Array Packing Challenge

You are given n arrays A₁..A_n of n_k elements each, of which each element in A_n is either 0 or n. Your goal is to find an arrangement of the arrays such that no two nonzero elements of the arrays may share the same position, and the total length of the arrangement is minimised. For example, given the input file containing the lines

1010101
20002
303

One possible optimal arrangement is

121012303

Your program must read an input file of the form specified above from standard input and print out the optimal arrangement to standard output.

You have until 2012-07-01 00:00:00 4chan time.

>>13
The same position in the sequence, duh.

Basically you're finding where to put the arrays so that the 0s in them line up with not more than 1 nonzero element in all of the other arrays like >>9 showed.

>>14
I have a feeling it is, but can't think of how to prove it.