Order Book Imbalance

Problem

You are given a snapshot of a limit order book with $N$ price levels on each side. Compute three key quantities:

1. Mid price: $\text{mid} = (\text{best\_bid} + \text{best\_ask}) / 2$

2. Weighted mid price: $\text{wmid} = \frac{\text{best\_bid} \cdot a_1 + \text{best\_ask} \cdot b_1}{b_1 + a_1}$ where $b_1$ is the bid size at the best bid and $a_1$ is the ask size at the best ask.

3. Order book imbalance: $\text{imbalance} = \frac{\sum b_i - \sum a_i}{\sum b_i + \sum a_i}$ summed over all $N$ levels.

Input Format

A single line: best_bid best_ask bid_sizes ask_sizes where bid_sizes and ask_sizes are comma-separated lists of sizes at each price level (level 1 = best).

Output Format

A single line: mid weighted_mid imbalance, each to 4 decimal places.