Remove a Longest Road

You are given a connected road network of n cities and m bidirectional roads. Each road is described by three integers u, v and w, where w represents the length (or weight) of the road connecting cities u and v.

Your task is to remove exactly one road – specifically one of the roads with the maximum length – such that the remaining network still connects all the cities. In other words, after removal, there should be a path between any two cities.

Note: If there are multiple roads of the same maximum length, remove the first one encountered in the input order.

The problem can be formally described by the formula:

$$\text{Find } r_{max} = \max_{1 \leq i \leq m} \{ w_i \}$$

and remove exactly one road with weight \(r_{max}\), then print the remaining roads.

inputFormat

The first line contains two integers n and m (1 \leq n \leq 10^5, 0 \leq m \leq 10^5), where n is the number of cities and m is the number of roads.

Each of the following m lines contains three integers u, v, and w (1 \leq u,v \leq n, 1 \leq w \leq 10^9), representing a road between cities u and v with weight w.

You should read the input from standard input (stdin).

outputFormat

Output the remaining roads after removing the one road with the maximum weight. For each road, output a line containing three integers u, v, and w separated by spaces, following the same order as the input except for the removed road.

If no roads remain, output nothing. The output must be written to standard output (stdout).

## sample

5 7
1 2 5
1 3 10
2 3 12
2 4 15
3 4 7
4 5 6
5 1 14

1 2 5
1 3 10
2 3 12
3 4 7
4 5 6
5 1 14

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