Problem Statement

There are $n$ pieces of trash in a park.
A group of $n$ neighborhood volunteers is going to collect them.

Person $i (0 \le i < n)$ is initially at $(a_i, 0)$. Trash $j (0 \le j < n)$ is initially at $(x_j, y_j)$.
Initially, person $i$ and trash $j$ are sorted along the x-axis ($a_0 \le a_1 \le \cdots \le a_{n-1}$, $x_0 \le x_1 \le \cdots \le x_{n-1}$).

The effort for person $i$ to collect all of trash $j$, trash $j+1$, ..., trash $i (0 \le j \le i)$ is the cube of the 3-norm between trash $j$ and person $i$.
The cube of the 3-norm between point $(x_0, y_0)$ and point $(x_1, y_1)$ is $|x_0-x_1|^3+|y_0-y_1|^3$.
Person $i$ cannot collect trash $j > i$. If person $i$ collects no trash, that person's effort is $0$.

Minimize the total effort required to collect all the trash.

Input

n
a_0 a_1 ... a_{n-1}
x_0 x_1 ... x_{n-1}
y_0 y_1 ... y_{n-1}

$1 \le n \le 3\times 10^5$
$0 \le a_i, x_i, y_i \le 10^5 (0 \le i < n)$
$a_0 \le a_1 \le \cdots \le a_{n-1}$
$x_0 \le x_1 \le \cdots \le x_{n-1}$

Output

The answer may not fit in a 32-bit integer.
Print a newline at the end.

Sample