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Existing few-shot learning (FSL) methods usually assume base classes and novel classes are from the same domain (in-domain setting). However, in practice, it may be infeasible to collect sufficient training samples for some special domains to construct base classes. To solve this problem, cross-domain FSL (CDFSL) is proposed very recently to transfer knowledge from general-domain base classes to special-domain novel classes. Existing CDFSL works mostly focus on transferring between near domains, while rarely consider transferring between distant domains, which is in practical need as any novel classes could appear in real-world applications, and is even more challenging. In this paper, we study a challenging subset of CDFSL where the novel classes are in distant domains from base classes, by revisiting the mid-level features, which are more transferable yet under-explored in main stream FSL work. To boost the discriminability of mid-level features, we propose a residual-prediction task to encourage mid-level features to learn discriminative information of each sample. Notably, such mechanism also benefits the in-domain FSL and CDFSL in near domains. Therefore, we provide two types of features for both cross- and in-domain FSL respectively, under the same training framework. Experiments under both settings on six public datasets, including two challenging medical datasets, validate the our rationale and demonstrate state-of-the-art performance. Code will be released.