Problem: You are given two rectangles on a plane. The centers of both rectangles are located in the origin of coordinates (meaning the center of the rectangle's symmetry). The first rectangle's sides are parallel to the coordinate axes: the length of the side that is parallel to the Ox axis, equals w, the length of the side that is parallel to the Oy axis, equals h. The second rectangle can be obtained by rotating the first rectangle relative to the origin of coordinates by angle α.

<image>

Your task is to find the area of the region which belongs to both given rectangles. This region is shaded in the picture.

Input

The first line contains three integers w, h, α (1 ≤ w, h ≤ 106; 0 ≤ α ≤ 180). Angle α is given in degrees.

Output

In a single line print a real number — the area of the region which belongs to both given rectangles.

The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.

Examples

Input

1 1 45


Output

0.828427125


Input

6 4 30


Output

19.668384925

Note

The second sample has been drawn on the picture above.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const double PI = 3.14159265358979323846264338327950288419716939937510;
struct coord_t {
  double x, y;
  coord_t() {}
  coord_t(const double& x, const double& y) : x(x), y(y) {}
  coord_t operator-(const coord_t& that) const {
    return coord_t(x - that.x, y - that.y);
  }
  coord_t rotate(const double&);
};
struct lines_t {
  coord_t p, q;
  double a, b, c;
  lines_t(const coord_t& p, const coord_t& q) : p(p), q(q) {
    a = q.y - p.y;
    b = p.x - q.x;
    c = p.y * q.x - p.x * q.y;
  }
  double get_x(const double&);
  double get_y(const double&);
  bool contains(const coord_t&);
  bool intersects(const lines_t&);
};
double rad(const double&);
double ccw(const coord_t&, const coord_t&, const coord_t&);
int main(int argc, const char* argv[]) {
  double size_x, size_y, deg;
  scanf("%lf%lf%lf", &size_x, &size_y, &deg);
  if (size_x < size_y) {
    swap(size_x, size_y);
  }
  if (deg > 90) {
    deg = 180 - deg;
  }
  if (deg == 0) {
    printf("%.8lf\n", size_x * size_y);
  } else if (deg == 90) {
    printf("%.8lf\n", pow(min(size_x, size_y), 2));
  } else {
    auto top_left = coord_t(-size_x / 2, size_y / 2);
    auto top_right = coord_t(size_x / 2, size_y / 2);
    auto bottom_left = coord_t(-size_x / 2, -size_y / 2);
    auto bottom_right = coord_t(size_x / 2, -size_y / 2);
    auto top = lines_t(top_left, top_right);
    auto left = lines_t(top_left, bottom_left);
    auto right = lines_t(top_right, bottom_right);
    auto bottom = lines_t(bottom_left, bottom_right);
    auto rot_top = lines_t(top_left.rotate(deg), top_right.rotate(deg));
    auto rot_right = lines_t(top_right.rotate(deg), bottom_right.rotate(deg));
    if (rot_right.intersects(top)) {
      printf("%.8lf\n", size_x * size_y -
                            (size_y / 2 - rot_right.get_y(size_x / 2)) *
                                (size_x / 2 - rot_right.get_x(size_y / 2)) -
                            (rot_top.get_x(size_y / 2) + size_x / 2) *
                                (size_y / 2 - rot_top.get_y(-size_x / 2)));
    } else {
      printf("%.8lf\n",
             -1 * (rot_top.get_x(size_y / 2) + rot_top.get_x(-size_y / 2)) *
                 size_y);
    }
  }
  return 0;
}
coord_t coord_t::rotate(const double& deg) {
  double ang = rad(deg);
  return coord_t(cos(ang) * x - sin(ang) * y, sin(ang) * x + cos(ang) * y);
}
double lines_t::get_x(const double& y) { return (b * y + c) / -a; }
double lines_t::get_y(const double& x) { return (a * x + c) / -b; }
bool lines_t::contains(const coord_t& o) {
  return ccw(o, p, q) == 0 && (p.x - o.x) * (q.x - o.x) <= 0 &&
         (p.y - o.y) * (q.y - o.y) <= 0;
}
bool lines_t::intersects(const lines_t& that) {
  return ccw(p, q, that.p) * ccw(p, q, that.q) <= 0 &&
         ccw(that.p, that.q, p) * ccw(that.p, that.q, q) <= 0;
}
double rad(const double& deg) { return deg * PI / 180; }
double ccw(const coord_t& o, const coord_t& p, const coord_t& q) {
  return (p.x - o.x) * (q.y - o.y) - (p.y - o.y) * (q.x - o.x);
}