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.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.Scanner;



public class Main {


	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		
		HashMap<Integer, ArrayList<Integer>> graph = new HashMap<>();
		for (int i=0;i<n-1;i++) {
			int a = sc.nextInt();
			int b = sc.nextInt();
			if (!graph.containsKey(a)) {
				graph.put(a, new ArrayList<Integer>());
			}
			if (!graph.containsKey(b)) {
				graph.put(b, new ArrayList<Integer>());
			}
			graph.get(a).add(b);
			graph.get(b).add(a);
		}
		
		ArrayList<Integer> c = new ArrayList<>();
		for (int i=0;i<n;i++) {
			c.add(sc.nextInt());
		}
		
		c.sort(Collections.reverseOrder());
		
		int[] counter = new int[1];
		HashMap<Integer, Integer> num = new HashMap<>();
		dfs(graph, num, 1, counter);
		
		long sum = 0;
		for (int i=1;i<n;i++) {
			sum+=c.get(i);
		}
		
		System.out.println(sum);
		StringBuffer str = new StringBuffer();
		for (int i=1; i<=n; i++) {
			str.append(c.get(num.get(i)));
			if (i<n) {
				str.append(" ");
			}
		}
		System.out.println(str);
	}
	
	static void dfs (HashMap<Integer, ArrayList<Integer>> graph, HashMap<Integer, Integer> num, int k, int[] counter) {
		if (!num.containsKey(k)) {
			num.put(k, counter[0]);
			counter[0]++;
			for (Integer intg : graph.get(k)) {
				dfs(graph, num, intg, counter);
			}
		}

	}
}