\(\left| a-1 \right| +\left| b-1 \right| =\left| a \right| +\left| b \right| =\left| a+1 \right| +\left| b+1 \right| \)

Let \(a\) and \(b\) be distinct real numbers such that the above equation is satisfied.

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

This problem is part of the set Hard Equations

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