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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using Training20200606.Questions;
using Training20200606.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Training20200606.Questions
{
    /// <summary>
    /// https://atcoder.jp/contests/m-solutions2019/tasks/m_solutions2019_d
    /// </summary>
    public class QuestionB : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var nodeCount = inputStream.ReadInt();
            var edgeCount = nodeCount - 1;

            var edges = new Edge[edgeCount];
            for (int i = 0; i < edgeCount; i++)
            {
                var ab = inputStream.ReadIntArray().Select(n => n - 1).ToArray();
                edges[i] = new Edge(ab[0], ab[1]);
            }

            var c = inputStream.ReadIntArray();
            Array.Sort(c);
            Array.Reverse(c);

            var numbers = new int[nodeCount];
            numbers[edges[0].Node1] = c[0];
            numbers[edges[0].Node2] = c[1];

            for (int i = 2; i < c.Length; i++)
            {
                for (int j = 0; j < edges.Length; j++)
                {
                    if (numbers[edges[j].Node1] == 0 && numbers[edges[j].Node2] != 0)
                    {
                        numbers[edges[j].Node1] = c[i];
                        break;
                    }
                    else if (numbers[edges[j].Node1] != 0 && numbers[edges[j].Node2] == 0)
                    {
                        numbers[edges[j].Node2] = c[i];
                        break;
                    }
                }
            }

            yield return c.Skip(1).Sum();
            yield return string.Join(" ", numbers);
        }

        struct Edge
        {
            public int Node1 { get; }
            public int Node2 { get; }

            public Edge(int node1, int node2)
            {
                Node1 = node1;
                Node2 = node2;
            }
        }
    }
}


namespace Training20200606
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionB();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace Training20200606.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace Training20200606.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion