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We present the discovery and analysis of J1316+2614 at z=3.6130, a UV-bright star-forming galaxy ($M_{\rm UV} \simeq -24.7$) with large escape of Lyman continuum (LyC) radiation. J1316+2614 is a young ($\simeq 10$ Myr) star-forming galaxy with $SFR \simeq 500 M_{\odot}$ yr$^{-1}$ and a starburst mass of log($M_{\star}/M_{\odot}) \simeq 9.7$. It shows a very steep UV continuum, $β_{\rm UV} \simeq -2.59 \pm 0.05$, consistent with residual dust obscuration, $E(B-V)\simeq 0$. LyC emission is detected with high significance ($\simeq 17 σ$) down to $830$Å, for which a very high relative (absolute) LyC escape fraction $f_{\rm esc} \rm (LyC) \simeq 0.92$ ($\simeq 0.87$) is inferred. The contribution of a foreground or AGN contamination to the LyC signal is discussed but is unlikely. J1316$+$2614 is the most powerful ionizing source known among the star-forming galaxy population, both in terms of production ($Q_{\rm H} \approx 10^{56}$ s$^{-1}$) and escape of ionizing photons ($f_{\rm esc} \rm (LyC) \approx 0.9$). Nebular emission in Ly$α$, H$β$, and other rest-frame optical lines are detected, but these are weak ($EW_{0} \rm [Hβ] \simeq 35$Å), with their strengths reduced roughly by $\simeq 90\%$. J1316+2614 is the first case known where the effect of large escape of ionizing photons on the strength of nebular lines and continuum emission is clearly observed. Gas inflows are detected in J1316+2614 from the blue-dominated peak Ly$α$ emission (with a blue-to-red peak line ratio $I_{\rm blue}/I_{\rm red} \simeq 3.7$) and redshifted ISM absorption ($\simeq 100$ km s$^{-1}$). Our results suggest that J1316+2614 is undergoing a gas compaction event, possibly representing a short-lived phase in the evolution of massive and compact galaxies, where strong gas inflows have triggered an extreme star formation episode and nearly $100\%$ LyC photons are escaping.