We present a new approach to example-based style transfer which combines neural methods with patch-based synthesis to achieve compelling stylization quality even for high-resolution imagery. We take advantage of neural techniques to provide adequate stylization at the global level and use their output as a prior for subsequent patch-based synthesis at the detail level. Thanks to this combination, our method keeps the high frequencies of the original artistic media better, thereby dramatically increases the fidelity of the resulting stylized imagery. We also show how to stylize extremely large images (e.g., 340 Mpix) without the need to run the synthesis at the pixel level, yet retaining the original high-frequency details.