CF1789D Serval and Shift-Shift-Shift

Serval has two $ n $ -bit binary integer numbers $ a $ and $ b $ . He wants to share those numbers with Toxel. Since Toxel likes the number $ b $ more, Serval decides to change $ a $ into $ b $ by some (possibly zero) operations. In an operation, Serval can choose any positive integer $ k $ between $ 1 $ and $ n $ , and change $ a $ into one of the following number: - $ a\oplus(a\ll k) $ - $ a\oplus(a\gg k) $ In other words, the operation moves every bit of $ a $ left or right by $ k $ positions, where the overflowed bits are removed, and the missing bits are padded with $ 0 $ . The bitwise XOR of the shift result and the original $ a $ is assigned back to $ a $ . Serval does not have much time. He wants to perform no more than $ n $ operations to change $ a $ into $ b $ . Please help him to find out an operation sequence, or determine that it is impossible to change $ a $ into $ b $ in at most $ n $ operations. You do not need to minimize the number of operations. In this problem, $ x\oplus y $ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of $ x $ and $ y $ . $ a\ll k $ and $ a\gg k $ denote the [logical left shift](https://en.wikipedia.org/wiki/Logical_shift) and [logical right shift](https://en.wikipedia.org/wiki/Logical_shift).

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1\le t\le2\cdot10^{3} $ ). The description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 1\le n\le2\cdot10^{3} $ ) — the number of bits in numbers $ a $ and $ b $ . The second and the third line of each test case contain a binary string of length $ n $ , representing $ a $ and $ b $ , respectively. The strings contain only characters 0 and 1. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot10^{3} $ .

For each test case, if it is impossible to change $ a $ into $ b $ in at most $ n $ operations, print a single integer $ -1 $ . Otherwise, in the first line, print the number of operations $ m $ ( $ 0\le m\le n $ ). If $ m>0 $ , in the second line, print $ m $ integers $ k_{1},k_{2},\dots,k_{m} $ representing the operations. If $ 1\le k_{i}\le n $ , it means logical left shift $ a $ by $ k_{i} $ positions. If $ -n\le k_{i}\le-1 $ , it means logical right shift $ a $ by $ -k_{i} $ positions. If there are multiple solutions, print any of them.

In the first test case: The first operation changes $ a $ into $ 00111\oplus\sout{001}11\underline{000}=11111 $ . The second operation changes $ a $ into $ 11111\oplus\underline{00}111\sout{11}=11000 $ . The bits with strikethroughs are overflowed bits that are removed. The bits with underline are padded bits. In the second test case, $ a $ is already equal to $ b $ , so no operations are needed. In the third test case, it can be shown that $ a $ cannot be changed into $ b $ .