This is a run-twice (communication) interactive problem. There are two players: Ja the Ghost and Quack the Duck. The jury (otherwise known as the interactor of this problem) will first interact with Ja. After Ja ends the interaction, the jury will interact with Quack. Note that Ja and Quack may not directly pass information to each other; both players are only able to send information to or receive information from the jury. Before the interaction, the jury determines an integer (n) and an array of (n) positive integers (a_1, a_2, \ldots, a_n). These values are consistent across both players. Ja receives (n) and an array of (n) positive integers (a_1, a_2, \ldots, a_n) from the jury, which he wants to send to Quack, where (a_i \le 10^6). To do this, Ja will select an integer (k), where ()k \le \left\lceil \frac{10n}{9} \right\rceil + 150,() and create an array of positive integers (b_1, b_2, \ldots, b_k), where (b_i \le 10^6), and send it back to the jury. Then the jury will give Quack the integers (n) and (k). Quack can ask the jury at most (180n + 150) queries in the following form: Choose any two integers (i) and (j) ((1 \le i, j \le k), (i \neq j)), and the jury will respond with (\mathrm{gcd}(b_i, b_j)). Here, (\gcd(x, y)) denotes the greatest common divisor (GCD) of integers (x) and (y). Note that both (a) and (b) are hidden from Quack; Quack can only get information from queries. Ja wants to ensure that Quack can determine the original array (a). Your task is to act as both players and determine an optimal interaction strategy for both players so that Quack determines the original array (a) correctly. First Run Your code will run exactly twice on each test. On the first run, you will be Ja. Input The first line of the input contains the string first . The purpose of this is so your program recognizes that this is its first run, and it should a