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 PYTHON):

Solution:
import collections, heapq, sys

n = int(sys.stdin.readline().rstrip())
g = collections.defaultdict(list)
visited = set()
deg = collections.defaultdict(int)
for i in range(n-1):
    a, b = map(int, sys.stdin.readline().rstrip().split(' '))
    deg[a] += 1
    deg[b] += 1
    g[a].append(b)
    g[b].append(a)

pq = []
for i in range(1, n+1):
    heapq.heappush(pq, [deg[i], i])
wts = map(int, sys.stdin.readline().rstrip().split(' '))
wts.sort(reverse=True)
    
vToWt = [-1 for _ in range(n+1)]
sm = 0
while len(pq):
    _, v = heapq.heappop(pq)
    
    if vToWt[v] != -1:
        continue
    vToWt[v] = wts.pop()
    for nei in g[v]:
        if vToWt[nei] != -1:
            continue
        sm += vToWt[v]
        deg[nei] -= 1
        heapq.heappush(pq, [deg[nei], nei])

print(sm)
print(' '.join(map(str, [x for x in vToWt[1:]])))