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(float,input().split())
det = x1 - x2
if det != 0:
    a = (y1 - y2) / det
    b = (-(y1 * x2) + y2 * x1) / det

q = int(input())
x,y = [],[]
for i in range(q):
    x_t,y_t = map(float,input().split())
    x.append(x_t)
    y.append(y_t)

if det == 0:
    for i in range(q):
        print(-x[i],y[i])
elif y2 == y1:
    for i in range(q):
        print(x[i],-y[i])
else:
    for i in range(q):
        k = y[i] + 1/a * x[i]
        s = (k - b)/(a + 1/a)
        print(s+(s-x[i]),-1/a * (s+(s-x[i])) + k)