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A search for the rare decays Bs->mumu and Bd->mumu is performed using data collected in 2011 and 2012 with the LHCb experiment at the Large Hadron Collider. These decays are highly suppressed in the Standard Model and are sensitive to possible contributions from as-yet undiscovered particles. The data samples comprise 1.1/fb of proton-proton collisions at sqrt(s) = 8 TeV and 1.0/fb at sqrt(s)=7 TeV. We observe an excess of Bs->mumu candidates with respect to the background expectation corresponding to a signal significance of 3.5 standard deviations.