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We report the measurement of the cross sections for$e^+e^-$$\rightarrow${nOCH} (nOCH stands for non-open charm hadrons) withimproved precision at center-of-mass energies from 3.645 to 3.871 GeV. Weobserve for the first time a three-resonance structure in the energy-dependentlineshape of the cross sections, which are $\mathcal R(3760)$, $\mathcalR(3780)$ and $\mathcal R(3810)$ with significances of $9.4\sigma$,$15.7\sigma$, and $9.8\sigma$, respectively. The $\mathcal R(3810)$ is observedfor the first time. We found two solutions in analysis of the cross sections.For solution I [solution II], we measure the mass, the total width and theproduct of electronic width and nOCH decay branching fraction to be $(3805.8\pm 1.1 \pm 2.7)$ [$(3805.8 \pm 1.1 \pm 2.7)$] MeV/$c^2$, $(11.6 \pm 2.6 \pm1.9)$ [$(11.5 \pm 2.5 \pm 1.8)$] MeV, and $(10.8\pm 3.2\pm 2.3)$ [$(11.0\pm2.9\pm 2.4)$] eV for the $\mathcal R(3810)$, respectively. In addition, wemeasure the branching fractions ${\mathcal B}({\mathcalR}(3760)$$\rightarrow${nOCH}$)=(24.5 \pm 13.4 \pm 27.4)\% [(6.8 \pm 5.4 \pm7.6)\%]$ for the first time, and ${\mathcal B}(\mathcalR(3780)$$\rightarrow${nOCH}$)=(11.6 \pm 5.8 \pm 7.8)\% [(10.3 \pm 4.5 \pm6.9)\%]$. Moreover, we determine the open-charm (OC) branching fraction${\mathcal B}({\mathcal R}$$(3760)\rightarrow${OC}$)=(75.5 \pm 13.4 \pm 27.4)\%[(93.2 \pm 5.4 \pm 7.6)\%]$, which supports the interpretation of $\mathcalR(3760)$ as an OC pair molecular state, but contained a simple four-quark statecomponent. The first uncertainties are from fits to the cross sections, and thesecond are systematic.

First Observation of a Three-Resonance Structure in $e^+e^-\rightarrow${non-open} Charm Hadrons