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We consider the problem of grasping novel objects and its application to cleaning a desk. A recent successful approach applies machine learning to learn one grasp point in an image and a point cloud. Although those methods are able to generalize to novel objects, they yield suboptimal results because they rely on motion planner for finger placements. In this paper, we extend their method to accommodate grasps with multiple contacts. This approach works well for many human-made objects because it models the way we grasp objects. To further improve the grasping, we also use a method that learns the ranking between candidates. The experiments show that our method is highly effective compared to a state-of-the-art competitor.