Skyline Silhouette

In this problem, you are given a list of buildings where each building is represented by a triplet $(l, r, h)$, with $l$ being the left x-coordinate, $r$ the right x-coordinate, and $h$ the height of the building. The goal is to compute the skyline silhouette formed by these buildings when viewed from the front. The skyline is defined as a set of key points $(x, y)$ such that the height of the silhouette changes at these x-coordinates. More formally, if you denote the silhouette as a sequence of points $(x_1, h_1), (x_2, h_2), \dots,(x_k, h_k)$, then for each segment, the height of the silhouette remains constant between consecutive key points. Your task is to generate these key points in increasing order of $x$.

inputFormat

The input is given via standard input (stdin). The first line contains an integer $n$ indicating the number of buildings. Each of the next $n$ lines contains three space-separated integers: $l$, $r$, and $h$, representing the left x-coordinate, right x-coordinate, and height of a building respectively.

outputFormat

Print the key points of the skyline to standard output (stdout). Each line should contain two integers $x$ and $h$, where $x$ is an x-coordinate where the skyline changes and $h$ is the new height at that point. The points must be printed in increasing order of $x$.## sample

3
1 4 10
2 6 15
5 8 12

1 10
2 15
6 12
8 0