## Goal

A **happy number** is defined by the following process:

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 **unhappy** numbers.

Given a list of numbers, classify each of them as happy or unhappy.
Input

**Line 1:** An integer `N` for the number of numbers to test.

**Following **`N` Lines: Each line has a positive integer you should test whether it is happy or not.

Be aware that some input numbers are really BIG, much bigger than your Integer type can handle. Find a way to overcome it.

Output

Output `N` lines.

Following the same order as inputs, each line starts with a given number from the list, a space, and then an ascii art **:)** or **:(** to indicate this number is happy or unhappy.

Constraints

1 ≤ `N` ≤ 100

0 < each number ≤ 10^26