# Odd Tally Counter

A normal tally counter has $4$ digits and counts $1$ by $1$, hence there are $10000$ different numbers can be shown on it (in range $0000 ... 9999$).

Suppose you have an odd tally counter. Instead $1$ by $1$, it counts $x$ by $x$. In case of overflow, the counter only shows the last $4$ digits of the number.

For example, if $x = 1001$ the counter will show these numbers : $0000, 1001, 2002, ..., 9009, 0010, 1011, ...$

Let $F(n)$ be the function returning the number of different numbers can be shown on odd tally counter with $x = n$, find the last $3$ digits of $\sum_{i=1}^{9999} F(i)$.

As an explicit example : $F(1) = 10000$

This problem is taken from TOKI Open Contest January 2013 (Problemsetter : Me)

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