VN-TST 1993 Problem 3

Let's consider the real numbers $x_1, x_2, x_3, x_4$ satisfying the condition

$$\dfrac{1}{2}\le x_1^2+x_2^2+x_3^2+x_4^2\le 1$$

Find the maximal and the minimal values of expression:

$$A = (x_1 - 2 \cdot x_2 + x_3)^2 + (x_2 - 2 \cdot x_3 + x_4)^2 + (x_2 - 2 \cdot x_1)^2 + (x_3 - 2 \cdot x_4)^2$$