B. Binary Pathtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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:   Find the lexicographically smallest^\dagger string you can attain by choosing any available path;  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.InputEach 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.OutputFor each test case, output two lines:   The lexicographically smallest string you can attain by choosing any available path;  The number of paths that yield this string. ExampleInput
32000041101110080010011111101101Output
000
2
11000
1
001001101
4
NoteIn 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:  
32000041101110080010011111101101
000 2 11000 1 001001101 4 
['dp', 'greedy', 'implementation', '*1300']