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:
x1, y1, x2, y2 = map(int, input().split())
q = int(input())

p1, p2 = complex(x1, y1), complex(x2, y2)
p1p2 = p2 - p1
d2_p1p2 = p1p2.real ** 2 + p1p2.imag ** 2

while q:
    q -= 1
    p0 = complex(*map(int, input().split()))
    p1p0 = p0 - p1
    t = (p1p2.real * p1p0.real + p1p2.imag * p1p0.imag) / d2_p1p2
    ref = p0 + 2 * (p1p2 * t - p1p0)
    print(ref.real, ref.imag)