#D12817. There Are Two Types Of Burgers
There Are Two Types Of Burgers
There Are Two Types Of Burgers
There 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 ≤ t ≤ 100) – the number of queries.
The first line of each query contains three integers b, p and f (1 ≤ b, ~p, ~f ≤ 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 ≤ h, ~c ≤ 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 ⋅ 5 + 3 ⋅ 10 = 40.
In second query you have to ell one hamburgers and two chicken burgers. Your income is 1 ⋅ 10 + 2 ⋅ 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.
inputFormat
Input
The first line contains one integer t (1 ≤ t ≤ 100) – the number of queries.
The first line of each query contains three integers b, p and f (1 ≤ b, ~p, ~f ≤ 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 ≤ h, ~c ≤ 100) — the hamburger and chicken burger prices in your restaurant.
outputFormat
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 ⋅ 5 + 3 ⋅ 10 = 40.
In second query you have to ell one hamburgers and two chicken burgers. Your income is 1 ⋅ 10 + 2 ⋅ 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.
样例
3
15 2 3
5 10
7 5 2
10 12
1 100 100
100 100
40
34
0