Aurora Wednesday 18:30 Python Practice 22.08.03.

Question for Linear Search:
Creatnx now wants to decorate his house by flower pots. He plans to buy exactly N ones. He can only buy them from Triracle’s shop. There are only two kind of flower pots available in that shop. The shop is very strange. If you buy X flower pots of kind 1 then you must pay A×X² and B×Y² if you buy Y flower pots of kind 2. Please help Creatnx buys exactly N flower pots that minimizes money he pays.

Input Format
The first line contains a integer T denoting the number of test cases.
Each of test case is described in a single line containing three space-separated integers N,A,B.

Output Format
For each test case, print a single line containing the answer.

Constraints
1≤T≤105
1≤N,A,B≤105

Sample Input
2
5 1 2
10 2 4

Sample Output
17
134

Explanation
Query 1: we have to buy exactly 5 pots. There are six possible options:
Buy 0 pot of first kind, 5 pots of second kind. The cost is: 1×02+2×52=50.
Buy 1 pot of first kind, 4 pots of second kind. The cost is: 1×12+2×42=33.
Buy 2 pots of first kind, 3 pots of second kind. The cost is: 1×22+2×32=22.
Buy 3 pots of first kind, 2 pots of second kind. The cost is: 1×32+2×22=17.
Buy 4 pots of first kind, 1 pot of second kind. The cost is: 1×42+2×12=18.
Buy 5 pots of first kind, 0 pot of second kind. The cost is: 1×52+2×02=25.
So, the optimal cost is 17.