Merge columns with same index into 1 single column (pandas)

Question

I have a dataframe I would like to transform. I want to merge the columns together and have the values that have the same id appear as separate rows.

So From This:

id  children1       children2     children3
1   No Children    NaN           NaN
2   12-16 years    17+ years     Nan
3   No Children    Nan           Nan
4   5-7 years      8-11 years    12-16 years

To This:

id  children       
1   No Children    
2   12-16 years
2   17+ years     
3   No Children   
4   5-7 years
4   8-11 years
4   12-16 years

Is there an easy way to do this?

Data:

{'id': [1, 2, 3, 4],
 'children1': ['No Children', '12-16 years', 'No Children', '5-7 years'],
 'children2': [nan, '17+ years', nan, '8-11 years'],
 'children3': [nan, nan, nan, '12-16 years']}

Answer 1

new = (df.set_index('id').agg(list,1)#Put all row values into a list except id
   .explode()#Ensure each element in a list is put in a row
   .replace('Nan', np.nan)# Make Nan -> NaN
   .dropna()#Drop all NaNs
   .to_frame('Children')#Rename column 0 to Childresn
  )

outcome

     Children
id            
1   NoChildren
2   12-16years
2     17+years
3   NoChildren
4     5-7years
4    8-11years
4   12-16years
?