Consider a cantilever beam, fixed at the left end and subject to a vertical force $F=10$ ton at the right end. The beam consists of $3$ segments, each of length $L,$ so the total length of the cantilever is $3m.$ Segment number $N$ is to the left, at the built$-$in end, and segment $1$ is at the free end. Each segment cross section has a hollow square form. Please design best section for this beam.

$E=2{10}^{6}k\frac{g}{c}{m}^2,=7800k\frac{g}{m^3}$