The government of Treeland wants to build a new road network. There are \(2N\) cities in Treeland. The unfinished plan of the road network already contains \(N\) road segments, each of which connects two cities with a straight line. No two road segments have a common point (including their endpoints). Your task is to determine \(N-1\) additional road segments satisfying the following conditions:
- Every new road segment must connect two cities with a straight line.
- If two segments (new or old) have a common point, then this point must be an endpoint of both segments.
- The road network connects all cities: for each pair of cities there is a path consisting of segments that connects the two cities.
Output
The standard output must contain \(N-1\) lines, each of them containing four integers, \(x_1, y_1, x_2, y_2\), where \((x_1,y_1)\) and \((x_2, y_2)\) are the coordinates of the cities that are the endpoints of a new road segment. If there are multiple solutions, your program may output any of them.
Scoring
\( \begin{array}{|c|c|l|} \hline \text{Subtask} & \text{Points} & \text{Constraints} \\ \hline 1 & 0 & \text{samples}\\ \hline 2 & 15 & \text{all input segments are vertical.} \\ \hline 3 & 15 & \text{each pair of input segments are parallel.} \\ \hline 4 & 15 & \text{each input segment is either horizontal or vertical.} \\ \hline 5 & 15 & N \le 10\,000 \\ \hline 6 & 40 & \text{no additional constraints}\\ \hline \end{array} \) Note
Примеры
| № | Входные данные | Выходные данные |
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1
|
5
1 3 3 6
5 1 5 3
3 3 6 5
2 1 4 1
2 3 4 2
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2 1 1 3
2 3 2 1
3 3 2 3
5 1 4 2
|