There is a polygon A₁A₂…A_N (the vertices A_i are numbered in clockwise order). On each side A_iA_i+1 an isosceles triangle A_iM_iA_i+1 is built on the outer side of the polygon (M_iA_i = M_iA_i+1). The angle A_iM_iA_i+1 is equal to α_i. Here we assume that A_N+1 = A₁.

The set of angles α_i satisfies a condition that the sum of angles in any of its nonempty subsets is not aliquot to 360 degrees.

You are given N, coordinates of vertices M_i and angles α_i (measured in degrees). Write a program, which restores coordinates of the polygon vertices.

The first line contains an integer N (3 ≤ N ≤ 50). The next N lines contain pairs of real numbers x_i, y_i which are coordinates of points M_i (–100 ≤ x_i, y_i ≤ 100). And the last N lines of the input consist of degree values of angles α_i. All real numbers in the input contain at most 2 digits after decimal point.

Output N lines with points coordinates, i-th line should contain the coordinates of A_i. Coordinates must be accurate to 2 digits after decimal point. You may assume that solution always exists.