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We are reporting on a search for flavour-changing neutral current decays $D^0\to \mu^+ \mu^-$ and $D^0 \to e^+ e^-$, and for lepton-flavour violating decays$D^0 \to e^\pm \mu^\mp$, the measurement of $D^+_{(s)} \to K_S^0 \pi^+$ and$D^+_{(s)}\to K_S^0 K^+$ branching fractions, and the search for CP violationin $D^+_{(s)} \to K_S^0 \pi^+$ and $D^+_{(s)} \to K_S^0 K^+$ decays. Theanalyses are based on 600 fb$^{-1}$ to 700 fb$^{-1}$ of data collected in$e^+e^-$ collisions at the centre-of-mass (CM) energy of the $\Upsilon(4S)$resonance and 60 MeV below by the Belle detector at the KEKB collider.

Search for $D^0 -> \ell^+\ell^-$ decays and for CP violation in $D^+_{(s)} \to K_S^0\pi^+$ and $D^+_{(s)} \to K_S^0K^+$ at BELLE