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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Queue;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		Map<Integer, List<Integer>> map = new HashMap<Integer, List<Integer>>();
		for (int i = 0; i < n - 1; i++) {
			String[] sa = br.readLine().split(" ");
			int a = Integer.parseInt(sa[0]) - 1;
			int b = Integer.parseInt(sa[1]) - 1;
			putMap(map, a, b);
			putMap(map, b, a);
		}
		String[] sa = br.readLine().split(" ");
		List<Integer> c = new ArrayList<Integer>(n);
		for (int i = 0; i < n; i++) {
			c.add(Integer.parseInt(sa[i]));
		}
		br.close();

		Collections.sort(c);
		Collections.reverse(c);

		PrintWriter pw = new PrintWriter(System.out);

		long m = 0;
		for (int i = 1; i < c.size(); i++) {
			m += c.get(i);
		}
		pw.println(m);

		int[] d = new int[n];
		Queue<Integer> que = new ArrayDeque<Integer>();
		que.add(0);
		d[0] = c.get(0);
		int idx = 1;
		while (!que.isEmpty()) {
			Integer cur = que.poll();
			List<Integer> list = map.get(cur);
			for (int i = 0; i < list.size(); i++) {
				if (d[list.get(i)] == 0) {
					que.add(list.get(i));
					d[list.get(i)] = c.get(idx);
					idx++;
				}
			}
		}

		pw.print(d[0]);
		for (int i = 1; i < d.length; i++) {
			pw.print(" " + d[i]);
		}
		pw.println();
		pw.flush();
	}

	static void putMap(Map<Integer, List<Integer>> map, int a, int b) {
		List<Integer> listA = map.get(a);
		if (listA == null) {
			listA = new ArrayList<Integer>();
			map.put(a, listA);
		}
		listA.add(b);
	}
}