A SNIP$-$N$-$FLIP$($i$)$ operation splits a string into two parts at character i and swaps the two parts. For example, applying SNIP$-$N$-$FLIP$(4)$ to the string salamalaikum gives alaikumsalam.

A string s is said to be a FLIP$-$FLOP of another string t if it can be produced by applying a SNIP$-$N$-$FLIP operation on t$.$ For example, the strings $\{$aabbcc$,$ bbccaa, ccaabb, abbcca,

bccaab$\}$ are all FLIP$-$FLOPs of each other. However, none of the following strings is a FLIP$-$FLOP of the other: $\{$aabbcc$,$ ccbbaa, cabbca, abcabc$\}.$

Given NN distinct strings, each having the same number of characters L$,$ where L$$N$,$ design an efficient algorithm to check if there are two strings that are FLIP$-$FLOPs of each other.

Analyze the running time and space requirements of your solution.