A writ of review may be granted by:
(1) the supreme court and any justice of the supreme court, in proceedings for contempt in the district court; or
(2) the supreme court or the district court or any judge of those courts, when a lower tribunal, board, or officer exercising judicial functions has exceeded the jurisdiction of the tribunal, board, or officer and there is no appeal or, in the judgment of the court, any plain, speedy, and adequate remedy.