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Happy Numbers

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A happy number is defined by the following Sequence: Starting with any positive integer, replace the number by the sum of the squares of its digits in base-ten, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle that does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are sad numbers.

For example, 19 is happy, as the associated Sequence is:

12 + 92 = 82
82 + 22 = 68
62 + 82 = 100
12 + 02 + 02 = 1.

Print all the happy numbers from 1 to 200 inclusive, each on their own line.

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