The matrix service needs exact determinants for integer matrices. Implement the calculation without converting the arithmetic to floating point or losing the sign when rows are exchanged.
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 is a square integer matrix. Return its exact integer determinant; the empty matrix has determinant 1. Row swaps change the sign and singular matrices return zero. Use exact arithmetic. Reject nonsquare matrices or boolean/noninteger entries.
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.