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 <bits/stdc++.h>
using namespace std;

struct Point 
{
  double x, y;
  
  Point() {}
  
  Point(double x, double y) : x(x), y(y) {}
  
  void input() { scanf("%lf %lf", &x, &y); }
  void output() { printf("%.10f %.10f\n", x, y); }
  double abs() { return (sqrt(norm())); }
  double norm() { return (x * x + y * y); }
  
  Point operator + (Point d) { return (Point(x + d.x, y + d.y)); }
  Point operator - (Point d) { return (Point(x - d.x, y - d.y)); }
  Point operator - () { return (Point(-x, -y)); }
  Point operator * (double a) { return (Point(x * a, y * a)); }
  Point operator / (double a) { return (Point(x / a, y / a)); }
  
};

struct Segment
{
  Point p1, p2;
  
  Segment() {}
  Segment(Point p1, Point p2) : p1(p1), p2(p2) {}

  void input() { p1.input(); p2.input(); }
  
};

typedef Point Vector;
typedef vector < Point > Polygon;

double dot(Vector a, Vector b)
{
  return (a.x * b.x + a.y * b.y);
}

double cross(Vector a, Vector b)
{
  return (a.x * b.y - a.y * b.x);
}

Point project(Segment s, Point p)
{
  Vector base = s.p2 - s.p1;
  return (s.p1 + base * (dot(p - s.p1, base) / base.norm()));
}

Point reflect(Segment s, Point p)
{
  Point q = project(s, p);
  return (-p + q * 2);
}


int main()
{
  int n;
  Segment s;
  
  s.input();
  cin >> n;

  for(int i = 0; i < n; i++) {
    Point p;
    p.input();
    reflect(s, p).output();
  }
  
  
  return (0);
}