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We have developed a model in which the quantum fluctuations of the proton structure are characterised by hot spots, whose number grows with decreasing Bjorken-x. Our model reproduces the F2(x,Q2) data from HERA at the relevant scale, as well as the exclusive and dissociative J/ψ photoproduction data from H1 and ALICE. Our model predicts that for Wγp≈500 GeV, the dissociative J/ψ cross section reaches a maximum and then decreases steeply with energy, which is in qualitatively good agreement to a recent observation that the dissociative J/ψ background in the exclusive J/ψ sample measured in photoproduction by ALICE decreases as energy increases. Our prediction provides a clear signature for gluon saturation at LHC energies.