A9608 | Tree

Little X has a tree consisting of $n$ nodes (they are numbered from $1$ to $n$ ). Each edge of the tree has a positive length. Let's define the distance between two nodes $v$ and $u$ (we'll denote it $d(v,u)$ ) as the sum of the lengths of edges in the shortest path between $v$ and $u$ .

A permutation $p$ is a sequence of $n$ distinct integers $p_{1},p_{2},...,p_{n}$ $(1<=p_{i}<=n)$ . Little X wants to find a permutation $p$ such that sum  is maximal possible. If there are multiple optimal permutations, he wants to find the lexicographically smallest one. Help him with the task!

The first line contains an integer $n (1<=n<=10^{5})$ .

Each of the next $n-1$ lines contains three space separated integers $u_{i},v_{i},w_{i} (1<=u_{i},v_{i}<=n; 1<=w_{i}<=10^{5})$ , denoting an edge between nodes $u_{i}$ and $v_{i}$ with length equal to $w_{i}$ .

It is guaranteed that these edges form a tree.

In the first line print the maximum possible value of the described sum. In the second line print $n$ integers, representing the lexicographically smallest permutation.