Diogo is a child who loves to play by jumping on the steps of the park's staircase in his city. Each step of the staircase has a light, and Diogo enjoys jumping on the steps that are illuminated. He always jumps every $$$K$$$ steps where $$$K$$$ is greater than $$$1$$$, as he does not like to climb the stairs like everyone else normally does by stepping on every step. In other words, if we number the steps starting from $$$1$$$, Diogo will land on steps $$$K$$$, $$$2K$$$, $$$3K$$$, and so on.

Diogo always tries to find out the number $$$K$$$ that will allow him to jump on the largest number of illuminated steps. Therefore, he asked for your help to develop a program that calculates the maximum number of illuminated steps he can jump on.

Initially, all the step lights are off, and you will receive a list of numbers indicating which steps will toggle the state of its light in order. For each operation of toggling the light of a step, your program must respond with the maximum number of lights Diogo can step on by choosing the best possible $$$K$$$ to jump every $$$K$$$ steps $$$(K \gt 1)$$$.