"The ordinary year in the previous Roman calendar consisted of 12 months, for a total of 355 days. In addition, a 27-day intercalary month, the Mensis Intercalaris, was sometimes inserted between February and March. This intercalary month was formed by inserting 22 days after the first 23 or 24 days of February; the last five days of February, which counted down toward the start of March, became the last five days of Intercalaris. The net effect was to add 22 or 23 days to the year, forming an intercalary year of 377 or 378 days." (Wikipedia)

In the Gregorian calendar there sometimes will be a leap day as the last day of February:

"February 29 is the 60th day of the Gregorian calendar in such a year, with 306 days remaining until the end of the year." (Wikipedia)

So in an ordinary year the last day of February is the 59th day (as if to obstinately remind us of how the synodical month is the origin of time).

Instead of sometimes adding leap months to the basic measure of the year, viz.12 * 29½ = 354 nights, Caesar ignored the phases of the Moon and defined a basic solar measure of 365 days, with a regularly inserted leap day every 4th year:

"The leap day was introduced as part of the Julian reform. The day following the Terminalia (February 23) was doubled, forming the 'bis sextum - literally 'double sixth', since February 24 was 'the sixth day before the Kalends of March' using Roman inclusive counting (March 1 was the 'first day').

Although exceptions exist, the first day of the bis sextum (February 24) was usually regarded as the intercalated or 'bissextile' day since the third century. February 29 came to be regarded as the leap day when the Roman system of numbering days was replaced by sequential numbering in the late Middle Ages." (Wikipedia)

Thus the regular old Roman year ended with Februarius 23 and it was 350 nights long, 25 fortnights. Then followed 5 extra nights, or as the Romans saw it 5 + 1 = 6 nights in order to include March 1, the first day of the new regular year.

This means the last 4 months of the year contained 3 * 29 + 23 = 110 regular nights, or as the Romans saw it 110 + 1 = 111 regular nights, with 5 extra nights immediately before the last regular night.

355 = 5 * 71, which should remind us of the Egyptian system:

... Nut, whom the Greeks sometimes identified with Rhea, was goddess of the sky, but it was debatable if in historical times she was the object of a genuine cult. She was Geb's twin sister and, it was said, married him secretly and against the will of Ra. Angered, Ra had the couple brutally separated by Shu and afterwards decreed that Nut could not bear a child in any given month of any year. Thoth, Plutarch tells us, happily had pity on her. Playing draughts with the Moon, he won in the course of several games a seventy-second part of the Moon's light with which he composed five new days.

As these five intercalated days did not belong to the official Egyptian calendar of three hundred and sixty days, Nut was thus able to give birth successively to five children: Osiris, Haroeris (Horus), Set, Isis and Nepthys ...