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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

#define X first
#define Y second
typedef long long ll;
typedef pair<ll,ll> pll;

#define N 10005
vector<ll> e[N];
ll n, u, v, m, c[N], d[N], t;

void dfs(ll pa, ll curr) {
    d[curr] = c[t++];
    m+=c[t];
    for (auto child:e[curr]) {
        if (child == pa) continue;
        dfs(curr, child);
    }
}

int main(int argc, char const *argv[])
{
    //ios::sync_with_stdio(false);
    //cin.tie(NULL);
    cin >> n;
    for (ll i=1; i<n; i++) {
        cin >> u >> v;
        e[u].push_back(v);
        e[v].push_back(u);
    }
    for (ll i=0; i<n; i++) cin >> c[i];
    sort(c, c+n, greater<ll>());
    m=0; t=0;
    dfs(0,1);
    cout << m << endl;
    for (ll i=1; i<=n; i++) cout << d[i] << ' ';
    cout << endl;
    return 0;
}