Pride and Prejudice and Zombies

Pride and Prejudice and Zombies, by Jane Austen and Seth Grahame-Smith, reimagines the famous 1813 satire of marriage and social convention, now interrupted by zombies, skunks, ghouls, chipmunks, and ninjas. Most critics praised the novel as clever and insightful, though not everyone agreed.

A little-known fact: the book's release was delayed by some eight years because of heated disagreements between the author and the editors at the small Philadelphia publishing house that eventually printed it. The most impassioned argument centered on the controversial "Vampire Number" chapter, in which Mrs. Bennett -- desperate to rally the countryside's interest in matrimony -- stages a social event where 50 men and 50 women each draw a slip of paper from a large, feathery hat.

On each slip is a single three-digit number. The goal of the event: each woman must find the man whose three-digit number, when multiplied by her own, produces a six-digit number that reuses the digits of the two multiplicands in some order. The chapter was eventually cut, and its existence surfaced only recently.

Vampire numbers

A vampire number is a positive integer with an even number of digits -- say $2n$ -- such that its $2n$ digits can be split into two $n$-digit numbers whose product equals the original number. None of the three numbers may have leading zeros, and neither of the two $n$-digit numbers may contain two consecutive zeros anywhere.

For example:

• $125460 = 204 \times 615$, so $125460$ is a vampire number.
• $16758243290880 = 1982736 \times 8452080$, so it is a vampire number.
• $353$ has an odd number of digits, so it cannot be a vampire number.
• $3421$ cannot be split into two valid factors, so it is not a vampire number.

Given a series of numbers (each at most 18 digits), decide for each whether it is a vampire number.

The input consists of an arbitrary number of values, one per line, each with no leading zeros and no extra whitespace. Each number has at most 18 digits. The input ends with a single line containing 0, which must not produce any output.

For each input number, print the number, then a colon, then a space, then yes if the number is a vampire number or no if it is not.