“important factor” in the imposition of a sentence. Id. at 224. In assessing the sentencing transcript in this case, we consider those factors that the judge deemed important or salient in reaching his decision. We must conclude on the record before us that the district court, although certainly very cognizant of the need to protect the public and promote deterrence, nevertheless gave significant weight to its misapprehension of the defendant’s removal and reentry in order to commit drug trafficking offenses. Therefore, it simply is “not improbable that the trial judge was influenced by improper factors in imposing sentence.” Rizzo v. United States, 821 F.2d 1271, 1274 (7th Cir.1987) (internal quotation marks omitted); see also United States v. Barnes, 907 F.2d 693, 696 (7th Cir.1990) (<HOLDING>); United States v. Gomer, 764 F.2d 1221, 1223
recognizing that it is difficult to discern what factors district judges rely on during sentencing recognizing same factors holding that sentence is reasonable when the district court properly addresses sentencing factors of  3553a recognizing that sentencing judges have the discretion to reject any sentencing guideline but no judge is required to do so holding that where the aggravating circumstances are overwhelming it is particularly difficult to show prejudice at sentencing due to the alleged failure to present mitigation evidence