Pursuit
On a plane, there are N distinct lines and two different points. Each of these points lies on at least one of the lines. A point can move in either direction along the line it is on and can change direction at any time. Additionally, a point can switch to another line at any intersection point, as often as needed. Each point has a maximum speed, which is constant regardless of the line or direction of movement. The first point aims to avoid being caught by the second point, while the second point aims to catch the first.
Your task is to determine whether the second point can catch the first. Both points are idealized, meaning they always make optimal decisions.
Input
The first line contains the integer N (1 ≤ N ≤ 100000), representing the number of lines on the plane. Each of the following N lines contains three integers: a_i, b_i, and c_i (-1000000 ≤ a_i, b_i, c_i ≤ 1000000, |a_i|+|b_i| > 0), which are the coefficients of the line equation: [a_i x + b_i y + c_i = 0]. No two lines are identical. The next line contains three integers: x_1, y_1, and v_1 (-1000000 ≤ x_1, y_1 ≤ 1000000, 1 ≤ v_1 ≤ 1000000), representing the coordinates and maximum speed of the first point. The following line contains three integers: x_2, y_2, and v_2 (-1000000 ≤ x_2, y_2 ≤ 1000000, 1 ≤ v_2 ≤ 1000000), representing the coordinates and maximum speed of the second point. It is guaranteed that the points do not coincide and each point lies on at least one line.
Output
Print "Yes" if the second point can catch the first; otherwise, print "No".