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It is a challenge to reproduce the full 6D space-phase properties of Sagittarius (Sgr) dwarf galaxy and its Stream simultaneously. Using N-body simulations with a Milky Way mass of 5.2$\times10^{11}$ M$_{\odot}$ and a ``scaling down'' Sgr mass of 9.3$\times10^{8}$ M$_{\odot}$, from a qualitative point of view, we have been able to reproduce well all 3D spatial features of Sgr stream, including its core, leading and trailing arms, and their associated bifurcations, moreover, the overall trend of the reported 3D kinematics properties of the Sgr stream have also been reproduced without fine tuning. Furthermore, we also find that our model fails in reproducing the exact behaviours of the line-of-sight velocity and angular-energy distributions. It let us to suggest that significant further progress might be achievable after introducing a major component in the Sgr progenitor, which is the gas that dominates all Irregular dwarf galaxies in the Sgr mass range and can slow down the radial velocity of Sgr before its removal, if gas can not solve this problem then we will consider a non-spherical Milky Way halo with hot gas, LMC, etc. As the first step for us to towards the complete understanding of the Sgr system, this progress is also advancing our understanding of the bifurcations, the generation of which might be due to the MW shocks at each pericenter passage, and also be linked to the orientation and disk-shape in the initial conditions.