greater than that of the stiff symmetry energy. In other words, the supra-saturation (sub-saturation) density region is more neutron rich with $\gamma_i=1.5$ ($\gamma_i=0.5$). The effect from the sub- and supra-saturation density behaviors of symmetry energy will compete and contribute in the final observables. Due to the different behavior of density at different times, it is important to observe the isospin effects at the time of maximum compression and at the freeze-out time to understand the high-density behavior of symmetry energy. For this purpose, in the coming sections, the incident energy and isospin asymmetry dependencies of the single and double neutron-to-proton ratios from free nucleons and LCPs are analyzed.

![\[fig:4\](Color online) Excitation function of the single neutron-to-proton ratio for free nucleons (top panel) and LCPs (bottom panel) at semicentral geometry. The left and right panels are the same expect they are at the time of maximum compression and at the freeze-out time, respectively. Solid and open circles represent the soft and stiff symmetry energies, respectively. Solid and dashed lines corresponds to the systems of $^{112}$Sn + $^{112}$Sn and $^{124}$Sn + $^{124}$Sn, respectively. ](figure4.eps){width="90mm"}

Incident energy and isospin asymmetry dependencies of single neutron to proton ratio
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In order to address the 