apaz/codeforces-genesys huggingface dataset:
You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
You are given a $$$2 \times n$$$ grid filled with zeros and ones. Let the number at the intersection of the $$$i$$$-th row and the $$$j$$$-th column be $$$a_{ij}$$$.

There is a grasshopper at the top-left cell $$$(1, 1)$$$ that can only jump one cell right or downwards. It wants to reach the bottom-right cell $$$(2, n)$$$. Consider the binary string of length $$$n+1$$$ consisting of numbers written in cells of the path without changing their order.

Your goal is to:

1. Find the lexicographically smallest$$$^\dagger$$$ string you can attain by choosing any available path;
2. Find the number of paths that yield this lexicographically smallest string.

$$$^\dagger$$$ If two strings $$$s$$$ and $$$t$$$ have the same length, then $$$s$$$ is lexicographically smaller than $$$t$$$ if and only if in the first position where $$$s$$$ and $$$t$$$ differ, the string $$$s$$$ has a smaller element than the corresponding element in $$$t$$$.

## Input Format
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$).

The second line of each test case contains a binary string $$$a_{11} a_{12} \ldots a_{1n}$$$ ($$$a_{1i}$$$ is either $$$0$$$ or $$$1$$$).

The third line of each test case contains a binary string $$$a_{21} a_{22} \ldots a_{2n}$$$ ($$$a_{2i}$$$ is either $$$0$$$ or $$$1$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

## Output Format
For each test case, output two lines:

1. The lexicographically smallest string you can attain by choosing any available path;
2. The number of paths that yield this string.

## Examples
```input
3
2
00
00
4
1101
1100
8
00100111
11101101
```
```output
000
2
11000
1
001001101
4
```

## Note
In the first test case, the lexicographically smallest string is $$$\mathtt{000}$$$. There are two paths that yield this string:

In the second test case, the lexicographically smallest string is $$$\mathtt{11000}$$$. There is only one path that yields this string:

Now solve the problem and return the code.