In the training of a state, the coach proposes a game. The coach writes four real numbers on the board in order from least to greatest: $a < b < c < d$. Each Olympian draws the figure on the right in her notebook and arranges the numbers inside the corner shapes, however she wants, putting a number on each one. Once arranged, on each segment write the square of the difference of the numbers at its ends. Then, add the $4$ numbers obtained. For example, if Vania arranges them as in the figure on the right, then the result would be $$ (c - b)^2 + (b- a)^2 + (a - d)^2 + (d - c)^2.$$ The Olympians with the lowest result win. In what ways can you arrange the numbers to win? Give all the possible solutions.