class Node():
    def __init__(self, col, row):
        self.col = col
        self.row = row
        self.up, self.down, self.left, self.right = self, self, self, self


class ColumnNode(Node):
    def __init__(self, id):
        Node.__init__(self, self, id)
        self.row_cnt = 0


class DLX():
    def search(h: ColumnNode, k:int, s:list):
        if h.right == h:
            print_solution(s)
            return
        else:
            c = choose_column_object(h)
            r = c.down
            while r != c:
                s += [r]
                j = r.right
                while j != r:
                    cover(j.col)
                    j = r.right
                search(h, k+1, s)
                # Pop data object
                r = s.pop()
                c = r
                j = r.left
                while j != r:
                    uncover(j.col)
                    j = j.left
                r = r.down
        uncover(c)

    def cover(c):
        c.right.left = c.left
        c.left.right = c.right
        i = c.down
        while i != c:
            j = i.right
            while j != i:
                j.down.up = j.up
                j.up.down = j.down
                j.col.row_cnt -= 1
                j = j.right
            i = i.down

    def uncover(c):
        i = c.up
        while i != c:
            j = i.left
            while j != i:
                j.col.row_cnt -= 1
                j.down.up = j
                j.up.down = j
                j = j.left
            i = i.up
        c.right.left = c
        c.left.right = c