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A search for the baryon through the $\it{\Xi}^{++}{cc} \rightarrow D^{+} p K^{-} \pi^{+}$ decay is performed with a data sample corresponding to an integrated luminosity of 1.7 recorded by the LHCb experiment in collisions at a centre-of-mass energy of 13 TeV. No significant signal is observed in the mass range from the kinematic threshold of the decay to 3800 . An upper limit is set on the ratio of branching fractions $ = \frac{(\it{\Xi}^{++}{cc} \rightarrow D^{+} p K^{-} \pi^{+})}{(\it{\Xi}^{++}{cc} \rightarrow \Lambda^{+}{c} K^{-} \pi^{+}\pi^{+})} < 1.7 \hspace{2pt} (2.1) \times 10^{-2}$ at the 90% (95%) confidence level at the known mass of the state.

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