According to rousseau what is a defining characteristic of a republic

The government gives public funds to low-performing schools for new computers. they decide to give more money to the lowest performers, some of which happen to promote multi denominational religions. according to the establishment clause, how would a court rule on this case? as a direct violation of the clause because government institutions cannot support religious institutions for any reason as a violation of the clause because the government gave more money to religious schools than public schools as in compliance with the clause because the government's action was for a secular purpose, did not advance a particular religion, and was unentangled as in compliance with the clause because the government gave money to fewer religious schools than public schools