A. Joey Takes Moneytime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputJoey is low on money. His friend Chandler wants to lend Joey some money, but can't give him directly, as Joey is too proud of himself to accept it. So, in order to trick him, Chandler asks Joey to play a game.In this game, Chandler gives Joey an array a_1, a_2, \dots, a_n (n \geq 2) of positive integers (a_i \ge 1).Joey can perform the following operation on the array any number of times:   Take two indices i and j (1 \le i < j \le n).  Choose two integers x and y (x, y \ge 1) such that x \cdot y = a_i \cdot a_j.  Replace a_i by x and a_j by y. In the end, Joey will get the money equal to the sum of elements of the final array. Find the maximum amount of money \mathrm{ans} Joey can get but print 2022 \cdot \mathrm{ans}. Why multiplied by 2022? Because we are never gonna see it again!It is guaranteed that the product of all the elements of the array a doesn't exceed 10^{12}. InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \leq t \leq 4000). Description of the test cases follows.The first line of each test case contains a single integer n (2 \leq n \leq 50) — the length of the array a.The second line contains n integers a_1, a_2, \dots, a_n (1 \leq a_i \leq 10^6) — the array itself.It's guaranteed that the product of all a_i doesn't exceed 10^{12} (i. e. a_1 \cdot a_2 \cdot \ldots \cdot a_n \le 10^{12}).OutputFor each test case, print the maximum money Joey can get multiplied by 2022.ExampleInput
332 3 221 331000000 1000000 1Output
28308
8088
2022000000004044
NoteIn the first test case, Joey can do the following:   He chooses i = 1 and j = 2 (so he has a[i] \cdot a[j] = 6), chooses x = 6 and y = 1 and makes a[i] = 6 and a[j] = 1. [2, 3, 2] \xrightarrow[x = 6,\; y = 1]{i = 1,\; j = 2} [6, 1, 2] He chooses i = 1 and j = 3 (so he has a[i] \cdot a[j] = 12), chooses x = 12 and y = 1 and makes a[i] = 12 and a[j] = 1. [6, 1, 2] \xrightarrow[x = 12,\; y = 1]{i = 1,\; j = 3} [12, 1, 1]  The sum is 14 which is the maximum of all possible sums. The answer is 2022 \cdot 14 = 28308.
332 3 221 331000000 1000000 1
28308 8088 2022000000004044 
['greedy', 'math', '*800']