At a police line-up a witness to a crime sought to identify a criminal from among four men. The witness looked for a man who was not tall, not fair, not skinny, and not good-looking; though looking for any of these characteristics may not have been valid.

In the line-up:

1. Four men each stood next to at least one tall man.
2. Exactly three men each stood next to at least one fair man.
3. Exactly two men each stood next to at least one skinny man.
4. Exactly one man stood next to at least one good-looking man.

Of the four men:

5. The first man was fair, the second man was skinny, the third man was tall, and the fourth man was good-looking.
6. No two men have more than one characteristic - tall, fair, skinny, good-looking - in common.
7. Just one man had more than two looked-for characteristics, i.e. not tall, not fair, not skinny, not good-looking; this man was identified as the criminal by the witness.

Which man-first, second, third or fourth-was identified as the criminal by the witness?