Find Minimum Score Possible

Question

Problem statement:

We are given three arrays A1,A2,A3 of lengths n1,n2,n3. Each array contains some (or no) natural numbers (i.e > 0). These numbers denote the program execution times.
The task is to choose the first element from any array and then you can execute that program and remove it from that array.

For example:

if A1=[3,2] (n1=2),  
   A2=[7] (n2=1),  
   A3=[1] (n3=1) 

then we can execute programs in various orders like [1,7,3,2] or [7,1,3,2] or [3,7,1,2] or [3,1,7,2] or [3,2,1,7] etc.

Now if we take S=[1,3,2,7] as the order of execution the waiting time of various programs would be
for S[0] waiting time = 0, since executed immediately,
for S[1] waiting time = 0+1 = 1, taking previous time into account, similarly,
for S[2] waiting time = 0+1+3 = 4
for S[3] waiting time = 0+1+3+2 = 6

Now the score of array is defined as sum of all wait times = 0 + 1 + 4 + 6 = 11, This is the minimum score we can get from any order of execution.
Our task is to find this minimum score.

How can we solve this problem? I tried with approach trying to pick minimum of three elements each time, but it is not correct because it gets stuck when two or three same elements are encountered.

One more example:
if A1=[23,10,18,43], A2=[7], A3=[13,42] minimum score would be 307.