Mega Sudoku 16x16 200 Very Hard Puzzles

The puzzle a 16 x 16 grid made up of 4 x 4 subgrids (called "regions"). Some cells already contain numbers, known as "givens". The goal is to fill in the empty cells, one number in each, so that each column, row, and region contains the numbers 1 through 16 exactly once. Each number in the solution therefore occurs only once in each of three "directions", hence the "single numbers" implied by the puzzle's name.