Roman dates were counted inclusively forward to the next of three principal days: the first of the month (the kalends), a day shortly before the middle of the month (the ides), and eight days—nine, counting inclusively—before this (the nones). The original calendar consisted of ten months beginning in spring with March; winter was left as an unassigned span of days. These months ran for 38 nundinal cycles, each forming an eight-day week (nine days counted inclusively, hence the name) ended by religious rituals and a public market. The winter period was later divided into two months, January and February. The legendary early kings Romulus and Numa Pompilius were traditionally credited with establishing this early fixed calendar, which bears traces of its origin as an observational lunar one. In particular, the kalends, nones, and ides seem to have derived from the first sighting of the crescent moon, the first-quarter moon, and the full moon respectively. The system ran well short of the solar year, and it needed constant intercalation to keep religious festivals and other activities in their proper seasons. This is a typical element of lunisolar calendars. For superstitious reasons, such intercalation occurred within the month of February even after it was no longer considered the last month.