Shortest Bridge

The city is a square 1,000 units on a side. A large river runs through it from north to south and splits the city into exactly two parts, the west part and the east part.

The mayor has decided to build a highway from a point $s$ in the west part to a point $t$ in the east part. A highway is one bridge over the river plus two roads. One road joins $s$ to the west end of the bridge, and the other joins $t$ to the east end. The bridge is a straight segment between a point on the west riverside and a point on the east riverside. A road does not have to be a straight line, but the length of its intersection with the river must be zero.

To keep the cost down, the mayor builds a highway that meets both of these conditions.

• A bridge costs more than a road, so the length of the bridge joining the west part and the east part must be as short as possible.
• Under that condition, the sum of the lengths of the two roads must be as small as possible.

Write a program that computes the total length of a highway meeting both conditions.

The input is a single test case in the following format.

sx sy tx ty
N
wx1 wy1
:
:
wxN wyN
M
ex1 ey1
:
:
exM eyM

A point in the city is written as a coordinate $(x, y)$, where $x$ is the distance from the west side and $y$ is the distance from the north side.

The first line contains four integers $s_x$, $s_y$, $t_x$, $t_y$ ($0 \le s_x, s_y, t_x, t_y \le 1000$). Point $s$ is at $(s_x, s_y)$ and point $t$ is at $(t_x, t_y)$. The next line contains an integer $N$ ($2 \le N \le 20$), the number of points that make up the west riverside. Each of the next $N$ lines contains two integers $wx_i$ and $wy_i$ ($0 \le wx_i, wy_i \le 1000$), and the $i$-th point of the west riverside is $(wx_i, wy_i)$. The west riverside is the polygonal line built from the segments between $(wx_i, wy_i)$ and $(wx_{i+1}, wy_{i+1})$ for all $1 \le i \le N-1$. The next line contains an integer $M$ ($2 \le M \le 20$), the number of points that make up the east riverside. Each of the next $M$ lines contains two integers $ex_i$ and $ey_i$ ($0 \le ex_i, ey_i \le 1000$), and the $i$-th point of the east riverside is $(ex_i, ey_i)$. The east riverside is built the same way.

The input satisfies the following conditions.

• $wy_1$ and $ey_1$ are 0, and $wy_N$ and $ey_M$ are 1,000.
• Neither polygonal line intersects itself.
• The west riverside and the east riverside do not meet.
• Point $s$ lies in the west part of the city. That is, $s$ lies in the region bounded by the sides of the square and the west polygonal line that does not contain the points of the east riverside.
• Point $t$ lies in the east part of the city. That is, $t$ lies in the region bounded by the sides of the square and the east polygonal line that does not contain the points of the west riverside.
• Each polygonal line meets the square only at its two end points. In other words, $0 < wx_i, wy_i < 1000$ holds for $2 \le i \le N-1$, and $0 < ex_i, ey_i < 1000$ holds for $2 \le i \le M-1$.

Print the length of the bridge and the total length of the highway on one line, separated by a single space. The total length of the highway is the bridge plus the two roads. Print both values with exactly four digits after the decimal point.