Laser Test (APCS 2022-06 Advanced)

2.0s 256M

A laser starts at \((0,0)\) pointing right. There are \(n\) point mirrors: type \(0\) is / and type \(1\) is \. The laser travels to the nearest mirror ahead and turns ninety degrees according to its orientation. It stops when no mirror lies ahead. Count reflections, including repeated visits.

Input

Read \(n\), followed by \(n\) lines of \(x,y,t\).

Constraints

\(1\le n\le250000\), \(1\le x\le30000\), \(|y|\le30000\), \(t\in\{0,1\}\). Coordinates are distinct.

Output

Print the number of reflections.

Scoring

Each scored test independently awards 5 points, totaling 100. Samples award no points.

  • 1: 20% — \(n\le1000\), \(x\le100\), \(|y|\le100\)
  • 2: 80% — No additional restrictions.

Sample Input 1

10
2 0 1
2 -1 1
7 -1 0
7 2 1
4 2 0
4 1 0
3 1 1
3 2 0
1 -1 1
1 4 0

Sample Output 1

9

Sample Input 2

4
2 1 0
5 -3 1
4 2 1
6 -2 0

Sample Output 2

0

Source

i401 · 2022-06 APCS.

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