A $$12 × 12$$ board is divided into $$144$$ unit squares by drawing lines parallel to the sides. Two
rooks placed on two unit squares are said to be non attacking if they are not in the same
column or same row. Find the least number $$N$$ such that if $$N$$ rooks are placed on the unit
squares, one rook per square, we can always find $$7$$ rooks such that no two are attacking
each other.