\alpha _1 = f^*(A_1) = -1 -1 = -2 \\
\alpha _2 = f^*(A_2) = 3-2 =1 \\
\alpha _3 = f^*(A_3) = 2-1 = 1 \\
\alpha _4 = f^*(A_4) = 4-1 = 3 \\