Goal
Count all solutions to a partially filled Latin square.
A Latin square of order n is a n x n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. In this puzzle, you are given a n x n grid filled with digits between 0 and n. This grid forms a partially filled Latin square where digits above 0 cannot be changed (they are constrained) and zeroes can take any value between 1 and n. Your goal is to find the number of Latin squares that are solutions to this grid.
Input
Line 1 : an integer n, dimension of the square grid.
n lines : a string row with n digits corresponding to that row. A "0" is used for an unconstrained cell.
Output
Line 1: The number of solutions to the puzzle.
