Merge duplicate rows with same values across two columns in my mysql table and add the values in third column

See more:

MySQL

I have a mysql data  table with 3 columns like below:

Item1  Item2  Value

Apple   Orange  3

Apple  Banana  2

Mango  Apple  2

Banana  Apple  6

Apple   Mango   5

Orange  Banana   4

Orange   Apple   5

I want to remove the duplicate rows based on the combinations of two columns Item1 & Item2 and show only one in any order and want to add their values as a result, so as the final output in my table box  can be:

Item1   Item2   Value

Apple   Orange   8

Apple   Banana   8

Mango   Apple   7

Orange   Banana   4

Thank you for any help or attention !  or at least  can any one  answer me if its even possible to do that !! 

What I have tried:

select T1.item1 ,T1.Item2, sum(T1.Value)  from MyDB as T1 join MyDB as T2 
on T1.item1 = T2.item2 group by item1,item2 ;