Super Sudoku

Description

Here’s a great hexadecimal sudoku. You have to solve this sudoku by placing a hexadecimal character (between 0 and f) in each square, respecting the classic sudoku constraints: hexadecimal characters in the same row, column or highlighted square must all be different.

However, the diabolical designers, true to their traditional pettiness, have added a further constraint. You must provide the solution that maximizes the PGCD of the 16 lines, interpreted as 16-character hexadecimal numbers (i.e. between 0 and 16^16 - 1). For example, line 0 1 2 3 4 5 6 7 8 9 a b c d e f is represented by the integer 0x0123456789abcdef.

Once the grid is complete, concatenate all the lines from top to bottom, and frame the result S in FCSC{} (e.g. if concatenating the lines gives S = 1234abcd, the flag would be FCSC{1234abcd}).

Good luck!