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A. There Are Two Types Of Burgers

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere are two types of burgers in your restaurant — hamburgers and chicken burgers! To assemble a hamburger you need two buns and a beef patty. To assemble a chicken burger you need two buns and a chicken cutlet.

You have $$$b$$$ buns, $$$p$$$ beef patties and $$$f$$$ chicken cutlets in your restaurant. You can sell one hamburger for $$$h$$$ dollars and one chicken burger for $$$c$$$ dollars. Calculate the maximum profit you can achieve.

You have to answer $$$t$$$ independent queries.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 100$$$) – the number of queries.

The first line of each query contains three integers $$$b$$$, $$$p$$$ and $$$f$$$ ($$$1 \le b, ~p, ~f \le 100$$$) — the number of buns, beef patties and chicken cutlets in your restaurant.

The second line of each query contains two integers $$$h$$$ and $$$c$$$ ($$$1 \le h, ~c \le 100$$$) — the hamburger and chicken burger prices in your restaurant.

Output

For each query print one integer — the maximum profit you can achieve.

Example

Input

3 15 2 3 5 10 7 5 2 10 12 1 100 100 100 100

Output

40 34 0

Note

In first query you have to sell two hamburgers and three chicken burgers. Your income is $$$2 \cdot 5 + 3 \cdot 10 = 40$$$.

In second query you have to ell one hamburgers and two chicken burgers. Your income is $$$1 \cdot 10 + 2 \cdot 12 = 34$$$.

In third query you can not create any type of burgers because because you have only one bun. So your income is zero.

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