot] > ranks[yRoot] -> prevs[yRoot] = prevs[xRoot]
      ranks[xRoot] < ranks[yRoot] -> prevs[xRoot] = prevs[yRoot]
      prevs[xRoot] != prevs[yRoot] -> {
        prevs[yRoot] = prevs[xRoot]
        ranks[xRoot]++
      }
    }
  }
}

data class Edge(val v1: Int, val v2: Int, val weight: Long)

sealed class TreeNode(val size: Int, var value: Long) {
  class InternalNode(val child1: TreeNode, val child2: TreeNode,
                     size: Int, value: Long): TreeNode(size, value)
  class LeafNode(val leafIndex: Int, size: Int, value: Long): TreeNode(size, value)
}

fun makeLeafNode(leafIndex: Int) = TreeNode.LeafNode(leafIndex, 1, 0)

fun makeParentNode(child1: TreeNode, child2: TreeNode) =
    TreeNode.InternalNode(child1, child2, child1.size + child2.size, 0)

fun main(args: Array<String>) {
  val n = readLine()!!.toInt()
  val edges = mutableListOf<Edge>()
  repeat(n - 1) {
    val (v1Raw, v2Raw, w) = fastReadInts(3)
    val v1 = v1Raw - 1
    val v2 = v2Raw - 1
    edges.add(Edge(v1, v2, w.toLong()))
  }
  edges.sortByDescending { it.weight }

  val ufSet = UFSet(n)
  val componentToTreeNode = Array<TreeNode>(n, { makeLeafNode(it) })

  for (edge in edges) {
    val v1 = edge.v1
    val v2 = edge.v2
    val c1 = ufSet.find(v1)
    val c2 = ufSet.find(v2)
    val node1 = componentToTreeNode[c1]
    val node2 = componentToTreeNode[c2]
    node1.value += node2.size * edge.weight
    node2.value += node1.size * edge.weight
    val parentNode = makeParentNode(node1, node2)
    ufSet.union(v1, v2)
    val cMerged = ufSet.find(v1)
    componentToTreeNode[cMerged] = parentNode
  }

  val rootNode = componentToTreeNode[ufSet.find(0)]
  val answerValues = LongArray(n)
  fun dfs(node: TreeNode, value: Long) {
    when (node) {
      is TreeNode.LeafNode -> {
        answerValues[node.leafIndex] = value + node.value
      }
      is TreeNode.InternalNode -> {
        dfs(node.child1, value + node.value)
        dfs(node.child2, value + node.value)
      }
    }
  }
  dfs(rootNode, 0)
  println(answerValues.joinToString("\n"))
}