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.

Problem does not sound too difficult.
1010101 has 3 'free' positions

with the next 20002 you get
2001210101
21012101
1210121
10121012
1010121002
101010120002

with the 303 you basically get
2001213131
210121313 <-- optimal solution
1210121303
10121012303
1313121002 
131310120002
101313120002
101010123032

Actually, this problem seems quite trivial.