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 CPP):

Solution:
#include<iostream>
#include<cmath>
#include<iomanip>
using namespace std;
int main(){
	double x0, y0, x1, y1, x, y, xt, yt;
	int i,q;

	cin >> x0 >> y0 >> x1 >> y1;

	for (cin >> q, i = 0; cin >> x >> y, i < q; ++i){
		double ang = atan2(y-y0,x-x0) - atan2(y1-y0,x1-x0);

		xt = (x-x0)*cos(ang * 2) + (y-y0)*sin(ang * 2) + x0;
		yt = -(x-x0)*sin(ang * 2) + (y-y0)*cos(ang * 2) + y0;

		cout << fixed << setprecision(10) << xt << " " << yt << endl;
	}
}