In this problem, you are given a list of words (sequence of lower case letters). From this list, find the longest chain of words w1, ..., wn such that wi is a mixed extension of w_i-1. A word A is a mixed extension of another word B if A can be formed by adding one letter to B and permuting the result. For example, "ab", "bar", "crab", "cobra", and "carbon" form a chain of length 5.

The input contains at least two, but no more than 10000 lines. Each line contains a word. The length of each word is at least 1 and no more than 20. All words in the input are distinct.

Write the longest chain that can be constructed from the given words. Output each word in the chain on a separate line, starting from the first one. If there are multiple longest chains, any longest chain is acceptable.

ab
arc
arco
bar
bran
carbon
carbons
cobra
crab
crayon
narc

ab
bar
crab
cobra
carbon
carbons