Hidden Circuit Gates

This is an interactive challenge. The evaluator first prints N R, then N wiring lines Ui Vi. Slot i uses switch outputs Ui and Vi, where the hidden gate at slot i is either AND (&) or OR (|). The hidden gate string is evaluator-only.

For a query, print one line:

? s

s must be a binary string of length 2N + 1, setting switches 0..2N. The evaluator computes the circuit from high indices down to slot 0 and replies with the output of switch 0, either 0 or 1. At most 5000 queries are allowed. Flush after each query.

To answer, print one line:

! t

t must have length N and contain only & and |. It must exactly match all hidden slot types. Flush and then continue reading for another source case or exit on EOF.

Malformed strings, wrong lengths, invalid characters, query-limit failures, and wrong gate strings are rejected by the trusted evaluator. The evaluator writes result.json. The source score is full through 900 queries, zero from 5000 queries, and linear between those limits.