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We report an up-turn in the soft X-ray light curve of supernova remnant (SNR) 1987A in late 2003 (~6200 days after the explosion), as observed with the Chandra X-ray Observatory. Since early 2004, the rapid increase of the 0.5-2 keV band X-ray light curve can no longer be described by the exponential density distribution model with which we successfully fitted the data between 1990 and 2003. Around day ~6200, we also find that the fractional contribution to the observed soft X-ray flux from the decelerated shock begins to exceed that of the fast shock and that the X-ray brightening becomes "global" rather than "spotty". We interpret these results as evidence that the blast wave has reached the main body of the dense circumstellar material all around the inner ring. This interpretation is supported by other recent observations, including a deceleration of the radial expansion of the X-ray remnant, a significant up-turn in the mid-IR intensities, and the prevalence of the optical hot spots around the entire inner ring, all of which occur at around day 6000. In contrast to the soft X-ray light curve, the hard band (3-10 keV) X-ray light curve increases at a much lower rate which is rather similar to the radio light curve. The hard X-ray emission may thus originate from the reverse shock where the radio emission is likely produced. Alternatively, the low increase rate of the hard X-rays may simply be a result of the continuous softening of the overall X-ray spectrum.