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Using proton-proton collision data collected by the CMS experiment at (Formula presented) in 2016-2018, corresponding to an integrated luminosity of (Formula presented), the first full reconstruction of the three vector (Formula presented) meson states, (Formula presented), (Formula presented), and (Formula presented), is performed. The mass differences between the excited mesons and their corresponding ground states are measured to be (Formula presented), (Formula presented), and (Formula presented), where the first uncertainties are statistical and the second are systematic. These results improve on the precision of previous measurements by an order of magnitude.