Happy Number

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Bit Manipulation

Happy Number

Determine whether repeatedly replacing a number with the sum of the squares of its digits eventually reaches 1.

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Problem Statement

Given a positive integer n, repeatedly transform it by replacing the number with the sum of the squares of its decimal digits.

A number is called happy if this process eventually reaches 1. If the process enters a cycle that does not include 1, the number is unhappy.

Return whether the given number is happy.

Input Format

A single integer n.
You may assume n > 0.

Output Format

Return true if n is a happy number.
Otherwise, return false.

Constraints

1 <= n
The number may be transformed repeatedly until it reaches 1 or a cycle is detected.

Examples

Sample cases returned by the problem API.

Example 1

Input

n = 19

Output

true

Explanation

19 -> $1^{2}+9$ ^2 = 82 -> $8^{2}+2$ ^2 = 68 -> $1^{2}+8$ ^2 = 65 -> 61 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 ... The process eventually reaches a cycle that does not include 1, so 19 is not happy? Wait, this example should be the classic happy-number example. Correct sequence: 19 -> 82 -> 68 -> 100 -> 1. The number 19 is happy.

Example 2

Input

n = 2

Output

false

Explanation

2 -> 4 -> 16 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 ... The sequence repeats without reaching 1.

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