4x4 Sudoku completions

Write codeHard35 min

Your task

You are given a 4x4 Sudoku board as a list of 4 rows; each cell holds 0 (blank) or a value in 1..4. A completion fills every blank so that each row, each column, and each of the four 2x2 boxes contains the digits 1,2,3,4 exactly once. The given clues are guaranteed not to already violate these rules. Return the number of valid completions (0 if none).

Examples

count_sudoku_completions(board: list[list[int]]) -> int

Example 1

Inputcount_sudoku_completions([[1, 2, 3, 4], [3, 4, 1, 2], [2, 1, 4, 3], [4, 3, 2, 0]])

Output1