Pizza Delivery

A pizza house stands at a fixed point on a straight road, and many customer houses lie along that same road. To attract more orders, the owner promises a late-delivery discount: once a fixed grace period has passed after an order is placed, a penalty of 1 won accrues for every unit of time until the pizza is handed over.

Today every house ordered at the same moment, and delivery begins exactly when the grace period ends, so the penalty starts counting from time $0$. The owner drives at a speed of one unit of distance per unit of time, and handing a pizza to a customer takes no time.

The profit from serving a customer equals that customer's earning minus the accumulated late penalty, and that penalty equals the time at which the pizza reaches them. On a busy day the owner may skip a customer whenever the penalty would exceed the earning, since serving them would lose money. Decide which customers to serve, and in what order, so that the total profit is as large as possible.

For example, the figure below shows five customers $c_1, \ldots, c_5$, their positions relative to the pizza house, and the earning from each.

If the delivery order is $\langle c_4, c_3, c_2, c_5, c_1 \rangle$, the late penalties are $2$ for $c_4$, $5$ for $c_3$, $7$ for $c_2$, $15$ for $c_5$, and $26$ for $c_1$, so the per-customer profits are $3, -3, 3, 5, 1$. Because serving $c_3$ loses $3$, it is better to skip $c_3$, and this order yields a total profit of $12$. The best the owner can do for this instance is $32$, achieved by the order $\langle c_3, c_2, c_1, c_5 \rangle$ (skipping $c_4$).

Given the customers' positions relative to the pizza house and the earning from each, compute the maximum total profit.

The first line contains the number of test cases $T$. Each test case is given on three lines.

• The first line contains an integer $n$ ($1 \le n \le 100$), the number of customers.
• The second line contains $n$ integers $p_1 < p_2 < \cdots < p_n$ (each $p_i \ne 0$), where $p_i$ is the position of the $i$-th customer relative to the pizza house.
• The third line contains $n$ integers $e_1, e_2, \ldots, e_n$ (each $e_i > 0$), where $e_i$ is the earning from serving customer $i$.

Every integer on the second and third lines lies between $-100000$ and $100000$ inclusive.

For each test case, print a single line containing the maximum total profit obtainable by delivering pizzas to the customers.