Phil in the Blanks

Phil is trying to solve a series of puzzles in which he must fill in the blanks of a sentence with number words so that the statement becomes true. Being a programmer, you decide to write a program that finds all the possible solutions. Here is an example puzzle:

There are ___ Os and ___ Ts in this sentence.

One possible solution is to put "two" in the first blank and "five" in the second blank. Note that "one" would not work in the first blank, because the word "one" itself contains one "O" — the words written into the blanks are part of the puzzle and are counted too. Grammar is not considered.

The first line contains a single integer $D$ ($1 \le D \le 100$), the number of data sets. Each of the following $D$ lines contains one puzzle to solve.

Each puzzle is between 1 and 100 characters long (inclusive) and contains between 1 and 4 (inclusive) positive assertions, each of one of the following forms:

• ___ Cs — the blank is the number of occurrences (upper- and lowercase) of the indicated letter $C$ in the puzzle.
• ___ letters — the blank is the number of letters in the puzzle.
• ___ vowels — the blank is the number of vowels in the puzzle; for this problem only A, E, I, O, and U are vowels.
• ___ consonants — the blank is the number of consonants in the puzzle.

Each blank consists of three underscore characters (_) in a row, and the literal words letters, vowels, and consonants are always lowercase. Any underscore characters appearing in a puzzle are part of a blank.

For each data set, output the number of possible correct solutions. Every number word used ranges from "zero" to "one hundred".