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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using static Assistant.Input;
using static Assistant.Debug;
using System.Linq;
using Assistant;
using System.Text;

namespace MSOLUTIONSオープンD
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = RInt;

            List<int>[] edges = new List<int>[N].Select(x => new List<int>()).ToArray();
            for (int i = 0; i < N - 1; i++)
            {
                var a = RInt - 1;
                var b = RInt - 1;

                edges[a].Add(b);
                edges[b].Add(a);
            }

            //
            var c = RInts.OrderByDescending(x => x).ToArray();

            //前提条件
            int S = 0; //スタート
            //for (int i = 0; i < N; i++)
            //{
            //    if (edges[i].Count == 1)
            //    {
            //        S = i;
            //        break;
            //    }
            //}

            //幅優先探索
            Queue<int> que = new Queue<int>();
            que.Enqueue(S);
            int[] distance = new int[N].Select(x => int.MaxValue).ToArray();
            distance[S] = 0;

            long M = 0;

            int count = 0;
            int[] v = new int[N];
            v[S] = c[count];
            count++;
            while (que.Count > 0)
            {
                int q = que.Dequeue();
                foreach (var to in edges[q])
                {
                    int dis = distance[q] + 1;//コストの加算
                    if (distance[to] > dis)
                    {
                        v[to] = c[count];
                        M += c[count];
                        distance[to] = dis;
                        que.Enqueue(to);
                        count++;
                    }
                }
            }

            Console.WriteLine(M);
            Console.WriteLine(string.Join(" ", v));
        }
    }
}

namespace Assistant
{
    static class Input
    {
        static List<string> line = new List<string>();
        static int index = 0;
        static String RNext()
        {
            if (line.Count <= index) line.AddRange(Console.ReadLine().Split());
            return line[index++];
        }
        public static int RInt => int.Parse(RNext());
        public static long RLong => long.Parse(RNext());
        public static int[] RInts => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] RLongs => Console.ReadLine().Split().Select(long.Parse).ToArray();
        public static string RString => RNext();
        //以下未テスト
        public static int[] RIntsC(int c) => Enumerable.Repeat(0, c).Select(x => int.Parse(RNext())).ToArray();
        public static long[] RLongsC(int c) => Enumerable.Repeat(0, c).Select(x => long.Parse(RNext())).ToArray();
        public static char[][] RMap(int h) => Enumerable.Repeat(0, h).Select(x => Console.ReadLine().ToCharArray()).ToArray();
    }

    public struct Mlong
    {
        long _v;
        const long mod = 1000000007;
        public Mlong(long n = 0) : this() { _v = n >= mod ? n % mod : n; }

        public static implicit operator Mlong(long _x) => new Mlong(_x);
        public static implicit operator long(Mlong _x) => _x._v;
        public static Mlong operator +(Mlong m1, Mlong m2) { long m = m1._v + m2._v; return m >= mod ? m - mod : m; }
        public static Mlong operator -(Mlong m1, Mlong m2) { long m = m1._v - m2._v; return m >= 0 ? m : m + mod; }
        public static Mlong operator *(Mlong m1, Mlong m2) => m1._v * m2._v % mod;
        public static Mlong operator /(Mlong m1, Mlong m2) => m1._v * ModPow(m2._v, mod - 2) % mod;

        public static long ModPow(long a, long n)
        {
            if (n == 0) return 1;
            else if (n % 2 == 1) return a * ModPow(a, n - 1) % mod;
            else return ModPow(a * a, n / 2);
        }

        static Mlong[] fac, finv, inv;
        public static void nCkInit(int max)
        {
            fac = new Mlong[max]; finv = new Mlong[max]; inv = new Mlong[max];
            fac[0] = fac[1] = 1;
            finv[0] = finv[1] = 1;
            inv[1] = 1;
            for (int i = 2; i < max; i++)
            {
                fac[i] = fac[i - 1] * i;
                inv[i] = mod - inv[mod % i] * (mod / i);
                finv[i] = finv[i - 1] * inv[i];
            }
        }

        public static Mlong nCk(int n, int k)
        {
            if (n < k) return 0;
            if (n < 0 || k < 0) return 0;
            return fac[n] * finv[k] * finv[n - k];
        }
    }

    static class Debug
    {
        static public void Draw2D<T>(T[,] map, int mode = 1)
        {
#if DEBUG
            int W = map.GetLength(0);
            int H = map.GetLength(1);

            string[,] map2 = new string[W + 1, H + 1];
            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (i == 0 && j == 0) map2[i, j] = 0.ToString();
                    else if (i == 0) map2[i, j] = (j - 1).ToString();
                    else if (j == 0) map2[i, j] = (i - 1).ToString();
                    else map2[i, j] = map[i - 1, j - 1].ToString();
                }
            }

            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (mode == 0) Console.Write(map2[i, j].Last());
                    if (mode == 1) Console.Write(map2[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
#endif
        }

        public static void Draw1D<T>(T[] array, int mode = 0)
        {
#if DEBUG
            Console.WriteLine(string.Join(" ", array));
#endif
        }
    }
}