Karina, Leticia and Milena paint glass bottles and sell them as decoration. they had $100$ bottles, and they decorated them in such a way that each bottle was painted by a single person. After the finished, they put all the bottles on a table. In an oversight one of them pushed the table, falling and breaking exactly $\frac18$ of the bottles that Karina painted, $\frac13$ of the bottles that Milena, painted and $\frac16$ of the bottles that Leticia painted. In total, $82$ painted bottles remained unbroken. Knowing that the number of broken bottles that Milena had painted is equal to the average of the amounts of broken bottles painted by Karina and Leticia, how many bottles did each of them paint?