Several requested packages share dependencies, and adding their reported sizes overstates the installation footprint. Implement the inventory calculation so each installed package is counted once.
Build the implementation in Rust under /app, with /app/run.sh as its entry point. Read one JSON request from standard input and write one JSON result to standard output. Input has packages mapping names to size (nonnegative integer bytes) and deps, plus requested names. Return sorted installed names and total bytes, counting shared dependencies and cycles once. Validate every package size and dependency, including unused packages; reject unknown requested names, boolean/negative/noninteger sizes.
Reject inputs that violate an explicit validation rule with exit status 2, no standard output, and {"error":"invalid_input"} on standard error. For valid input, exit with status 0. Keep the implementation reusable for new inputs; it must work offline and must not depend on the example data being the only data it receives.
Repair or replace the unfinished /app/run.sh and add source files under /app. Malformed JSON must use the same invalid-input response. Do not read /tests or /oracle from the application.