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Codeforces
Medium
Arrays
Geometry
Math
Dima and Continuous Line

Determine whether a set of line segments forms one continuous, non-breaking line.

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Codeforces 358A

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Problem Statement

Problem

You are given several line segments drawn on a plane. Decide whether they can be viewed as one continuous line without gaps or breaks.

A valid continuous line means that the segments connect in a way that the whole figure is connected as a single chain or loop, with no isolated piece.

What to check

  • All segments belong to one connected structure.
  • There are no disconnected components.
  • Endpoints are the only places where segments may meet.

Task

Return whether the drawn segments form a continuous line.

Input Format

  • The input describes a collection of line segments.
  • Each segment is defined by its endpoints.
  • The exact input encoding may vary by platform, but the task is to determine if the whole set is connected as one continuous drawing.

Output Format

  • Print YES if the segments form one continuous line.
  • Otherwise print NO.

Constraints

  • Assume standard integer coordinates.
  • The number of segments is small enough for an O(n2)O(n^2) or similar geometric connectivity check.
  • Use exact geometric reasoning for intersections and shared endpoints.
Examples
Sample cases returned by the problem API.

Example 1

Input

3
0 0 2 0
2 0 4 0
4 0 6 0

Output

YES

Explanation

All three segments touch end-to-end, so together they form one continuous line.

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