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 <iomanip>
#include <algorithm>
#include <stack>
#include <queue>
#include <vector>
#include <map>
#include <bitset>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>

using namespace std;

// x軸方向にtx, y軸方向にtyだけ平行移動
void translation(double tx, double ty, double &x, double &y) 
{
    x += tx;
    y += ty;
}

// thetaだけ回転
void rotation(double theta, double &x, double &y) 
{
    double tx = x;
    double ty = y;

    x = cos(theta) * tx - sin(theta) * ty;
    y = sin(theta) * tx + cos(theta) * ty;
}

// x軸に関する鏡映
void x_reflection(double &x, double &y) 
{
    y *= -1;
}


int main()
{
    double x1, y1, x2, y2, xq, yq;
	cin >> x1 >> y1 >> x2 >> y2;
    double theta = atan((y2 - y1) / (x2 - x1));
	int q;
	cin >> q;
    while (q-->0) {
		cin >> xq >> yq;
        translation(-x1, -y1, xq, yq);
        rotation(-theta, xq, yq);
        x_reflection(xq, yq);
        rotation(theta, xq, yq);
        translation(x1, y1, xq, yq);
        cout << fixed << setprecision(12) << xq << " " << yq << endl;
    }
}