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;
int w, h;
double a;
double tv, pr;
double toDeg(double r);
struct pt {
  double x, y;
  pt(){};
  pt(double f, double s) {
    x = f;
    y = s;
  }
  double hypot() { return sqrt(x * x + y * y); }
  pt rot(double a) {
    double x1 = x * cos(a) - y * sin(a);
    double y1 = x * sin(a) + y * cos(a);
    return pt(x1, y1);
  }
  bool operator<(const pt& p) const {
    return x < p.x - 1e-9 || abs(x - p.x) < 1e-9 && y < p.y - 1e-9;
  }
  void print() { printf("(%f , %f)\n", x, y); }
};
struct line {
  double a, b, c;
  line() {}
  line(pt p, pt q) {
    a = p.y - q.y;
    b = q.x - p.x;
    c = -a * p.x - b * p.y;
    norm();
  }
  void norm() {
    double z = sqrt(a * a + b * b);
    if (abs(z) > 1e-9) a /= z, b /= z, c /= z;
  }
  double dist(pt p) { return a * p.x + b * p.y + c; }
};
bool betw(double l, double r, double x) {
  return min(l, r) <= x + 1e-9 && x <= max(l, r) + 1e-9;
}
inline bool intersect_1d(double a, double b, double c, double d) {
  if (a > b) swap(a, b);
  if (c > d) swap(c, d);
  return max(a, c) <= min(b, d) + 1e-9;
}
bool intersect(pt a, pt b, pt c, pt d, pt& left, pt& right) {
  if (!intersect_1d(a.x, b.x, c.x, d.x) || !intersect_1d(a.y, b.y, c.y, d.y))
    return false;
  line m(a, b);
  line n(c, d);
  double zn = (m.a * n.b - m.b * n.a);
  if (abs(zn) < 1e-9) {
    if (abs(m.dist(c)) > 1e-9 || abs(n.dist(a)) > 1e-9) return false;
    if (b < a) swap(a, b);
    if (d < c) swap(c, d);
    left = max(a, c);
    right = min(b, d);
    return true;
  } else {
    left.x = right.x = -(m.c * n.b - m.b * n.c) / zn;
    left.y = right.y = -(m.a * n.c - m.c * n.a) / zn;
    return betw(a.x, b.x, left.x) && betw(a.y, b.y, left.y) &&
           betw(c.x, d.x, left.x) && betw(c.y, d.y, left.y);
  }
}
double triangle_area_2(double x1, double y1, double x2, double y2, double x3,
                       double y3) {
  return (x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1);
}
bool cmp(pt a, pt b) { return a.x < b.x || a.x == b.x && a.y < b.y; }
bool cw(pt a, pt b, pt c) {
  return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) < 0;
}
bool ccw(pt a, pt b, pt c) {
  return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) > 0;
}
void convex_hull(vector<pt>& a) {
  if (a.size() == 1) return;
  sort(a.begin(), a.end(), &cmp);
  pt p1 = a[0], p2 = a.back();
  vector<pt> up, down;
  up.push_back(p1);
  down.push_back(p1);
  for (size_t i = 1; i < a.size(); ++i) {
    if (i == a.size() - 1 || cw(p1, a[i], p2)) {
      while (up.size() >= 2 && !cw(up[up.size() - 2], up[up.size() - 1], a[i]))
        up.pop_back();
      up.push_back(a[i]);
    }
    if (i == a.size() - 1 || ccw(p1, a[i], p2)) {
      while (down.size() >= 2 &&
             !ccw(down[down.size() - 2], down[down.size() - 1], a[i]))
        down.pop_back();
      down.push_back(a[i]);
    }
  }
  a.clear();
  for (size_t i = 0; i < up.size(); ++i) a.push_back(up[i]);
  for (size_t i = down.size() - 2; i > 0; --i) a.push_back(down[i]);
}
void first() {
  vector<pt> v1;
  vector<pt> v2;
  double x = w / 2.0;
  double y = h / 2.0;
  v1.push_back(pt(x, y));
  v1.push_back(pt(-x, y));
  v1.push_back(pt(-x, -y));
  v1.push_back(pt(x, -y));
  v2 = v1;
  for (int i = 0; i < 4; i++) v2[i] = v1[i].rot(a);
  vector<pt> pts;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < 4; j++) {
      pt l, r;
      if (intersect(v1[i], v1[(i + 1) % 4], v2[j], v2[(j + 1) % 4], l, r)) {
        pts.push_back(l);
      }
    }
  }
  convex_hull(pts);
  double ans = 0;
  int sp = int((pts).size());
  for (int i = 0; i < sp; i++) {
    ans += triangle_area_2(0, 0, pts[i].x, pts[i].y, pts[(i + 1) % sp].x,
                           pts[(i + 1) % sp].y);
  }
  ans = abs(ans) / 2.0;
  printf("%.7f", ans);
}
void second() {}
double toDeg(double rad) { return rad * 180 / 3.1415926535897932384626433; }
double toRad(double deg) { return deg * 3.1415926535897932384626433 / 180.0; }
void oku() {
  cin >> w >> h >> a;
  a = toRad(a);
  tv = atan(h / w);
  pr = 2.0 * tv;
  first();
}
int main() {
  oku();
  return 0;
}