Task

Given binary true labels and predicted probability scores, sweep thresholds t ∈ {0.1, 0.2, …, 0.9} and for each compute precision, recall, and F1. Classify as positive if score >= t. Output one row per threshold.

Input

• Line 1: integer n
• Line 2: n space-separated ints (true labels: 0 or 1)
• Line 3: n space-separated floats (predicted scores in [0, 1])

Output

9 lines, format: threshold precision recall f1

Example

Input:

5
1 0 1 1 0
0.9 0.2 0.8 0.6 0.4

Output:

0.1 0.6 1 0.75
0.2 0.6 1 0.75
0.3 0.6 1 0.75
0.4 0.6 1 0.75
0.5 0.6 1 0.75
0.6 0.6 1 0.75
0.7 1 0.6666666667 0.8
0.8 1 0.6666666667 0.8
0.9 1 0.3333333333 0.5

Scaffolding

def threshold_grid(labels: list[int], scores: list[float]) -> list[tuple]: ...

Notes

Track A: use NumPy vectorised comparisons. Studying this grid visualises the precision–recall tradeoff across the full threshold range.