Travelling Salesman

The travelling salesman, starting from a certain city, wants to visit all the other cities exactly once and return. Given a map of the cities and the roads connecting them, he wants to make the trip as short as possible.

Find a path in the graph that starts and ends in a specific vertex and visits all other vertices exactly once. This kind of a path is also known as a Hamiltonian cycle.

Input

The input consists of the graph. The start vertex is always the one with ID 0. The graph is represented as a list of edges. An edge is represented as a tuple of 3 integers: v u w, where v and u are the vertices making the edge, and w is the weight of the edge.

Vertex IDs are consecutive range starting from 0, i.e. 0, 1, 2, ..., N - 1, N, where N is an arbitrary number. No edge connects a vertex to itself. Any pair of vertices has zero or one edge. The graph is connected, i.e. any vertex is reachable from any other.

Output

The output is space (' ') separated list of integers denoting vertex IDs.

Validation and Scoring

The output must:

• start and end with 0
• must be of length V + 1, where V is the number of vertices
• contain only vertex IDs
• contain all vertex IDs only once (except for 0)

The score is the length of the path. The objective is to minimize the score.

Example

Consider the following graph:

The travelling salesman starts from town "0" and has a few options of traversing the whole map. Having chosen this path the travelling salesman crosses a path of distance 70.

There is however a shorter path of distance 64.

Sample input

0 4 2
2 7 9
6 1 15
0 3 6
7 0 11
5 6 9
1 2 12
5 3 7
4 2 9
4 7 11
2 6 10
1 5 11
0 6 8
2 5 13
1 4 9
0 1 7
3 7 7
3 4 9

Inputs

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