Task

Given n true binary labels and n predicted binary labels, compute precision, recall, and F1 score.

If TP + FP = 0, precision = 0. If TP + FN = 0, recall = 0. If both are 0, F1 = 0.

Input

• Line 1: integer n
• Line 2: n space-separated ints (true labels: 0 or 1)
• Line 3: n space-separated ints (predicted labels: 0 or 1)

Output

Three space-separated floats: precision recall f1

Example

Input:

6
1 0 1 1 0 0
1 1 1 0 0 0

Output:

0.6666666667 0.6666666667 0.6666666667

Scaffolding

def confusion_matrix_score(y_true: list[int], y_pred: list[int]) -> tuple: ...

Notes

Track A: use NumPy boolean indexing. Precision = TP / (TP+FP); Recall = TP / (TP+FN); F1 = 2·P·R / (P+R).