Quad-tenburg

Normal sudoku rules apply, i.e. each row, column and 3x3 region has to contain the digits from 1 to 9 once each. A digit in a circle must appear in one of the four surrounding cells. Battenburg: Whenever 2 odd and 2 even digits form a 2x2 checkerboard pattern, a Battenburg marking is given. If there is no such marking, the above pattern is not allowed.