[whuang369]

The interactor built the hidden array with testlib's rnd, which registerInteraction() never seeds, and the .ans files were empty. Every test with the same n got the same array, and a program that replays testlib's generator, as in the issue, scored 100 with zero queries on all 10 tests.

Each testdata/N.ans now holds a distinct secret 63-bit seed, drawn with Python's secrets.randbits(63). The interactor reads it before printing n and builds the array from std::mt19937_64(seed) with the same swap rule as before. mt19937_64 is fully specified by the C++ standard, so a seed gives the same array with any compiler and testlib build; testlib's rnd keeps only 48 bits of state, and its stream depends on the testlib version and build flags. Problem 143 already reads hidden mt19937_64 seeds from its .ans files the same way. A missing seed is a judge failure (_fail), and the seed is never printed to the contestant or the log. Like every hidden answer file, the seeds are public in this repo; the fix removes the replay that needs no outside data.

The arrays still follow the statement, so honest scores barely change: the archived algorithmic/solutions/59/gpt5.2_3.cpp averages 64.064088 on the old arrays and 64.064036 on the new ones.

Verified in the frontier-cs-judge image (g++ 11.4, -O2 -std=gnu++17) and with g++ 15.2: all 25 tests in the new algorithmic/tests/test_problem59.py pass. They check that the replay from the issue is rejected on tests 2 to 10 (test 1 has n = 1, where zero queries is the honest answer), pin each hidden array by hash, check that tests with equal n get different arrays, and check that the seed never appears in the interactor's output. On main, 24 of them fail and the replay scores 100 on every test. test_problem59_budget_reference.py now writes a seed to its answer file, and its 6 tests pass.

Relation to #209: #209 also puts a per-test seed in the .ans files, but seeds testlib's rnd with it instead of using mt19937_64. Both PRs add algorithmic/tests/test_problem59.py, so only one can merge as is.

Fixes #208.