Description
Wendy has an LED clock radio, which is a 12-hour clock, displaying times from 12:00 to 11:59.
The hours do not have leading zeros but minutes may have leading zeros,
such as 2:07 or 11:03.
When looking at her LED clock radio, Wendy likes to spot arithmetic sequences in the digits. For
example, the times 12:34 and 2:46 are some of her favourite times,
since the digits form an
arithmetic sequence.
A sequence of digits is an arithmetic sequence if each digit after the first digit is obtained by adding
a constant common difference.
For example, 1,2,3,4 is an arithmetic sequence with a common
difference of 1, and 2,4,6 is an arithmetic sequence with a common difference of 2.
Suppose that we start looking at the clock at noon (that is, when it reads 12:00) and watch the
clock for some number of minutes.
How many instances are there such that the time displayed on
the clock has the property that the digits form an arithmetic sequence?
Input
The input contains one integer D (0 ≤ D ≤ 1 000 000 000), which represents the duration that the
clock is observed.
For 4 of the 15 available marks, D ≤ 10 000.
Output
Output the number of times that the clock displays a time where the digits form an arithmetic
sequence
starting from noon (12:00) and ending after D minutes have passed, possibly including
the ending time.
HINT
Between 12:00 and 12:34, there is only the time 12:34 for which the digits form an arithmetic
sequence.