Shape Factory

The factory method pattern hides how objects are created: you ask the factory for a shape by name and get back an object that knows how to compute its own area.

Each description is a shape name followed by its numbers, separated by spaces:

• circle r: area π·r²
• square s: area s²
• rectangle w h: area w·h
• triangle b h: area b·h / 2

Implement shape_factory_areas(shapes).

Input

shapes: The descriptions. Numbers may have decimals.

Output

Return the area of each shape, in order. Answers within 1e-6 are accepted.

Constraints

1 ≤ number of shapes ≤ 1,000

0 < every number ≤ 1,000

Examples

Input:
shapes = ["square 3", "rectangle 2 5", "triangle 4 3"]

Expected output:
expected = [9.0, 10.0, 6.0]

Input:
std::vector<std::string> shapes = {"square 3", "rectangle 2 5", "triangle 4 3"};

Expected output:
std::vector<double> expected = {9.0, 10.0, 6.0};

Input:
string[] shapes = new string[] {"square 3", "rectangle 2 5", "triangle 4 3"};

Expected output:
double[] expected = new double[] {9.0, 10.0, 6.0};

Input:
shapes = ["circle 1"]

Expected output:
expected = [3.141592653589793]

Input:
std::vector<std::string> shapes = {"circle 1"};

Expected output:
std::vector<double> expected = {3.141592653589793};

Input:
string[] shapes = new string[] {"circle 1"};

Expected output:
double[] expected = new double[] {3.141592653589793};

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• Refactoring.Guru, Design Patterns
• Gamma, Helm, Johnson, Vlissides, Design Patterns: Elements of Reusable Object-Oriented Software