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Deep learning has proven to be promising for traffic fingerprinting that explores features of packet timing and sizes. Although well-known for automatic feature extraction, it is faced with a gap between the heterogeneousness of the traffic (i.e., raw packet timing and sizes) and the homogeneousness of the required input (i.e., input-specific). To address this gap, we design an input-agnostic hierarchical deep learning framework for traffic fingerprinting that can hierarchically abstract comprehensive heterogeneous traffic features into homogeneous vectors seamlessly digestible by existing neural networks for further classification. The extensive evaluation demonstrates that our framework, with just one paradigm, not only supports heterogeneous traffic input but also achieves better or comparable performance compared to state-of-the-art methods black across a wide range of traffic fingerprinting tasks.