Chinese Rings

Dumbear likes to play the Chinese Rings (Baguenaudier). It’s a game played with nine rings on a bar. The rules of this game are very simple: At first, the nine rings are all on the bar.
The first ring can be taken off or taken on with one step.
If the first k rings are all off and the (k + 1)th ring is on, then the (k + 2)th ring can be taken off or taken on with one step. (0 ≤ k ≤ 7)

Now consider a game with N (N ≤ 1,000,000,000) rings on a bar, Dumbear wants to make all the rings off the bar with least steps. But Dumbear is very dumb, so he wants you to help him.

Each line of the input file contains a number N indicates the number of the rings on the bar. The last line of the input file contains a number "0".

For each line, output an integer S indicates the least steps. For the integers may be very large, output S mod 200907.

1
4
0

1
10

2009 Multi-University Training Contest 3 - Host by WHU