Set-Theoretic Number Notation

Seonyeong relies heavily on calculators and computers, so she cannot do arithmetic in her head at all. She is not alone: many of her friends also cannot perform even simple calculations without an electronic device.

So Seonyeong invented a new way of adding based on set theory. With this notation you can add non-negative integers. First, every non-negative integer is written as a set using the following rules.

• $0$ is the empty set {}.
• A number $n > 0$ is written as the set containing every number smaller than $n$.

Below is how $0$ through $3$ are written in this notation.

0 => {}
1 => {{}}
2 => {{},{{}}}
3 => {{},{{}},{{},{{}}}}

The number of elements in a set equals the value it represents. The elements of a set have no order, but to avoid confusion they are always written in increasing order of the size of each element (every element is itself a set).

Given two numbers written in this set notation, write a program that outputs their sum in the same set notation.

The first line contains the number of test cases $T$. Each test case consists of two lines, and each line contains one number written in the set notation. The sum of the two numbers is always at most $15$.

For each test case, print the sum of the two given numbers in the set notation on its own line.