  We present Star Formation Histories (SFHs) for a sample of 104 massive
(stellar mass M > 10$^{10}$ M$_{\odot}$) quiescent galaxies (MQGs) at
$z$=1.0-1.5 from the analysis of spectro-photometric data from the SHARDS and
HST/WFC3 G102 and G141 surveys of the GOODS-N field, jointly with broad-band
observations from ultraviolet (UV) to far-infrared (Far-IR). The sample is
constructed on the basis of rest-frame UVJ colours and specific star formation
rates (sSFR=SFR/Mass). The Spectral Energy Distributions (SEDs) of each galaxy
are compared to models assuming a delayed exponentially declining SFH. A Monte
Carlo algorithm characterizes the degeneracies, which we are able to break
taking advantage of the SHARDS data resolution, by measuring indices such as
MgUV and D4000. The population of MQGs shows a duality in their properties. The
sample is dominated (85%) by galaxies with young mass-weighted ages, tM $<$ 2
Gyr, short star formation timescales, $\langle \tau \rangle$ $\sim$ 60-200 Myr,
and masses log(M/M$_{\odot}$) $\sim$ 10.5. There is an older population (15%)
with tM$=$2 - 4 Gyr, longer star formation timescales, $\langle \tau
\rangle$$\sim$ 400 Myr, and larger masses, log(M/M$_{\odot}$) $\sim$ 10.7. The
SFHs of our MQGs are consistent with the slope and the location of the Main
Sequence (MS) of star-forming galaxies at $z$ $>$ 1.0, when our galaxies were
0.5-1.0 Gyr old. According to these SFHs, all the MQGs experienced a Luminous
Infrared Galaxy (LIRG) phase that lasts for $\sim$ 500 Myr, and half of them an
Ultra Luminous Infrared Galaxy (ULIRG) phase for $\sim$ 100 Myr. We find that
the MQG population is almost assembled at $z$ $\sim$ 1, and continues evolving
passively with few additions to the population.
