Republic Day and Independence Day of one year are circled. How many days lie strictly between them?

Days after 26 January: 5 in January, then Feb 28, Mar 31, Apr 30, May 31, Jun 30, Jul 31 (186 in total), plus 14 days of August before the 15th: 5 + 181 + 14 = 200. (201 includes one of the two days; 199 drops a day.)