In the coordinate plane, the graph of
\[|x + y - 1| + \Big| |x| - x \Big| + \Big| |x - 1| + x - 1 \Big| = 0\]is a certain curve.  Find the length of this curve.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
In the coordinate plane, the graph of
\[|x + y - 1| + \Big| |x| - x \Big| + \Big| |x - 1| + x - 1 \Big| = 0\]is a certain curve.  Find the length of this curve.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\sqrt{2}
In the coordinate plane, the graph of
\[|x + y - 1| + \Big| |x| - x \Big| + \Big| |x - 1| + x - 1 \Big| = 0\]is a certain curve.  Find the length of this curve.
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