The sparse input may contain several entries for the same coordinate. Finish accumulation and matrix-vector multiplication so those contributions are combined before producing the result.
Build the implementation in C++ 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 nonnegative integer rows and cols, entries [row,column,value] with finite numeric values and valid integer coordinates, and finite vector of length cols. Duplicate coordinates add; their combined zero values do not count toward nnz. Return product, rounded to six decimals, and nnz of the combined matrix. Reject invalid dimensions or coordinates.
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.