User Prompt where list $0$ has length $1,$ and every list $i+1$ is one item longer than list $i.$ The order of the elements in the staircase doesn't matter.

Here are some input$/$output examples that show what I mean:

Input: $1,2,3,4,5,6$

Output $[[1],[2,3],[4,5,6]]$

Input: $1,2,3,4,5,6,7$

Output False

In the example $,$ the list of lists only has one element in its fourth list:

$[[1],[2,3],[4,5,6],[7]$

That is NOT equal to the length of the previous list plus one. The last list would have to have four elements to be a valid staircase.