SHELF SENTINEL

Difficulty: Easy Tags: Activation Functions, Autograd

Story

Walmart's smart-shelf sensors report a raw weight-delta signal every time an item is picked up or placed back, and that signal is noisy in both directions: small negative jitters from shelf vibration, and clean positive spikes from genuine removals. Before this feeds the restock-trigger model, every value below zero must be clamped away. You are implementing the exact ReLU layer used in the sensor-ingestion pipeline, forward and backward.

The Math

f(x) = max(0, x)         forward
f'(x) = 1 if x > 0 else 0   backward

Given a batch of raw readings x and, separately, an upstream gradient g from the next layer, compute the forward activation and the backward gradient g * f'(x).

Input Format

n
x_1 x_2 ... x_n
g_1 g_2 ... g_n

Output Format

Two lines: the activated values, then the backward gradient, each space-separated to 6 decimal places.

Constraints

• 1 <= n <= 10^5
• Time limit: 1.0 second. Memory: 64 MB.

Example

Input

5
-2.0 0.0 3.0 -0.5 1.5
1.0 1.0 1.0 1.0 1.0

Output

0.000000 0.000000 3.000000 0.000000 1.500000
0.000000 0.000000 1.000000 0.000000 1.000000