Flower gives Gellyfish two permutations(^{\text{∗}}) of (0, 1, \ldots, n-1): (p_0, p_1, \ldots, p_{n-1}) and (q_0, q_1, \ldots, q_{n-1}). Now Gellyfish wants to calculate an array (r_0,r_1,\ldots,r_{n-1}) through the following method: For all (i) ((0 \leq i \leq n-1)), (r_i = \max\limits_{j=0}^{i} \left(2^{p_j} + 2^{q_{i-j}} \right)) But since Gellyfish is very lazy, you have to help her figure out the elements of (r). Since the elements of (r) are very large, you are only required to output the elements of (r) modulo (998\,244\,353). (^{\text{∗}})An array (b) is a permutation of an array (a) if (b) consists of the elements of (a) in arbitrary order. For example, (4,2,3,4) is a permutation of (3,2,4,4) while (1,2,2) is not a permutation of (1,2,3). 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) ((1 \leq n \leq 10^5)). The second line of each test case contains (n) integers (p_0, p_1, \ldots,p_{n-1}) ((0 \leq p_i < n)). The third line of each test case contains (n) integers (q_0, q_1, \ldots,q_{n-1}) ((0 \leq q_i < n)). It is guaranteed that both (p) and (q) are permutations of (0, 1, \ldots, n-1). It is guaranteed that the sum of (n) over all test cases does not exceed (10^5). For each test case, output (n) integers (r_0, r_1, \ldots, r_{n-1}) in a single line, modulo (998\,244\,353). In the first test case: (r_0 = 2^{p_0} + 2^{q_0} = 1+2=3) (r_1 = \max(2^{p_0} + 2^{q_1}, 2^{p_1} + 2^{q_0}) = \max(1+4, 4+2) = 6) (r_2 = \max(2^{p_0} + 2^{q_2}, 2^{p_1}+2^{q_1}, 2^{p_2}+2^{q_0}) = (1+1, 4+4, 2+2) = 8)