Problem: For given three points p1, p2, p, find the reflection point x of p onto p1p2.

<image>

Constraints

* 1 ≤ q ≤ 1000
* -10000 ≤ xi, yi ≤ 10000
* p1 and p2 are not identical.

Input


xp1 yp1 xp2 yp2
q
xp0 yp0
xp1 yp1
...
xpq−1 ypq−1


In the first line, integer coordinates of p1 and p2 are given. Then, q queries are given for integer coordinates of p.

Output

For each query, print the coordinate of the reflection point x. The output values should be in a decimal fraction with an error less than 0.00000001.

Examples

Input

0 0 2 0
3
-1 1
0 1
1 1


Output

-1.0000000000 -1.0000000000
0.0000000000 -1.0000000000
1.0000000000 -1.0000000000


Input

0 0 3 4
3
2 5
1 4
0 3


Output

4.2400000000 3.3200000000
3.5600000000 2.0800000000
2.8800000000 0.8400000000

Solution (in PYTHON):

Solution:
# coding: utf-8
class Point():
    def __init__(self, x, y):
        self.x = x
        self.y = y

init_point = map(float,raw_input().split())
p0 = Point(init_point[0], init_point[1])
p1 = Point(init_point[2], init_point[3])

q = int(raw_input())
for i in range(q):
    xp2,yp2 = map(float,raw_input().split())
    p2 = Point(xp2,yp2)
    p0p2 = Point(p2.x - p0.x, p2.y - p0.y)
    p0p1 = Point(p1.x - p0.x, p1.y - p0.y)
    k = ((p0p2.x * p0p1.x + p0p2.y * p0p1.y)/(p0p1.x ** 2 + p0p1.y ** 2))
    # p2t??¨p0p1????????????T??¨??????
    p0T = Point(k * p0p1.x, k * p0p1.y)
    OT = Point(p0.x + p0T.x, p0.y + p0T.y)
    p2t = Point(2*(OT.x - p2.x), 2*(OT.y - p2.y))
    Ot =  Point(p2t.x + xp2, p2t.y + p2.y)
    print "%.10f %.10f" % (Ot.x, Ot.y)