You are given two arrays (a_1, a_2, \ldots, a_n) and (b_1, b_2, \ldots, b_n). You must perform the following operation exactly once : choose any indices (l) and (r) such that (1 \le l \le r \le n); swap (a_i) and (b_i) for all (i) such that (l \leq i \leq r). Find the maximum possible value of (\text{gcd}(a_1, a_2, \ldots, a_n) + \text{gcd}(b_1, b_2, \ldots, b_n)) after performing the operation exactly once. Also find the number of distinct pairs ((l, r)) which achieve the maximum value. In the first line of the input, you are given a single integer (t) ((1 \le t \le 10^5)), the number of test cases. Then the description of each test case follows. In the first line of each test case, you are given a single integer (n) ((1 \le n \le 2 \cdot 10^5)), representing the number of integers in each array. In the next line, you are given (n) integers (a_1, a_2, \ldots, a_n) ((1 \le a_i \le 10^9)) — the elements of the array (a). In the last line, you are given (n) integers (b_1, b_2, \ldots, b_n) ((1 \le b_i \le 10^9)) — the elements of the array (b). The sum of values of (n) over all test cases does not exceed (5 \cdot 10^5). For each test case, output a line with two integers: the maximum value of (\text{gcd}(a_1, a_2, \ldots, a_n) + \text{gcd}(b_1, b_2, \ldots, b_n)) after performing the operation exactly once, and the number of ways. In the first, third, and fourth test cases, there's no way to achieve a higher GCD than (1) in any of the arrays, so the answer is (1 + 1 = 2). Any pair ((l, r)) achieves the same result; for example, in the first test case there are (36) such pairs. In the last test case, you must choose (l = 1), (r = 2) to maximize the answer. In this case, the GCD of the first array is (5), and the GCD of the second array is (1), so the answer is (5 + 1 = 6), and the number of ways is (1).