Beautiful Lyrics
Contest: Codeforces Round 566 (Div. 2)
Difficulty rating: 1700
Tags: data structures, greedy, strings

You are given $$$n$$$ words, each of which consists of lowercase alphabet letters. Each word contains at least one vowel. You are going to choose some of the given words and make as many beautiful lyrics as possible.

Each lyric consists of two lines. Each line consists of two words separated by whitespace.

A lyric is beautiful if and only if it satisfies all conditions below.

- The number of vowels in the first word of the first line is the same as the number of vowels in the first word of the second line.
- The number of vowels in the second word of the first line is the same as the number of vowels in the second word of the second line.
- The last vowel of the first line is the same as the last vowel of the second line. Note that there may be consonants after the vowel.

Also, letters "a", "e", "o", "i", and "u" are vowels. Note that "y" is never vowel.

For example of a beautiful lyric,

"hello hellooowww" "whatsup yowowowow"

For example of a not beautiful lyric,

"hey man""iam mcdic"

How many beautiful lyrics can you write from given words? Note that you cannot use a word more times than it is given to you. For example, if a word is given three times, you can use it at most three times.

Input format:
The first line contains single integer $$$n$$$ ($$$1 \le n \le 10^{5}$$$) — the number of words.

The $$$i$$$-th of the next $$$n$$$ lines contains string $$$s_{i}$$$ consisting lowercase alphabet letters — the $$$i$$$-th word. It is guaranteed that the sum of the total word length is equal or less than $$$10^{6}$$$. Each word contains at least one vowel.

Output format:
In the first line, print $$$m$$$ — the number of maximum possible beautiful lyrics.

In next $$$2m$$$ lines, print $$$m$$$ beautiful lyrics (two lines per lyric).

If there are multiple answers, print any.

Constraints:
Time limit: 1.0 s
Memory limit: 256.0 MB

Note:
In the first example, those beautiful lyrics are one of the possible answers. Let's look at the first lyric on the sample output of the first example. "about proud hooray round" forms a beautiful lyric because "about" and "hooray" have same number of vowels, "proud" and "round" have same number of vowels, and both lines have same last vowel. On the other hand, you cannot form any beautiful lyric with the word "codeforces".

In the second example, you cannot form any beautiful lyric from given words.

In the third example, you can use the word "same" up to three times.

Example input:
14
wow
this
is
the
first
mcdics
codeforces
round
hooray
i
am
proud
about
that

Example output:
3
about proud
hooray round
wow first
this is
i that
mcdics am

Example input:
7
arsijo
suggested
the
idea
for
this
problem

Example output:
0

Editorial:
Let's make some definitions;
• $$$s_{1}$$$ and $$$s_{2}$$$ are complete duo if two word $$$s_{1}$$$ and $$$s_{2}$$$ have same number of vowels and the last vowels of $$$s_{1}$$$ and $$$s_{2}$$$ are same. For example, "hello" and "hollow" are complete duo.
• $$$s_{1}$$$ and $$$s_{2}$$$ are semicomplete duo if two word $$$s_{1}$$$ and $$$s_{2}$$$ have same number of vowels but the last vowels of $$$s_{1}$$$ and $$$s_{2}$$$ are different. For example, "hello" and "hola" are semicomplete duo.
If you want to form a beautiful lyric with $$$4$$$ words, then the lyric must be one of the things listed below;
• Consist of two complete duos.
• Consist of one semicomplete duo and one complete duo.
Since the order of lyrics is not important, make complete duos as many as possible, then make semicomplete duos as many as possible. This can be done with the greedy approach with the usage of the red-black tree or hashmap.
After you formed all duos, make beautiful lyrics using one semicomplete duo and one complete duo first, then make beautiful lyrics using two complete duos. With this method, you can make the maximum possible number of beautiful lyrics.
Time complexity is $$$O(n \text{ log } n)$$$ or $$$O(n)$$$.