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;
typedef long long ll;
#define INF 1LL<<62
#define inf 1000000007 

vector<vector<ll>>a(10002);
vector<ll>b;ll p;
ll c[10002],ans;
void dep(ll now){
	for(ll i=0;i<a[now].size();i++){
		ll next=a[now][i];
		if(c[next]!=0){
			continue;
		}
		c[next]=b[p];
		p++;
		ans+=min(c[now],c[next]);
		dep(next);
	}
}
int main() {
	ll n;
	cin>>n;
	for(ll i=0;i<n-1;i++){
		ll x,y;
		cin>>x>>y;
		x--;y--;
		a[x].push_back(y);
		a[y].push_back(x);
	}
	for(ll i=0;i<n;i++){
		ll x;
		cin>>x;
		b.push_back(x);
	}
	sort(b.begin(),b.end());
	reverse(b.begin(),b.end());
	c[0]=b[0];
	p++;
	dep(0);
	cout << ans<<endl;
	for(ll i=0;i<n;i++){
		cout << c[i]<<" ";
	}
	// your code goes here
	return 0;
}