Lou 1 Zhuang

All members of Hulafly love playing the famous network game called 'Lou 1 Zhuang' so much that Super Da Lord got mad with them. So he thought over and over and finally came up with a good idea to stop them. He consulted an ACM master and asked for the hardest problem ever in the world. Hulafly must solve this problem in order to get permission of playing 'Lou 1 Zhuang'. They, however, are so eager to play 'Lou 1 zhuang' and have no interest in this problem at all, so they turn to you for help. You can do this only if you swear that you will never tell Da Lord that you have helped them.

'Lou 1 Zhuang' is a game with only one but a very tall buiding in it and everybody runs a shop in this buiding ---- either a cake shop or a barbershop, each one occupies a whole floor. (Log in at www.xiaonei.com and check details at http://apps.xiaonei.com/soletower/tower.php?origin=2807) Super Da Lord asks that if the buiding is N stories high, how can we devided the floors(or the shops) and multiply the number of floors(or shops) in each part to make the product P as large as possible. Neverthless, Super Da Lord thought that it's still too hard for them, so he gave them some hints, he said:"Go and find the solutoin in 'Lou 1 Zhuang'!"

Given the buidings' height N, you are to find the largest P.

The buidings' height N. (1 <= N <= 10^9)

The product you've found P (mod 2009).

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Hint
You can apply to be huhupao, flytosky and koala's friends at xiaonei.com.

2009 Multi-University Training Contest 9 - Host by HIT