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Default adding values if the same - SUMIF in range of cells?

hiya, i have a small project and i've spent too much time on this already -
can't figure it out myself. What i need to do is to create a formula which
will find the same values in column A and will sum the corresponding to them
values from columns B:E.
this is a sort of result i want to get:
A B C D E F RESULT:
1 A1 1 5 2 3 A1 31
2 B5 2 6 3 3 A2 19
3 C1 3 7 4 3 B1 22
4 A1 4 8 5 3 B5 37
5 B5 5 9 6 3 C1 33
6 C2 6 1 6 3 C2 16
7 A2 7 2 7 3
8 B1 8 3 8 3
9 C1 9 4 0 3

I would appreciate any ideas how to do this. Thanks and regards,

 
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