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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;
import java.util.function.Function;

public class Main {

    static int N;
    static int[] A, B;
    static int[] C;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextInt();
        A = new int[N-1];
        B = new int[N-1];
        for (int i = 0; i < N-1; i++) {
            A[i] = sc.nextInt()-1;
            B[i] = sc.nextInt()-1;
        }
        C = sc.nextIntArray(N);

        solve(new PrintWriter(System.out));
    }

    static void solve(PrintWriter out) {
        PriorityQueue<Integer> q = new PriorityQueue<>(Comparator.reverseOrder());
        long sum = 0;
        for (int i = 0; i < N; i++) {
            q.add(C[i]);
            sum += C[i];
        }
        sum -= q.peek();
        out.println(sum);

        int[][] G = adjB(N, A, B);
        int root = findRoot(G);
        int[] ans = new int[N];
        for (Node node : order(N, G, root, true)) {
            ans[node.a] = q.poll();
        }

        StringJoiner j = new StringJoiner(" ");
        for (int i = 0; i < N; i++) {
            j.add(String.valueOf(ans[i]));
        }
        out.println(j.toString());
        out.flush();
    }

    // どこからでもいいような気もする...
    static int findRoot(int[][] G) {
        int ret = -1;
        int max = 0;
        for (int i = 0; i < N; i++) {
            if( G[i].length > max ) {
                max = G[i].length;
                ret = i;
            }
        }
        return ret;
    }

    static class Node {
        int parent, a;

        public Node(int parent, int a) {
            this.parent = parent;
            this.a = a;
        }
    }

    static Node[] order(int N, int[][] G, int root, boolean fromRoot) {
        Node[] q = new Node[N];
        int u = 0, v = 0;
        Node[] ret = new Node[N];
        int idx = fromRoot ? 0 : N-1;
        int d = fromRoot ? 1 : -1;
        q[v++] = new Node(-1, root);
        while( u != v ) {
            Node n = q[u++];
            ret[idx] = n;
            idx += d;
            for (int b : G[n.a]) {
                if( b == n.parent ) continue;

                q[v++] = new Node(n.a, b);
            }
        }
        return ret;
    }

    static int[][] adjB(int n, int[] from, int[] to) {
        int[][] adj = new int[n][];
        int[] cnt = new int[n];
        for (int f : from) {
            cnt[f]++;
        }
        for (int t : to) {
            cnt[t]++;
        }
        for (int i = 0; i < n; i++) {
            adj[i] = new int[cnt[i]];
        }
        for (int i = 0; i < from.length; i++) {
            adj[from[i]][--cnt[from[i]]] = to[i];
            adj[to[i]][--cnt[to[i]]] = from[i];
        }
        return adj;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }

    static <A> void writeLines(A[] as, Function<A, String> f) {
        PrintWriter pw = new PrintWriter(System.out);
        for (A a : as) {
            pw.println(f.apply(a));
        }
        pw.flush();
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }
}