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

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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 PYTHON3):

Solution:
from sys import stdin
readline = stdin.readline

def main():
    x1, y1, x2, y2 = map(int, readline().split())
    p1, p2 = x1 + y1 * 1j, x2 + y2 * 1j
    q = int(readline())
    for i in range(q):
        xi, yi = map(int, readline().split())
        pi = xi + yi * 1j
        cross = p1 + (p2 - p1) * projecter(p2 - p1, pi - p1)
        cross = cross * 2 - pi
        print('{:.10f} {:.10f}'.format(cross.real, cross.imag))


def projecter(a, b):
    return dot(a, b) / dot(a, a)


def dot(a, b):
    return a.real * b.real + a.imag * b.imag
main()