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 <complex>
#include <cstdio>
#include <utility>
using namespace std;
typedef complex<double> P;
typedef pair<P,P> L;
#define X real()
#define Y imag()
const double EPS = (1e-10);

P line_symmetry(L l, P p){
  P f = l.first, s = l.second - f, q = p - f;
  if(abs(q) < EPS) return p;
  return f + norm(q/s)*s*s/q;
}

int main(){
  double x1, x2, y1, y2;
  cin >> x1 >> y1 >> x2 >> y2;
  L l = L(P(x1,y1),P(x2,y2));
  int q;
  cin >> q;
  for(int i = 0; i < q; ++i){
    cin >> x1 >> y1;
    P p = line_symmetry(l, P(x1,y1));
    printf("%.9lf %.8lf\n",p.X,p.Y);
  }
  return 0;
}