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 long double pi = acos(-1.0);
const long double inf = 1e+9;
const long double eps = 1e-9;
struct vec_t {
  long double x, y;
  vec_t() {}
  vec_t(long double x, long double y) : x(x), y(y) {}
  vec_t rotate(long double alpha) {
    return vec_t(x * cos(alpha) - y * sin(alpha),
                 x * sin(alpha) + y * cos(alpha));
  }
  friend bool operator<(const vec_t &a, const vec_t &b) {
    return atan2(a.y, a.x) < atan2(b.y, b.x);
  }
  friend vec_t operator-(const vec_t &a, const vec_t &b) {
    return vec_t(a.x - b.x, a.y - b.y);
  }
  friend long double cross_product(const vec_t &a, const vec_t &b) {
    return a.x * b.y - a.y * b.x;
  }
};
vec_t intersection(const vec_t &a, const vec_t &b, const vec_t &c,
                   const vec_t &d) {
  if (cross_product(d - a, b - a) * cross_product(c - a, b - a) <= 0 &&
      cross_product(a - c, d - c) * cross_product(b - c, d - c) <= 0) {
    long double A1 = a.y - b.y;
    long double A2 = c.y - d.y;
    long double B1 = b.x - a.x;
    long double B2 = d.x - c.x;
    long double C1 = cross_product(a, b);
    long double C2 = cross_product(c, d);
    long double det = A1 * B2 - B1 * A2;
    long double det1 = -C1 * B2 + C2 * B1;
    long double det2 = -C2 * A1 + C1 * A2;
    long double x = det1 / det;
    long double y = det2 / det;
    return vec_t(x, y);
  }
  return vec_t(-inf, -inf);
}
int main() {
  long double w, h, alpha;
  cin >> w >> h >> alpha;
  if (alpha == 0 || alpha == 180) {
    cout << fixed << setprecision(9) << w * h << endl;
    return 0;
  }
  alpha *= pi / 180.0;
  vector<vec_t> u, v;
  u.push_back(vec_t(-w / 2, +h / 2));
  u.push_back(vec_t(+w / 2, +h / 2));
  u.push_back(vec_t(+w / 2, -h / 2));
  u.push_back(vec_t(-w / 2, -h / 2));
  for (int i = 0; i < (int)4; ++i) v.push_back(u[i].rotate(alpha));
  vector<vec_t> pts;
  for (int i = 0; i < (int)4; ++i)
    for (int j = 0; j < (int)4; ++j) {
      vec_t p = intersection(u[i], u[(i + 1) % 4], v[j], v[(j + 1) % 4]);
      if (p.x - eps > -inf) pts.push_back(p);
    }
  sort(pts.begin(), pts.end());
  long double res = 0;
  for (int i = 1; i <= (int)pts.size() - 2; ++i)
    res += fabs(cross_product(pts[i] - pts[0], pts[i + 1] - pts[0]));
  res /= 2;
  cout << fixed << setprecision(9) << res << endl;
  return 0;
}