Each of the capital letters in bold denotes a different base ten digit from 0 to 9 to satisfy each of the following alphametic relationships. None of the numbers can contain any leading zero.

(i) ONE is a perfect square and:

(ii) Precisely one of TWO, THREE and FOUR is a perfect square, and:

(iii) Precisely one of TWO + 1, THREE + 1 and FOUR + 1 is a perfect square, and:

(iv) Precisely one of TWO + 2, THREE + 2 and FOUR + 2 is a perfect square.

Determine the number that is represented by FORTUNE.