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 PYTHON):

Solution:
x1,y1,x2,y2=map(float,raw_input().split(" "))
for i in xrange(int(raw_input())):
    px,py=map(float,raw_input().split(" "))
    dxa=(x2-x1)
    dya=(y2-y1)
    da=dxa**2+dya**2
    dxb=(px-x1)
    dyb=(py-y1)
    ip=dxb*dxa+dya*dyb
    r=ip/da
    kouten_x=x1+r*dxa
    kouten_y=y1+r*dya
    ref_x=px+2.0*(kouten_x-px)
    ref_y=py+2.0*(kouten_y-py)
    print "{0:.10f} {1:.10f}".format(ref_x,ref_y)