Time train

Michelangelo has attended the 75 AD gladiator fights at the Colosseum
and now wants to travel back to his own time in 1505 AD. He decides to
take the time train at the Termini station.

Instead of stopping at different stations, the time train stops at the
same station, but at different times. Specifically, the regular time
train stops every minute at the Termini station. Every minute there are
also express trains that only stop every three minutes.

Since Michelangelo has been taking math lessons by his good friend
Leonardo, he starts thinking about the number of different ways in which
he can travel home. For example, if he has to travel a total of 5
minutes, there are 4 ways of going home:

- Take the regular time train for 5 minutes.

- Take the express train for 3 minutes, then the regular train for 2
  minutes.

- Take the regular train for 1 minute, then the express train, then the
  regular train.

- Take the regular train for 2 minutes, then the express train.

Input

The input consists of several test cases. Each test case consists of a
number of minutes n such that 1 ≤ n ≤ 1000000000000.

Output

For each test case, compute the number of ways in which Michelangelo can
travel home. Since this number can be very large, output the number
modulo 1000003.

Problem information

Author: Anders Jonsson

Generation: 2026-01-25T22:06:22.071Z

© Jutge.org, 2006–2026.
https://jutge.org
