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:
import sys
input = sys.stdin.readline

def main():
    x1, y1, x2, y2 = map(int, input().split())
    q = int(input())
    if x2 - x1 == 0:# x = x1　の直線
        for i in range(q):
            xp, yp = map(int, input().split())
            print(xp + 2 * (x1 - xp), yp)
    else:
        m = (y2 - y1) / (x2 - x1)
        for i in range(q):
            xp, yp = map(int, input().split())
            yq = (2 * m * (xp - x1) + yp * (m * m - 1) + 2 * y1) / (1 + m * m)
            xq = xp - m * (yq - yp)
            print(xq, yq)

if __name__ == "__main__":
    main()