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 PYTHON3):

Solution:
#!/usr/bin/env python3
# CGL_1_B: Points/Vectors - Reflection


def dprod(v1, v2):
    x1, y1 = v1
    x2, y2 = v2
    return x1 * x2 + y1 * y2


def proj(p1, p2, p):
    x1, y1 = p1
    x2, y2 = p2
    x, y = p

    v1 = (x2-x1, y2-y1)
    v2 = (x-x1, y-y1)
    r = dprod(v1, v2) / dprod(v1, v1)

    return (x1 + r*v1[0], y1 + r*v1[1])


def refl(p1, p2, p):
    px, py = p
    hx, hy = proj(p1, p2, p)
    return (px + 2.0*(hx - px), py + 2.0*(hy - py))


def run():
    x1, y1, x2, y2 = [int(i) for i in input().split()]
    q = int(input())

    for _ in range(q):
        x, y = [int(i) for i in input().split()]
        print("{:.10f} {:.10f}".format(*refl((x1, y1), (x2, y2), (x, y))))


if __name__ == '__main__':
    run()