There is a city whose shape is a 1,000 $\times$ 1,000 square. The city has a big river, which flows from the north to the south and separates the city into just two parts: the west and the east.
Recently, the city mayor has decided to build a highway from a point $s$ on the west part to a point $t$ on the east part. A highway consists of a bridge on the river, and two roads: one of the roads connects $s$ and the west end of the bridge, and the other one connects $t$ and the east end of the bridge. Note that each road doesn't have to be a straight line, but the intersection length with the river must be zero.
In order to cut building costs, the mayor intends to build a highway satisfying the following conditions:
Your task is to write a program computing the total length of a highway satisfying the above conditions.
The input consists of a single test case. The test case is formatted as follows.
$sx$ $sy$ $tx$ $ty$
$N$
$wx_1$ $wy_1$
...
$wx_N$ $wy_N$
$M$
$ex_1$ $ey_1$
...
$ex_M$ $ey_M$
At first, we refer to a point on the city by a coordinate ($x, y$): the distance from the west side is $x$ and the distance from the north side is $y$.
The first line contains four integers $sx$, $sy$, $tx$, and $ty$ ($0 \leq sx, sy, tx, ty \leq 1,000$): points $s$ and $t$ are located at ($sx, sy$) and ($tx, ty$) respectively. The next line contains an integer $N$ ($2 \leq N \leq 20$), where $N$ is the number of points composing the west riverside. Each of the following $N$ lines contains two integers $wx_i$ and $wy_i$ ($0 \leq wx_i, wy_i \leq 1,000$): the coordinate of the $i$-th point of the west riverside is ($wx_i, wy_i$). The west riverside is a polygonal line obtained by connecting the segments between ($wx_i, wy_i$) and ($wx_{i+1}, wy_{i+1}$) for all $1 \leq i \leq N -1$. The next line contains an integer $M$ ($2 \leq M \leq 20$), where $M$ is the number of points composing the east riverside. Each of the following $M$ lines contains two integers $ex_i$ and $ey_i$ ($0 \leq ex_i, ey_i \leq 1,000$): the coordinate of the $i$-th point of the east riverside is ($ex_i, ey_i$). The east riverside is a polygonal line obtained by connecting the segments between ($ex_i, ey_i$) and ($ex_{i+1}, ey_{i+1}$) for all $1 \leq i \leq M - 1$.
You can assume that test cases are under the following conditions.
Output single-space separated two numbers in a line: the length of a bridge and the total length of a highway (i.e. a bridge and two roads) satisfying the above mayor's demand. The output can contain an absolute or a relative error no more than $10^{-8}$.
200 500 800 500 3 400 0 450 500 400 1000 3 600 0 550 500 600 1000
100 600
300 300 700 100 5 300 0 400 100 300 200 400 300 400 1000 4 700 0 600 100 700 200 700 1000
200 541.421356237
300 400 700 600 2 400 0 400 1000 2 600 0 600 1000
200 482.842712475
200 500 800 500 3 400 0 450 500 400 1000 5 600 0 550 500 600 100 650 500 600 1000
100 1200.326482915