What is not working with my "map" usage?

[Victor]

Let me use a different input args and display them below.  Basically, I am hoping to add up all elements of each nested list.  So at first it should start with [1,11,111] ==> 1+11+111 = 123.  But instead, it appears to take the 1st element from each nested list to add up [1,2,3] = 6.   How should it be corrected?  Thx.


>>> alist = [[1,11,111], [2,22,222], [3,33,333]]

>>> list(map(add_all_elements,*alist))
My args =  (1, 2, 3)
<class 'int'>
i = 1
BEFORE total = 0
AFTER total = 1

<class 'int'>
i = 2
BEFORE total = 1
AFTER total = 3

<class 'int'>
i = 3
BEFORE total = 3
AFTER total = 6

FINAL total = 6

My args =  (11, 22, 33)
<class 'int'>
i = 11
BEFORE total = 0
AFTER total = 11

<class 'int'>
i = 22
BEFORE total = 11
AFTER total = 33

<class 'int'>
i = 33
BEFORE total = 33
AFTER total = 66

FINAL total = 66

My args =  (111, 222, 333)
<class 'int'>
i = 111
BEFORE total = 0
AFTER total = 111

<class 'int'>
i = 222
BEFORE total = 111
AFTER total = 333

<class 'int'>
i = 333
BEFORE total = 333
AFTER total = 666

FINAL total = 666

[6, 66, 666]