Given the order e=[1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p], find a vector x with these conditions:

1. sum(x)==sumofx
2. length of x is the shortest possible
3. x has positive integers only
4. if e(k) contains s,p,d,f,g, then x(k) must be less than 3,7,11,15,19, respectively
5. if x(k+1)>0 then x(k) must be maximum possible.

For example, if sumofx=3 then x=[2 1]. Return x embedded in e in the following style: electrons='1s2,2s1'. Please see more info: Aufbau Principle, Electron Shell.