Determining a Happy Number

Given a positive integer \( n \), determine if it is a Happy Number. A happy number is defined by the following process:

• Replace the number by the sum of the squares of its digits, i.e. compute \( s(n)=\sum_{i=1}^{k} d_i^2 \), where \( d_i \) represents each digit of \( n \).
• Repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle that does not include 1.

If the process results in 1 within 100 iterations, then \( n \) is considered a Happy Number. Otherwise, if a cycle is detected or 100 iterations are reached without arriving at 1, \( n \) is Not Happy.

Examples:

• For \( n=19 \), the sequence eventually reaches 1, so the answer is "Happy".
• For \( n=4 \), the process does not reach 1 in 100 steps and falls into a cycle, so it is "Not Happy".

inputFormat

The input consists of a single integer \( n \) provided via standard input.

outputFormat

Output a single line to standard output containing either "Happy" if \( n \) is a happy number, or "Not Happy" otherwise.

## sample

19

Happy

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