#! /usr/bin/env python3
'''
Usage: %s [FILE]
Find all solutions for a Sudoku puzzle.

Options:
  -h, --help    print this help and exit

If FILE is omitted or `-', then the initial board is read from stdin.

The input board should consist of a series of cells, each either a positive 
integer or a `.' to denote an unknown value, separated by any characters not in 
/[0-9.]/. The order of the board is automatically detected as the fourth root of 
the number of cells, and it must be an integer. The numerical values are 
constrained from 1 to order**2 inclusive.

The solutions will always be ``pretty-printed'', e.g.,

  solution 1:
  4 2 7 | 1 3 6 | 5 8 9
  6 5 1 | 9 2 8 | 4 7 3
  3 8 9 | 5 4 7 | 1 6 2
  ------+-------+------
  2 3 5 | 8 1 9 | 7 4 6
  9 6 8 | 3 7 4 | 2 1 5
  7 1 4 | 2 6 5 | 9 3 8
  ------+-------+------
  8 9 6 | 7 5 1 | 3 2 4
  1 4 3 | 6 9 2 | 8 5 7
  5 7 2 | 4 8 3 | 6 9 1

  solution 2:
  ...

It is the case that a ``proper'' Sudoku can have only one solution; however, 
``improper'' Sudoku puzzles do exist.
'''
import sys
import sudoku as sd
def main(argv):
    fn = argv[0] if argv else '-'
    try:
        bd = sd.load_board((sys.stdin if fn == '-' else open(fn)).read())
    except ValueError:
        sys.exit('ill-formed board')

    for (i, soln) in enumerate(sd.solve(bd), start=1):
        assert sd.isvalid(soln) and sd.issolved(soln)
        print('solution %s:' % i)
        print(sd.dump_board(soln))
        print()
import sys

def usage():
    return __doc__.lstrip() % sys.argv[0]

if __name__ == '__main__':
    if set(sys.argv) & {'-h', '--help'}:
        sys.exit(usage())
    else:
        main(sys.argv[1:])