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 PYTHON3):

Solution:
import sys
input=sys.stdin.readline
from collections import deque
n=int(input())
Edges=[[] for _ in range(n)]
Cnt=[0]*n
for _ in range(n-1):
    a,b=map(int,input().split())
    Edges[a-1].append(b-1)
    Edges[b-1].append(a-1)
C=list(map(int,input().split()))
C.sort()
print(sum(C)-C[-1])
Used=[False]*n
for i,e in enumerate(Edges):
    if len(e)==1:
        start=i
        break
Ans=[0]*n
q=deque()
q.append(start)
Used[start]=True
while q:
    v=q.popleft()
    Ans[v]=C.pop()
    for u in Edges[v]:
        if not Used[u]:
            Used[u]=True
            q.append(u)
print(*Ans)