Solve the programming task below in a Python markdown code block.
Chef has an integer N. He repeats the following operation until N becomes 1.

- Chef chooses an integer X such that X > 1 and X is a divisor of N and then divides N by X (the new value of N becomes N/X). If X is even, Chef gets A points otherwise he gets B points

Can you find the maximum points Chef can get if he performs the operations optimally?

------ Input Format ------ 

- First line will contain T, number of testcases. Then the testcases follow.
- Each testcase contains of a single line of input containing three integers N, A, B.

------ Output Format ------ 

For each testcase, output in a single line the maximum points Chef can get.

------ Constraints ------ 

$1 ≤ T ≤ 2\cdot10^{3}$
$2 ≤ N ≤ 10^{9}$
$-10^{3}≤ A, B ≤ 10^{3}$

----- Sample Input 1 ------ 
4
10 2 3
15 5 -2
12 2 3
8 -1 0

----- Sample Output 1 ------ 
5
-2
7
-1

----- explanation 1 ------ 
Test case $1$: First Chef divides $N = 10$ by $2$ and gets $2$ points and then divides by $5$ and thus gets $3$ points. Hence Chef gets a total of $2 + 3 = 5$ points.

Test case $2$: Chef divides $N$ by $15$. Hence he gets $-2$ points.