Problem: 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.

Examples

Input

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


Output

10
1 2 3 4 5


Input

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


Output

197
59 26 3141 59 53

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.AbstractCollection;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Comparator;
import java.util.LinkedList;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author cunbidun
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DMaximumSumOfMinimum solver = new DMaximumSumOfMinimum();
        solver.solve(1, in, out);
        out.close();
    }

    static class DMaximumSumOfMinimum {
        private InputReader in;
        private PrintWriter out;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            this.in = in;
            this.out = out;
            int n = in.nextInt();
            ArrayList<Integer>[] tree = in.nextTree(n);
            int pos = 0;
            int max = 0;
            for (int i = 1; i <= n; i++) {
                if (tree[i].size() > max) {
                    max = tree[i].size();
                    pos = i;
                }
            }
            int[] d = in.nextIntArray(n, 1);
            MergeSort.sort(d, 1, n, Comparator.reverseOrder());
            LinkedList<Integer> q = new LinkedList<>();
            q.add(pos);
            int cur = 1;
            int[] ans = new int[n + 1];
            while (!q.isEmpty()) {
                int u = q.pop();
                ans[u] = d[cur];
                cur++;
                for (int v : tree[u]) {
                    if (ans[v] == 0) q.add(v);
                }
            }
            int res = 0;
            for (int i = 1; i <= n; i++) {
                for (int j : tree[i]) {
                    res += MaxMin.Min(ans[i], ans[j]);
                }
            }
            out.println(res / 2);
            for (int i = 1; i <= n; i++) out.print(ans[i] + " ");
        }

    }

    static class MaxMin {
        public static <T extends Comparable<T>> T Min(T x, T y) {
            T min = x;
            if (y.compareTo(min) < 0) min = y;
            return min;
        }

    }

    static class InputReader extends InputStream {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int length, int stIndex) {
            int[] arr = new int[length + stIndex];
            for (int i = stIndex; i < stIndex + length; i++)
                arr[i] = nextInt();
            return arr;
        }

        public ArrayList<Integer>[] nextTree(int n) {
            ArrayList<Integer>[] tree = new ArrayList[n + 1];
            for (int i = 1; i <= n; i++) {
                tree[i] = new ArrayList<>();
            }
            for (int i = 1; i < n; i++) {
                int u = nextInt();
                int v = nextInt();
                tree[u].add(v);
                tree[v].add(u);
            }
            return tree;
        }

        private static boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }

    static class MergeSort {
        private static final int CUTOFF = 7;

        private MergeSort() {
        }

        private static void swap(Object[] a, int i, int j) {
            Object swap = a[i];
            a[i] = a[j];
            a[j] = swap;
        }

        private static boolean less(Object a, Object b, Comparator comparator) {
            return comparator.compare(a, b) < 0;
        }

        private static void merge(Object[] src, Object[] dst, int lo, int mid, int hi, Comparator comparator) {
            int i = lo, j = mid + 1;
            for (int k = lo; k <= hi; k++) {
                if (i > mid) dst[k] = src[j++];
                else if (j > hi) dst[k] = src[i++];
                else if (less(src[j], src[i], comparator)) dst[k] = src[j++];
                else dst[k] = src[i++];
            }
        }

        private static void sort(Object[] src, Object[] dst, int lo, int hi, Comparator comparator) {
            if (hi <= lo + CUTOFF) {
                insertionSort(dst, lo, hi, comparator);
                return;
            }
            int mid = lo + (hi - lo) / 2;
            sort(dst, src, lo, mid, comparator);
            sort(dst, src, mid + 1, hi, comparator);
            if (!less(src[mid + 1], src[mid], comparator)) {
                System.arraycopy(src, lo, dst, lo, hi - lo + 1);
                return;
            }

            merge(src, dst, lo, mid, hi, comparator);
        }

        private static void insertionSort(Object[] a, int lo, int hi, Comparator comparator) {
            for (int i = lo; i <= hi; i++)
                for (int j = i; j > lo && less(a[j], a[j - 1], comparator); j--)
                    swap(a, j, j - 1);
        }

        public static void sort(Object[] a, int lo, int hi, Comparator comparator) {
            Object[] aux = a.clone();
            sort(aux, a, lo, hi, comparator);
        }

        public static int[] sort(int[] input, int lo, int hi, Comparator comparator) {
            Integer[] a = new Integer[input.length];
            for (int ctr = 0; ctr < input.length; ctr++) a[ctr] = input[ctr];
            sort(a, lo, hi, comparator);
            for (int ctr = 0; ctr < a.length; ctr++) input[ctr] = a[ctr];
            return input;
        }

    }
}