Add column with unique row value

I have a table like this:

SELECT 
    parent_id,  
    parent2_id,   
    parent3_id,  
    parent4_id  
FROM 
    parents

I need to make it like this:

I need to add column with an unique value of a row, but since we have 4 columns, then there are four rows. But, if anyone can make this result table without zero value in id column, it would be very cool.

upd: I found an answer, but it seems very large. Can the solution be simplified?

SELECT * FROM 
(SELECT 
    parent_id as id,
    parent_id,  
    parent2_id,   
    parent3_id,  
    parent4_id  
FROM 
    parents
UNION ALL
SELECT parent2_id as id,
    parent_id,  
    parent2_id,   
    parent3_id,  
    parent4_id  
FROM 
    parents
UNION ALL
SELECT parent3_id as id,
    parent_id,  
    parent2_id,   
    parent3_id,  
    parent4_id  
FROM 
    parents
UNION ALL
SELECT parent4_id as id,
    parent_id,  
    parent2_id,   
    parent3_id,  
    parent4_id  
FROM 
    parents) as src
WHERE src.id != 0