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Let $ 0 le a , $ $b , $ $c , $ $d le 1 . $ Find the possible values of

Let $0\le a,$ $b,$ $c,$ $d \le 1.$ Find the possible values of the expression
\[\sqrt{a^2+(1- b)^2}+\sqrt{b^2+(1- c)^2}+\sqrt{c^2+(1- d)^2}+\sqrt{d^2+(1- a)^2}.\]
The answer is in the form of an interval (x, y), where x and y are the endpoints. Please calculate the value of x + y.

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