Now we need to define arrays. Each array consists of a finite sequence of zero or more entries. Each entry consists of either a positive integer or another array (and these arrays can only nest finitely). An example of a valid array is [1,1,[1,2,[3],4,[],1,1],1,3,10,1,[4,[4,3,1],5,6],1,[1,2],1,1] First, we define the following notation: \(n!m = n\uparrow^{m}(n-1)\uparrow^{m}(n-2)\cdots 4\uparrow^{m} 3 \uparrow^{m} 2 \uparrow^{m} 1\)