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>
const int MAX = 300010;
const int MOD = 998244353;
const int INF = 0x3f3f3f3f;
const long long LLINF = 0x3f3f3f3f3f3f3f3f;
const long double EPS = 1e-4;
const long double PI = acosl(-1.0);
using namespace std;
bool eq(long double a, long double b) { return fabsl(a - b) <= EPS; }
struct point {
  long double x, y;
  int id;
  point(long double x = 0, long double y = 0) : x(x), y(y) {}
  point operator+(const point &o) const { return {x + o.x, y + o.y}; }
  point operator-(const point &o) const { return {x - o.x, y - o.y}; }
  point operator*(long double t) const { return {x * t, y * t}; }
  point operator/(long double t) const { return {x / t, y / t}; }
  bool operator<(const point &o) const {
    if (!eq(x, o.x)) return x < o.x;
    return y < o.y;
  }
  bool operator==(const point &o) const { return eq(x, o.x) and eq(y, o.y); }
};
struct line {
  point p1, p2;
  line(point p1 = 0, point p2 = 0) : p1(p1), p2(p2) {}
  long double a = p2.y - p1.y;
  long double b = p1.x - p2.x;
  long double c = p1.x * p2.y - p1.y * p2.x;
};
pair<long double, long double> inter(line p, line q) {
  long double base = p.a * q.b - p.b * q.a;
  if (fabs(base) < 1e-5) return pair<long double, long double>(1e9, 1e9);
  return pair<long double, long double>((p.b * q.c - q.b * p.c) / base,
                                        (p.c * q.a - q.c * p.a) / base);
}
long double func(line a, pair<long double, long double> b) {
  return a.a * b.first + a.b * b.second + a.c;
}
vector<point> half_plane_intersect(vector<line> &v) {
  vector<point> ret;
  int n = v.size();
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      pair<long double, long double> crs = inter(v[i], v[j]);
      if (crs.first == 1e9) continue;
      bool bad = 0;
      for (int k = 0; k < n; k++)
        if (func(v[k], crs) < -EPS) {
          bad = 1;
          break;
        }
      if (!bad) ret.push_back(point(crs.first, crs.second));
    }
  }
  return ret;
}
point rotccw(point p, long double a) {
  a = PI * a / 180;
  return point((p.x * cos(a) - p.y * sin(a)), (p.y * cos(a) + p.x * sin(a)));
}
long double cross(point a, point b) { return a.x * b.y - a.y * b.x; }
long double area(vector<point> &p) {
  long double ret = 0;
  for (int i = 2; i < (int)p.size(); i++)
    ret += cross(p[i] - p[0], p[i - 1] - p[0]);
  return fabsl(ret / 2);
}
int ccw(point a, point b, point e) {
  long double tmp = cross(b - a, e - a);
  return (tmp > EPS) - (tmp < -EPS);
}
int quarter(point a) {
  if (a.x >= 0 and a.y > 0) return 0;
  if (a.x < 0 and a.y >= 0) return 1;
  if (a.x <= 0 and a.y < 0) return 2;
  return 3;
}
bool comp(point a, point b) {
  int qa = quarter(a);
  int qb = quarter(b);
  if (qa == qb)
    return cross(a, b) > 0;
  else
    return qa < qb;
}
vector<point> convex_hull(const vector<point> &points) {
  vector<point> P(points);
  sort(P.begin(), P.end());
  vector<point> lower, upper;
  for (const auto &p : P) {
    int n = int(lower.size());
    while (n >= 2 and ccw(lower[n - 2], lower[n - 1], p) != -1) {
      lower.pop_back();
      n = int(lower.size());
    }
    lower.push_back(p);
  }
  reverse(P.begin(), P.end());
  for (const auto &p : P) {
    int n = int(upper.size());
    while (n >= 2 and ccw(upper[n - 2], upper[n - 1], p) != -1) {
      upper.pop_back();
      n = int(upper.size());
    }
    upper.push_back(p);
  }
  lower.pop_back();
  lower.insert(lower.end(), upper.begin(), upper.end() - 1);
  return lower;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  vector<point> resp;
  vector<line> lines;
  long double w, h, ang;
  cin >> w >> h >> ang;
  point a = point(w / 2, h / 2);
  point b = point(-w / 2, h / 2);
  point c = point(-w / 2, -h / 2);
  point d = point(w / 2, -h / 2);
  lines.push_back(line(a, b));
  lines.push_back(line(b, c));
  lines.push_back(line(c, d));
  lines.push_back(line(d, a));
  a = rotccw(a, ang);
  b = rotccw(b, ang);
  c = rotccw(c, ang);
  d = rotccw(d, ang);
  lines.push_back(line(a, b));
  lines.push_back(line(b, c));
  lines.push_back(line(c, d));
  lines.push_back(line(d, a));
  resp = half_plane_intersect(lines);
  sort(resp.begin(), resp.end(), comp);
  resp = convex_hull(resp);
  cout << fixed << setprecision(10);
  cout << area(resp) << '\n';
  return 0;
}