#include <bits/stdc++.h>
using namespace std;
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << "\n";
  err(++it, args...);
}
const double PI = acos(-1);
const double eps = (1e-9);
const long long int INF = 2e9;
const int M = (1e9) + 7;
const int N = 403;
struct Point {
  int x, y;
  Point(int a = 0, int b = 0) { x = a, y = b; }
  void reassign(int a, int b) { x = a, y = b; }
  void input() { scanf("%d%d", &x, &y); }
  void print() { printf("%d %d\n", x, y); }
  Point operator+=(Point A) {
    x += A.x, y += A.y;
    return *this;
  }
  Point operator-=(Point A) {
    x -= A.x, y -= A.y;
    return *this;
  }
  Point operator+(Point A) {
    Point tp(x + A.x, y + A.y);
    return tp;
  }
  Point operator-(Point A) {
    Point tp(x - A.x, y - A.y);
    return tp;
  }
  Point operator*(int f) {
    Point tp(x * f, y * f);
    return tp;
  }
  Point operator*=(int f) {
    x *= f, y *= f;
    return *this;
  }
  Point operator/=(int f) {
    x /= f, y /= f;
    return *this;
  }
  bool operator==(Point A) {
    if (x == A.x && y == A.y) return true;
    return false;
  }
  bool operator!=(Point A) {
    if (x != A.x || y != A.y) return true;
    return false;
  }
  void ulta() { swap(x, y); }
};
Point makepoint(int a, int b) {
  Point temp(a, b);
  return temp;
}
void swap(Point &A, Point &B) {
  swap(A.x, B.x);
  swap(A.y, B.y);
}
bool cmp(Point a, Point b) {
  if (a.x != b.x) return (a.x < b.x);
  return (a.y < b.y);
}
long long int dotproduct(Point a, Point b) {
  return (long long int)a.x * (long long int)b.x +
         (long long int)a.y * (long long int)b.y;
}
long long int crossproduct(Point a, Point b) {
  return (long long int)a.x * (long long int)b.y -
         (long long int)a.y * (long long int)b.x;
}
int ccw(Point a, Point b, Point origin = makepoint(0, 0)) {
  long long int x = crossproduct(a - origin, b - origin);
  if (x > 0) x = 1;
  if (x < 0) x = -1;
  return (int)x;
}
long long int sqrdist(Point a, Point b = makepoint(0, 0)) {
  long long int q = 0, temp;
  temp = a.x - b.x;
  temp *= temp, q += temp;
  temp = a.y - b.y;
  temp *= temp, q += temp;
  return q;
}
double dist(Point a, Point b = makepoint(0, 0)) {
  long long int temp = sqrdist(a, b);
  return sqrt(temp);
}
double anglepolar(Point a) { return atan2(a.y, a.x); }
double anglebetween(Point a, Point b, Point origin = makepoint(0, 0)) {
  return atan2(crossproduct(a - origin, b - origin),
               dotproduct(a - origin, b - origin));
}
Point perp(Point a) { return makepoint(-a.y, a.x); }
struct Line {
  Point a, b, ab;
  bool isline;
  Line() {
    a = makepoint(0, 0);
    b = a, ab = a, isline = 0;
  }
  Line(Point p, Point q) {
    a = p, b = q;
    ab = b - a;
    if (a != b)
      isline = 1;
    else
      isline = 0;
  }
  void update(Point p, Point q) {
    a = p, b = q;
    ab = b - a;
    if (a != b)
      isline = 1;
    else
      isline = 0;
    return;
  }
  bool operator==(Line other) {
    return ((crossproduct(ab, other.ab) == 0) && online(other.a));
  }
  bool online(Point point) {
    if (!isline) return (point == a);
    return (crossproduct(point - a, ab) == 0);
  }
  bool onsegment(Point point) {
    if (!isline) return (point == a);
    Point va, vb;
    va = a - point, vb = b - point;
    return (crossproduct(va, vb) == 0 && dotproduct(va, vb) <= 0);
  }
  bool parallel(Line other) { return (crossproduct(ab, other.ab) == 0); }
  bool perpendicular(Line other) { return (dotproduct(ab, other.ab) == 0); }
  double distline(Point point) {
    if (!isline) return dist(a, point);
    long double t = abs(crossproduct(point - a, ab));
    t /= dist(ab);
    return t;
  }
  double distsegment(Point point) {
    if (dotproduct(point - a, ab) <= 0) return dist(a, point);
    if (dotproduct(point - b, ab) >= 0) return dist(b, point);
    return distline(point);
  }
  bool lineintersectcheck(Line ray) { return (crossproduct(ab, ray.ab) != 0); }
  bool inter1(int a, int b, int c, int d) {
    if (a > b) swap(a, b);
    if (c > d) swap(c, d);
    return max(a, c) <= min(b, d);
  }
  bool segmentintersectcheck(Line ray) {
    if (crossproduct(ab, ray.ab) == 0) {
      if (online(ray.a))
        return inter1(a.x, b.x, ray.a.x, ray.b.x) &&
               inter1(a.y, b.y, ray.a.y, ray.b.y);
      return false;
    }
    return (crossproduct(ray.a - a, ray.a - b) !=
            crossproduct(ray.b - a, ray.b - b)) &&
           (crossproduct(a - ray.a, a - ray.b) !=
            crossproduct(b - ray.a, b - ray.b));
  }
};
int squarechecker(vector<Point> &point) {
  if (point[0] == point[2] || point[1] == point[3]) return 0;
  double x = dist(point[0], point[3]);
  if (dist(point[0], point[1]) == x && dist(point[1], point[2]) == x &&
      dist(point[2], point[3]) == x)
    return (dotproduct(point[1] - point[2], point[3] - point[2]) == 0);
  return 0;
}
int main() {
  int a, b, c;
  scanf("%d%d%d", &a, &b, &c);
  double d, ans = 0;
  int V;
  cout << setprecision(12) << fixed;
  V = a * a * a;
  {
    string _s = "V";
    replace(_s.begin(), _s.end(), ',', ' ');
    stringstream _ss(_s);
    istream_iterator<string> _it(_ss);
    err(_it, V);
  };
  double s = sqrt(2);
  d = V / (6 * s);
  ans += d;
  a = b;
  V = a * a * a;
  {
    string _s = "V";
    replace(_s.begin(), _s.end(), ',', ' ');
    stringstream _ss(_s);
    istream_iterator<string> _it(_ss);
    err(_it, V);
  };
  d = V / (3 * s);
  ans += d;
  a = c;
  V = a * a * a;
  {
    string _s = "V";
    replace(_s.begin(), _s.end(), ',', ' ');
    stringstream _ss(_s);
    istream_iterator<string> _it(_ss);
    err(_it, V);
  };
  double h;
  h = 1 / (2 * sin(PI / 5));
  d = 1 - h * h;
  d = sqrt(d);
  d *= V;
  d = d / (12 * tan(PI / 5));
  d *= 5;
  ans += d;
  cout << ans << "\n";
}

### Prompt

Please formulate a cpp solution to the following 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.

<image>

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << "\n";
  err(++it, args...);
}
const double PI = acos(-1);
const double eps = (1e-9);
const long long int INF = 2e9;
const int M = (1e9) + 7;
const int N = 403;
struct Point {
  int x, y;
  Point(int a = 0, int b = 0) { x = a, y = b; }
  void reassign(int a, int b) { x = a, y = b; }
  void input() { scanf("%d%d", &x, &y); }
  void print() { printf("%d %d\n", x, y); }
  Point operator+=(Point A) {
    x += A.x, y += A.y;
    return *this;
  }
  Point operator-=(Point A) {
    x -= A.x, y -= A.y;
    return *this;
  }
  Point operator+(Point A) {
    Point tp(x + A.x, y + A.y);
    return tp;
  }
  Point operator-(Point A) {
    Point tp(x - A.x, y - A.y);
    return tp;
  }
  Point operator*(int f) {
    Point tp(x * f, y * f);
    return tp;
  }
  Point operator*=(int f) {
    x *= f, y *= f;
    return *this;
  }
  Point operator/=(int f) {
    x /= f, y /= f;
    return *this;
  }
  bool operator==(Point A) {
    if (x == A.x && y == A.y) return true;
    return false;
  }
  bool operator!=(Point A) {
    if (x != A.x || y != A.y) return true;
    return false;
  }
  void ulta() { swap(x, y); }
};
Point makepoint(int a, int b) {
  Point temp(a, b);
  return temp;
}
void swap(Point &A, Point &B) {
  swap(A.x, B.x);
  swap(A.y, B.y);
}
bool cmp(Point a, Point b) {
  if (a.x != b.x) return (a.x < b.x);
  return (a.y < b.y);
}
long long int dotproduct(Point a, Point b) {
  return (long long int)a.x * (long long int)b.x +
         (long long int)a.y * (long long int)b.y;
}
long long int crossproduct(Point a, Point b) {
  return (long long int)a.x * (long long int)b.y -
         (long long int)a.y * (long long int)b.x;
}
int ccw(Point a, Point b, Point origin = makepoint(0, 0)) {
  long long int x = crossproduct(a - origin, b - origin);
  if (x > 0) x = 1;
  if (x < 0) x = -1;
  return (int)x;
}
long long int sqrdist(Point a, Point b = makepoint(0, 0)) {
  long long int q = 0, temp;
  temp = a.x - b.x;
  temp *= temp, q += temp;
  temp = a.y - b.y;
  temp *= temp, q += temp;
  return q;
}
double dist(Point a, Point b = makepoint(0, 0)) {
  long long int temp = sqrdist(a, b);
  return sqrt(temp);
}
double anglepolar(Point a) { return atan2(a.y, a.x); }
double anglebetween(Point a, Point b, Point origin = makepoint(0, 0)) {
  return atan2(crossproduct(a - origin, b - origin),
               dotproduct(a - origin, b - origin));
}
Point perp(Point a) { return makepoint(-a.y, a.x); }
struct Line {
  Point a, b, ab;
  bool isline;
  Line() {
    a = makepoint(0, 0);
    b = a, ab = a, isline = 0;
  }
  Line(Point p, Point q) {
    a = p, b = q;
    ab = b - a;
    if (a != b)
      isline = 1;
    else
      isline = 0;
  }
  void update(Point p, Point q) {
    a = p, b = q;
    ab = b - a;
    if (a != b)
      isline = 1;
    else
      isline = 0;
    return;
  }
  bool operator==(Line other) {
    return ((crossproduct(ab, other.ab) == 0) && online(other.a));
  }
  bool online(Point point) {
    if (!isline) return (point == a);
    return (crossproduct(point - a, ab) == 0);
  }
  bool onsegment(Point point) {
    if (!isline) return (point == a);
    Point va, vb;
    va = a - point, vb = b - point;
    return (crossproduct(va, vb) == 0 && dotproduct(va, vb) <= 0);
  }
  bool parallel(Line other) { return (crossproduct(ab, other.ab) == 0); }
  bool perpendicular(Line other) { return (dotproduct(ab, other.ab) == 0); }
  double distline(Point point) {
    if (!isline) return dist(a, point);
    long double t = abs(crossproduct(point - a, ab));
    t /= dist(ab);
    return t;
  }
  double distsegment(Point point) {
    if (dotproduct(point - a, ab) <= 0) return dist(a, point);
    if (dotproduct(point - b, ab) >= 0) return dist(b, point);
    return distline(point);
  }
  bool lineintersectcheck(Line ray) { return (crossproduct(ab, ray.ab) != 0); }
  bool inter1(int a, int b, int c, int d) {
    if (a > b) swap(a, b);
    if (c > d) swap(c, d);
    return max(a, c) <= min(b, d);
  }
  bool segmentintersectcheck(Line ray) {
    if (crossproduct(ab, ray.ab) == 0) {
      if (online(ray.a))
        return inter1(a.x, b.x, ray.a.x, ray.b.x) &&
               inter1(a.y, b.y, ray.a.y, ray.b.y);
      return false;
    }
    return (crossproduct(ray.a - a, ray.a - b) !=
            crossproduct(ray.b - a, ray.b - b)) &&
           (crossproduct(a - ray.a, a - ray.b) !=
            crossproduct(b - ray.a, b - ray.b));
  }
};
int squarechecker(vector<Point> &point) {
  if (point[0] == point[2] || point[1] == point[3]) return 0;
  double x = dist(point[0], point[3]);
  if (dist(point[0], point[1]) == x && dist(point[1], point[2]) == x &&
      dist(point[2], point[3]) == x)
    return (dotproduct(point[1] - point[2], point[3] - point[2]) == 0);
  return 0;
}
int main() {
  int a, b, c;
  scanf("%d%d%d", &a, &b, &c);
  double d, ans = 0;
  int V;
  cout << setprecision(12) << fixed;
  V = a * a * a;
  {
    string _s = "V";
    replace(_s.begin(), _s.end(), ',', ' ');
    stringstream _ss(_s);
    istream_iterator<string> _it(_ss);
    err(_it, V);
  };
  double s = sqrt(2);
  d = V / (6 * s);
  ans += d;
  a = b;
  V = a * a * a;
  {
    string _s = "V";
    replace(_s.begin(), _s.end(), ',', ' ');
    stringstream _ss(_s);
    istream_iterator<string> _it(_ss);
    err(_it, V);
  };
  d = V / (3 * s);
  ans += d;
  a = c;
  V = a * a * a;
  {
    string _s = "V";
    replace(_s.begin(), _s.end(), ',', ' ');
    stringstream _ss(_s);
    istream_iterator<string> _it(_ss);
    err(_it, V);
  };
  double h;
  h = 1 / (2 * sin(PI / 5));
  d = 1 - h * h;
  d = sqrt(d);
  d *= V;
  d = d / (12 * tan(PI / 5));
  d *= 5;
  ans += d;
  cout << ans << "\n";
}

```