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 eps = 1e-6;
const double PI = acos(-1.0);
double sqr(double x) { return x * x; }
struct Point {
  double x, y;
  Point(double _x, double _y) : x(_x), y(_y) {}
  Point() {}
  Point operator+(const Point& r) const { return Point(x + r.x, y + r.y); }
  Point operator-(const Point& r) const { return Point(x - r.x, y - r.y); }
  Point operator*(double r) const { return Point(x * r, y * r); }
  Point operator/(double r) const { return Point(x / r, y / r); }
  Point spin(double ang) const {
    return Point(x * cos(ang) - y * sin(ang), x * sin(ang) + y * cos(ang));
  }
  double len() { return sqrt(x * x + y * y); }
  double len2() { return x * x + y * y; }
  double det(const Point& r) const { return x * r.y - r.x * y; }
  double dot(const Point& r) const { return x * r.x + y * r.y; }
  void scan() { scanf("%lf%lf", &x, &y); }
};
struct Line {
  Point a, b;
  Line() {}
  Line(Point _a, Point _b) : a(_a), b(_b) {}
  Point getIntersection(const Line& r) const {
    double s1 = (b - a).det(r.a - a), s2 = (b - a).det(r.b - a);
    if (abs(s1 - s2) < eps) throw "";
    return Point(r.b * s1 - r.a * s2) / (s1 - s2);
  }
  void scan() { a.scan(), b.scan(); }
};
struct Convex {
  vector<Point> con;
  Convex() {}
  Convex(const vector<Point>& points) {}
  Convex cut(Line l) {
    Convex newconvex;
    vector<Point>& newcon = newconvex.con;
    for (int i = 0; i < con.size(); i++) {
      if ((l.b - l.a).det(con[i] - l.a) > -eps) newcon.push_back(con[i]);
      if ((l.b - l.a).det(con[i] - l.a) *
              (l.b - l.a).det(con[(i + 1) % con.size()] - l.a) <
          -eps) {
        newcon.push_back(
            l.getIntersection(Line(con[i], con[(i + 1) % con.size()])));
      }
    }
    return newconvex;
  }
  double area() {
    double ret = 0;
    for (int i = 0; i < con.size(); i++) {
      ret += con[i].det(con[(i + 1) % con.size()]);
    }
    return abs(ret) / 2;
  }
};
void print(Point x) { printf("%f %f\n", x.x, x.y); }
int main() {
  double w, h, ar;
  cin >> w >> h >> ar;
  w /= 2;
  h /= 2;
  ar = ar / 180.0 * PI;
  Point a(-w, -h), b(w, -h), c(w, h), d(-w, h);
  Convex ori;
  ori.con.push_back(a);
  ori.con.push_back(b);
  ori.con.push_back(c);
  ori.con.push_back(d);
  Convex n = ori;
  for (int i = 0; i < 4; i++) {
    n.con[i] = n.con[i].spin(ar);
  }
  for (int i = 0; i < 4; i++) {
    ori = ori.cut(Line(n.con[i], n.con[(i + 1) % 4]));
  }
  printf("%.15lf\n", ori.area());
  return 0;
}