Find the minimum value of
\[\sqrt{x^2 + (1 - x)^2} + \sqrt{(1 - x)^2 + (1 + x)^2}\]over all real numbers $x.$The answer is in the form k\sqrt{m}+n,. Please provide the value of k + m + n.

Let's think step by step and output the final answer within \boxed{}.
user