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A search for decays of mesons to two charm mesons is performed for the first time using data corresponding to an integrated luminosity of 3.0 fb, collected by the LHCb experiment in collisions at centre-of-mass energies of 7 and 8 TeV. The decays considered are $B_c^+\to D^{()+}_{(s)} \overline{D}^{()0}B_c^+\to D^{()+}_{(s)} D^{()0}$, which are normalised to high-yield decays. No evidence for a signal is found and limits are set on twelve decay modes.

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