One less = The number = One more?

Algebra Level 4

a1+b1=a+b=a+1+b+1\left| a-1 \right| +\left| b-1 \right| =\left| a \right| +\left| b \right| =\left| a+1 \right| +\left| b+1 \right|

Let aa and bb be distinct real numbers such that the above equation is satisfied.

Find the least possible value of ab\left| a-b \right| .

This problem is part of the set Hard Equations

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