Ahaaa, it's typo ... I wanted to say,
ICN-NRT-SIN-NRT-ICN on UA --- no stopover allowed (20,000 miles)
ICN-NRT-SIN-NRT-ICN on Star Carriers --- one stopover allowed (40,000 miles)
ICN-NRT-TPE-ICN on Star Carriers --- one stopover allowed at NRT (20,000 miles)
You are right, I wanted to say, "ICN" instead of "SIN" as well as "TPE" instead of "HKG". I am sorry for making you confused. I should have double-checked before posing.