Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

10
1 2 3 4 5

If we write 1,2,3,4,5 on Vertex 1,2,3,4,5, respectively, the integers written on the four edges will be 1,2,3,4, for the score of 10. This is the maximum possible score.

Sample Input 2

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

Sample Output 2

197
59 26 3141 59 53

c_1,c_2,\ldots,c_N may not be pairwise distinct.

Solution in Haskell (GHC 8.8.3) (judge verdict: Accepted)

import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import Data.List
import Control.Monad
import Data.Ord
import qualified Data.Sequence as Sq

main = do
    n <- readLn :: IO Int
    ab <- replicateM (n-1) $ do
        [a,b] <- map read . words <$> getLine
        return (a-1,b-1)
    cs <- sortOn Down . map read . words <$> getLine :: IO [Int]

    let edge = V.create $ do
            vec <- VM.replicate n []
            forM_ ab $ \(a,b) -> do
                VM.modify vec (a:) b
                VM.modify vec (b:) a
            return vec
    
    let ans = sum $ tail cs
    let sq = Sq.fromList cs
    let result = VU.create $ do
            vec <- VUM.replicate n (0 :: Int)
            let go Sq.Empty _ = return ()
                go ((par,this) Sq.:<| qs) (x Sq.:<| xs) = do
                    VUM.write vec this x
                    let qs' = foldl (Sq.|>) qs $ map (\x -> (this,x)) $ filter (/= par) (edge V.! this)
                    go qs' xs
            go (Sq.singleton (0,0)) sq
            return vec
    print ans
    VU.forM_ result print