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:
def reflection(line, point):
    x0, y0, x1, y1 = line
    p, q = point
    x1 -= x0; y1 -= y0
    p -= x0; q -= y0
    cv = p*x1 + q*y1
    sv = p*y1 - q*x1
    cv2 = cv**2 - sv**2
    sv2 = 2*cv*sv
    dd = (p**2 + q**2)*(x1**2 + y1**2)
    if dd == 0:
        return x0 + p, y0 + q
    return x0 + (cv2 * p - sv2 * q) / dd, y0 + (sv2 * p + cv2 * q) / dd

def solve():
    x0, y0, x1, y1 = map(int, input().split())
    q = int(input())
    for i in range(q):
        x, y = map(int, input().split())
        print("%.16f %.16f" % reflection((x0, y0, x1, y1), (x, y)))
solve()