Problem:
Score : 500 points

Problem Statement

You are given a tree with N vertices 1,2,\ldots,N, and positive integers c_1,c_2,\ldots,c_N.
The i-th edge in the tree (1 \leq i \leq N-1) connects Vertex a_i and Vertex b_i.

We will write a positive integer on each vertex in T and calculate our score as follows:

On each edge, write the smaller of the integers written on the two endpoints.

Let our score be the sum of the integers written on all the edges.

Find the maximum possible score when we write each of c_1,c_2,\ldots,c_N on one vertex in T, and show one way to achieve it. If an integer occurs multiple times in c_1,c_2,\ldots,c_N, we must use it that number of times.

Constraints

1 \leq N \leq 10000

1 \leq a_i,b_i \leq N

1 \leq c_i \leq 10^5

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
:
a_{N-1} b_{N-1}
c_1 \ldots c_N

Output

Use the following format:

M
d_1 \ldots d_N

where M is the maximum possible score, and d_i is the integer to write on Vertex i.
d_1,d_2,\ldots,d_N must be a permutation of c_1,c_2,\ldots,c_N.
If there are multiple ways to achieve the maximum score, any of them will be accepted.

Sample Input 1

5
1 2
2 3
3 4
4 5
1 2 3 4 5

Sample Output 1

10
1 2 3 4 5

If we write 1,2,3,4,5 on Vertex 1,2,3,4,5, respectively, the integers written on the four edges will be 1,2,3,4, for the score of 10. This is the maximum possible score.

Sample Input 2

5
1 2
1 3
1 4
1 5
3141 59 26 53 59

Sample Output 2

197
59 26 3141 59 53

c_1,c_2,\ldots,c_N may not be pairwise distinct.

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

require "set"
class Node
  attr_accessor :i, :c
  attr_reader :linked_nodes
  def initialize(i)
    @i = i
    @c = nil
    @linked_nodes = Set.new
  end

  def add_link(node)
    @linked_nodes << node
  end

  def num_edge
    @linked_nodes.size
  end

  def set_c(c_ary)
    @c = c_ary.shift
    @linked_nodes.each do |node|
      next unless node.c.nil?
      node.set_c(c_ary)
    end
  end
end

class Edge
  def initialize(node1, node2)
    @node1 = node1
    @node2 = node2
    @node1.add_link(@node2)
    @node2.add_link(@node1)
  end

  def score
    [@node1.c, @node2.c].min
  end
end

class Tree
  def initialize
    @nodes = {}
    @edges = []
  end

  def add_node(i)
    @nodes[i] = Node.new(i)
  end

  def add_edge(i, j)
    @edges << Edge.new(@nodes[i], @nodes[j])
  end

  def solve(c_ary)
    max_num_edge_node = @nodes.sort_by { |i, n| n.num_edge }.last[1]
    c_ary = c_ary.sort.reverse
    max_num_edge_node.set_c(c_ary)
    score = @edges.map(&:score).inject(&:+)
    unless c_ary.empty?
      @nodes.each do |_, n|
        n.c = c_ary.shift if n.c.nil?
      end
    end
    puts score
    puts @nodes.map { |i, n| n.c }.join(" ")
  end
end

n = gets.chomp.to_i
tree = Tree.new
1.upto(n) { |i| tree.add_node(i) }

1.upto(n - 1) do
  i, j = gets.chomp.split(" ").map(&:to_i)
  tree.add_edge(i, j)
end
c_ary = gets.chomp.split(" ").map(&:to_i)
tree.solve(c_ary)