THE SKIP PREDICTOR

Difficulty: Easy Tags: Metrics & Evaluation, Classification

Story

Spotify's skip-predictor flags tracks a listener is likely to abandon within 5 seconds. Before the model is allowed near production traffic, it has to clear a basic precision/recall sanity check on a held-out batch.

The Math

Precision = TP / (TP + FP)
Recall    = TP / (TP + FN)
F1        = 2 * Precision * Recall / (Precision + Recall)

Input Format

n
p_1 y_1
p_2 y_2
...
p_n y_n

p_i is the predicted binary label, y_i the true label, both 0 or 1.

Output Format

precision recall f1, space-separated, to 6 decimals.

Constraints

• 1 <= n <= 10^6
• Time limit: 1.0 second.

Example

Input

8
1 1
1 0
0 0
1 1
0 0
0 1
1 1
0 0

Output

0.750000 0.750000 0.750000

Explanation: TP = 3 (rows 1, 4, 7), FP = 1 (row 2), FN = 1 (row 6). P = 3/4 = 0.75, R = 3/4 = 0.75, F1 = 0.75.