jmc

One of the ways to solve this problem is to make this parallelogram a straight line. So the whole length of the line is $APC$($AMC$ or $ANC$), and $ABC$ is $1000x+2009x=3009x.$ $AP$($AM$ or $AN$) is $17x.$ So the answer is $3009x/17x=\boxed{177}$