/amlich converts duong lich to am lich (defaults to today, Asia/Saigon);
/duonglich converts am lich to duong lich with a nhuan flag for leap
months. Dates accept d, d/m, or d/m/yyyy - missing parts fill from today
in the input's calendar. Conversion is a dependency-free port of Ho Ngoc
Duc's algorithm at UTC+7, with rejection of impossible lunar inputs,
anchored by known Tet/leap-month dates and a 1950-2050 round-trip test.