Knock-off the largest and smallest numbers with opposite sign conventions

Given a random set of numbers,

1. select and knock-off the numbers with the highest and lowest absolute values OR the highest or lowest distance from zero.
2. BUT these two numbers should have different sign conventions. i.e. one should be positive and other negative.
3. Zeros "0" are of no consequence as we are knocking off balances.
4. The other numbers are not to be disturbed.

#1
-5 is the smallest, 20 is the largest

A A1 A2
-5 10 20
0 10 15

#2
10 is the smallest, -50 is the largest

A A1 A2
-50 10 20
-40 0 20

#3
20 is the smallest, -100 is the largest
A A1 A2
-100 -10 20
-80 -10 0

#4
no knocking off requried
A A1 A2
-100 -10 -20
-100 -10 -20

#5
no knocking off requried
A A1 A2
100 10 20
100 10 20

#6
the zero value is ignored
A A1 A2
100 0 -20
80 0 0

in {-50 10 20} 10 is smallest as it is closest to zero value.

in {-100 -10 20} 20 is smallest as - 10 and -100 have the same sign convention. but i see that therein lies another issue, with the existing logic, no knocking-off will take place as the algo will pick -10 as smallest and not 20. Good point.