Problem: IT City administration has no rest because of the fame of the Pyramids in Egypt. There is a project of construction of pyramid complex near the city in the place called Emerald Walley. The distinction of the complex is that its pyramids will be not only quadrangular as in Egypt but also triangular and pentagonal. Of course the amount of the city budget funds for the construction depends on the pyramids' volume. Your task is to calculate the volume of the pilot project consisting of three pyramids — one triangular, one quadrangular and one pentagonal.

The first pyramid has equilateral triangle as its base, and all 6 edges of the pyramid have equal length. The second pyramid has a square as its base and all 8 edges of the pyramid have equal length. The third pyramid has a regular pentagon as its base and all 10 edges of the pyramid have equal length.

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Input

The only line of the input contains three integers l3, l4, l5 (1 ≤ l3, l4, l5 ≤ 1000) — the edge lengths of triangular, quadrangular and pentagonal pyramids correspondingly.

Output

Output one number — the total volume of the pyramids. Absolute or relative error should not be greater than 10 - 9.

Examples

Input

2 5 3


Output

38.546168065709

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
double INF = 1e100;
double EPS = 1e-12;
struct PT {
  double x, y;
  PT() {}
  PT(double x, double y) : x(x), y(y) {}
  PT(const PT &p) : x(p.x), y(p.y) {}
  PT operator+(const PT &p) const { return PT(x + p.x, y + p.y); }
  PT operator-(const PT &p) const { return PT(x - p.x, y - p.y); }
  PT operator*(double c) const { return PT(x * c, y * c); }
  PT operator/(double c) const { return PT(x / c, y / c); }
};
double dot(PT p, PT q) { return p.x * q.x + p.y * q.y; }
double dist2(PT p, PT q) { return dot(p - q, p - q); }
double cross(PT p, PT q) { return p.x * q.y - p.y * q.x; }
ostream &operator<<(ostream &os, const PT &p) {
  os << "(" << p.x << "," << p.y << ")";
}
PT RotateCCW90(PT p) { return PT(-p.y, p.x); }
PT RotateCW90(PT p) { return PT(p.y, -p.x); }
PT RotateCCW(PT p, double t) {
  return PT(p.x * cos(t) - p.y * sin(t), p.x * sin(t) + p.y * cos(t));
}
PT ProjectPointLine(PT a, PT b, PT c) {
  return a + (b - a) * dot(c - a, b - a) / dot(b - a, b - a);
}
PT ProjectPointSegment(PT a, PT b, PT c) {
  double r = dot(b - a, b - a);
  if (fabs(r) < EPS) return a;
  r = dot(c - a, b - a) / r;
  if (r < 0) return a;
  if (r > 1) return b;
  return a + (b - a) * r;
}
double DistancePointSegment(PT a, PT b, PT c) {
  return sqrt(dist2(c, ProjectPointSegment(a, b, c)));
}
double DistancePointPlane(double x, double y, double z, double a, double b,
                          double c, double d) {
  return fabs(a * x + b * y + c * z - d) / sqrt(a * a + b * b + c * c);
}
bool LinesParallel(PT a, PT b, PT c, PT d) {
  return fabs(cross(b - a, c - d)) < EPS;
}
bool LinesCollinear(PT a, PT b, PT c, PT d) {
  return LinesParallel(a, b, c, d) && fabs(cross(a - b, a - c)) < EPS &&
         fabs(cross(c - d, c - a)) < EPS;
}
bool SegmentsIntersect(PT a, PT b, PT c, PT d) {
  if (LinesCollinear(a, b, c, d)) {
    if (dist2(a, c) < EPS || dist2(a, d) < EPS || dist2(b, c) < EPS ||
        dist2(b, d) < EPS)
      return true;
    if (dot(c - a, c - b) > 0 && dot(d - a, d - b) > 0 && dot(c - b, d - b) > 0)
      return false;
    return true;
  }
  if (cross(d - a, b - a) * cross(c - a, b - a) > 0) return false;
  if (cross(a - c, d - c) * cross(b - c, d - c) > 0) return false;
  return true;
}
PT ComputeLineIntersection(PT a, PT b, PT c, PT d) {
  b = b - a;
  d = c - d;
  c = c - a;
  assert(dot(b, b) > EPS && dot(d, d) > EPS);
  return a + b * cross(c, d) / cross(b, d);
}
PT ComputeCircleCenter(PT a, PT b, PT c) {
  b = (a + b) / 2;
  c = (a + c) / 2;
  return ComputeLineIntersection(b, b + RotateCW90(a - b), c,
                                 c + RotateCW90(a - c));
}
bool PointInPolygon(const vector<PT> &p, PT q) {
  bool c = 0;
  for (int i = 0; i < p.size(); i++) {
    int j = (i + 1) % p.size();
    if ((p[i].y <= q.y && q.y < p[j].y || p[j].y <= q.y && q.y < p[i].y) &&
        q.x < p[i].x + (p[j].x - p[i].x) * (q.y - p[i].y) / (p[j].y - p[i].y))
      c = !c;
  }
  return c;
}
bool PointOnPolygon(const vector<PT> &p, PT q) {
  for (int i = 0; i < p.size(); i++)
    if (dist2(ProjectPointSegment(p[i], p[(i + 1) % p.size()], q), q) < EPS)
      return true;
  return false;
}
vector<PT> CircleLineIntersection(PT a, PT b, PT c, double r) {
  vector<PT> ret;
  b = b - a;
  a = a - c;
  double A = dot(b, b);
  double B = dot(a, b);
  double C = dot(a, a) - r * r;
  double D = B * B - A * C;
  if (D < -EPS) return ret;
  ret.push_back(c + a + b * (-B + sqrt(D + EPS)) / A);
  if (D > EPS) ret.push_back(c + a + b * (-B - sqrt(D)) / A);
  return ret;
}
vector<PT> CircleCircleIntersection(PT a, PT b, double r, double R) {
  vector<PT> ret;
  double d = sqrt(dist2(a, b));
  if (d > r + R || d + min(r, R) < max(r, R)) return ret;
  double x = (d * d - R * R + r * r) / (2 * d);
  double y = sqrt(r * r - x * x);
  PT v = (b - a) / d;
  ret.push_back(a + v * x + RotateCCW90(v) * y);
  if (y > 0) ret.push_back(a + v * x - RotateCCW90(v) * y);
  return ret;
}
double ComputeSignedArea(const vector<PT> &p) {
  double area = 0;
  for (int i = 0; i < p.size(); i++) {
    int j = (i + 1) % p.size();
    area += p[i].x * p[j].y - p[j].x * p[i].y;
  }
  return area / 2.0;
}
double ComputeArea(const vector<PT> &p) { return fabs(ComputeSignedArea(p)); }
PT ComputeCentroid(const vector<PT> &p) {
  PT c(0, 0);
  double scale = 6.0 * ComputeSignedArea(p);
  for (int i = 0; i < p.size(); i++) {
    int j = (i + 1) % p.size();
    c = c + (p[i] + p[j]) * (p[i].x * p[j].y - p[j].x * p[i].y);
  }
  return c / scale;
}
bool IsSimple(const vector<PT> &p) {
  for (int i = 0; i < p.size(); i++) {
    for (int k = i + 1; k < p.size(); k++) {
      int j = (i + 1) % p.size();
      int l = (k + 1) % p.size();
      if (i == l || j == k) continue;
      if (SegmentsIntersect(p[i], p[j], p[k], p[l])) return false;
    }
  }
  return true;
}
int main() {
  double l3, l4, l5;
  cin >> l3 >> l4 >> l5;
  double A1 = l3 * l3;
  A1 *= sqrt(3);
  A1 /= 4;
  double A2 = l4 * l4;
  double A3 = 5.0 * (5.0 + 2.0 * sqrt(5));
  A3 = sqrt(A3) / 4;
  A3 *= l5 * l5;
  double V2 = l4 * l4 * l4 / (3.0 * sqrt(2.0));
  double V1 = sqrt(2) * l3 * l3 * l3 / 12.0;
  double V3 = A3 / 3;
  V3 *= l5 * sqrt(1 - (5.0 + sqrt(5)) / 10.0);
  V1 += V2 + V3;
  printf("%.10f", V1);
}