(SPOILER) My solution

My solution is based on string hashing. Let's say that the strings from the input are s[1], s[2], ... , s[n]. First, let's iterate over all possible lengths from 1 to 100 (since the maximal length of a string is 100). Let's fix some length "len" and create a vector "all" which will contain all possible hashes of substrings of length "len" of all the strings s[i]. Additionally, for each i from 1 to n create a vector a[i] which will contain the hashes of substrings of length "len" of only the string s[i]. Now, sort all the vectors we've created so that we could binary search on them. Finally, go through each i from 1 to n and then for each of the substrings of s[i], using binary search count the number of occurrences of its hash in the vector "all" and the vector a[i]. If these numbers are equal, then this substring occurred only in the string s[i] and can be used as a key substring. By changing the base and modulo of the hash, you can pass the WA caused by collision of hashes (I used p = 2313 and mod = 1000000123). The time complexity will be O(max_len * n^2 * log(n)), where max_len is the maximal length of a string.