Compound Words

You are given a dictionary and must find all of its two-word compound words. A two-word compound word is a word in the dictionary that can be written as the concatenation of exactly two other words that are also in the dictionary. The two parts need not be distinct: a word formed by joining two copies of the same dictionary word also counts. Because each part is shorter than the whole, each part is necessarily a different word from the compound itself.

The input consists of a number of lowercase words, one per line, given in alphabetical order. There are at most 120,000 words.

Output all of the compound words, one per line, in alphabetical order.