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We report the measurement of the cross sections for e+e-$nOCH (nOCH stands for non-open charm hadrons) with improved precision at center-of-mass energies from 3.645 to 3.871 GeV. We observe for the first time a three-resonance structure in the energy-dependent lineshape of the cross sections, which are mathcal R(3760), mathcal R(3780) and mathcal R(3810) with significances of 9.4sigma, 15.7sigma, and 9.8sigma, respectively. The mathcal R(3810) is observed for the first time. We found two solutions in analysis of the cross sections. For solution I [solution II], we measure the mass, the total width and the product of electronic width and nOCH decay branching fraction to be (3805.8 pm 1.1 pm 2.7) [(3805.8 pm 1.1 pm 2.7)] MeV/c2, (11.6 pm 2.6 pm 1.9) [(11.5 pm 2.5 pm 1.8)] MeV, and (10.8pm 3.2pm 2.3) [(11.0pm 2.9pm 2.4)] eV for the mathcal R(3810), respectively. In addition, we measure the branching fractions mathcal B(mathcal R(3760)$$nOCH)=(24.5 pm 13.4 pm 27.4)% [(6.8 pm 5.4 pm 7.6)%] for the first time, and mathcal B(mathcal R(3780)$$nOCH)=(11.6 pm 5.8 pm 7.8)% [(10.3 pm 4.5 pm 6.9)%]. Moreover, we determine the open-charm (OC) branching fraction mathcal B(mathcal R$(3760)OC)=(75.5 pm 13.4 pm 27.4)% [(93.2 pm 5.4 pm 7.6)%], which supports the interpretation of mathcal R(3760) as an OC pair molecular state, but contained a simple four-quark state component. The first uncertainties are from fits to the cross sections, and the second are systematic.
