THE IMAGE NORMALIZATION CONTRACT

Difficulty: Medium Tags: Computer Vision, Preprocessing, Broadcasting

Story

A vision inference service normalizes each RGB channel with channel-specific means and standard deviations. A broadcasting bug applies the red channel's statistics to all three channels; the fix must use each channel's own mean and standard deviation.

The Math

For each channel c in {R, G, B}:

z_c = (x_c - mu_c) / sigma_c

Each channel has its own mean mu_c and its own strictly positive standard deviation sigma_c.

Input Format

x (length 3, the RGB pixel), mu (length 3), sigma (length 3).

Output Format

Three normalized RGB values, 6 decimal places.

Constraints

• All values finite, |x_c|, |mu_c| <= 10^6, 0 < sigma_c <= 10^6.
• Time limit: 1.0 second.

Example

Input

x = [255, 128, 0], mu = [127.5, 128, 10], sigma = [127.5, 64, 10]

Output

1.000000 0.000000 -1.000000

Explanation: Red is one standard deviation above its own mean, green is exactly at its mean, and blue is one standard deviation below its mean.