The intricacy of avoiding arrays is 2

Let A be any n×n array on the symbols [n], with at most one symbol in each cell. An n×n Latin square L avoids A if all entries in L differ from the corresponding entries in A. If A is split into two arrays B and C in a special way, there are Latin squares L_B and L_C avoiding B and C, respectively. In other words, the intricacy of avoiding arrays is 2, the number of arrays into which A has to be split.