How to draw the following figure in matlab script?

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Mabud Sarkar on 18 Jan 2021

Reopened: Mabud Sarkar on 19 Jan 2021

I want to plot the following figure in complex upper half plane which consists of all semi-circles.

Here all semi-circles forming a fundamental domain.

Please suggest me at least some approximate script that plots such figure. You can attach any name to the semi-circles.

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