Problem: Gaku decided to observe the ant's nest as a free study during the summer vacation. The transparent observation case that his grandpa prepared for his grandchildren is very unique and looks like Figure 1.

Ant nest
Figure 1



This case consists of two congruent convex polygons s1 and s2 and some rectangles. Place one of the rectangular faces other than s1 and s2 so that it touches the floor. Gogo, who started observing, noticed that the height of the soil changed depending on how the bottom was selected, even though the amount of soil contained was the same (Fig. 2).

Ant nest
Figure 2



Gogo wanted to know how high it would be depending on how the case was placed. Create a program that outputs the maximum value of the soil height by inputting the shape of the convex polygon s1, the distance d between s1 and s2, and the volume V of the soil. The soil shall level as soon as the bottom of the case is placed on the floor. The s1 shape of the transparent case is given by n vertices on the two-dimensional coordinate plane. These vertices are entered in a counterclockwise order. n is 3 or more and 100 or less, and d and V are integers of 1 or more and 10,000 or less, respectively. In addition, x and y of the coordinates (x, y) of the vertices of the polygon shall be integers of -1,000 or more and 1,000 or less, respectively. V does not exceed the volume of the case.



input

A sequence of multiple datasets is given as input. The end of the input is indicated by three zero lines. Each dataset is as follows.

1st line n d V (integer integer integer; half-width space delimited)
Coordinates of the first vertex on the second line x y (integer integer; half-width space delimited)
Coordinates of the second vertex on the third line
::
n + 1 Coordinates of the nth vertex on the 1st line


The number of datasets does not exceed 20.

output

Outputs the maximum soil height for each input dataset. The answer must not have an error greater than 0.00001.

Example

Input

4 1 1
0 0
1 0
1 2
0 2
0 0 0


Output

1.000000

Solution (in CPP):

Solution:
////////////////////////////////////////////////////////////////////////////////
// ?????¢??????

// ???????????§????????????
//   double  -> Point
//   Segment -> Line

// ???????????±?????¶???????????§?????????????????§????????¬???
// int main(){
//   const double EPS = 1e-9;
//   double a = 1.3, b = 1e8, c = a + b;
//   c = c - b;
//   printf("%d\n", equal(a, c));          // => 0
//   printf("%d\n", relative_equal(a, c)); // => 0
// }

////////////////////
// ???????????????
#include<cmath>
#include<algorithm>
#include<cassert>
////////////////////
// ?????°
const double EPS = 1e-9;                // |EPS|???????????°???0??¨????????±???
////////////////////
// ?§???????
struct Point {
  double x, y;
  Point(const double d = 0.0) : x(d), y(d) {}
  Point(const double x, const double y) : x(x), y(y) {}
};
struct Segment {
  Point initial, terminal;
  Segment(const Point& initial, const Point& terminal) : initial(initial), terminal(terminal) {}
  Segment(const double x1, const double y1, const double x2, const double y2) : initial(x1, y1), terminal(x2, y2) {}
};
struct Line {
  Point initial, terminal;
  Line(const Point& initial, const Point& terminal) : initial(initial), terminal(terminal) {}
  Line(const double x1, const double y1, const double x2, const double y2) : initial(x1, y1), terminal(x2, y2) {}
  Line(const Segment& s) : initial(s.initial), terminal(s.terminal) {}
};
////////////////////
// ????£?
bool relative_equal(const double d1, const double d2) {return d1 == 0 ? std::abs(d2) < EPS : std::abs((d1 - d2) / d1) < EPS;}
// ??????????????????????????????
bool operator==(const Point& lhs, const Point& rhs) {return relative_equal(lhs.x, rhs.x) && relative_equal(lhs.y, rhs.y);}
bool operator<(const Point& lhs, const Point& rhs) {return relative_equal(lhs.x, rhs.x) ? lhs.y < rhs.y : lhs.x < rhs.x;}
bool operator>(const Point& lhs, const Point& rhs) {return relative_equal(lhs.x, rhs.x) ? lhs.y > rhs.y : lhs.x > rhs.x;}
bool operator!=(const Point& lhs, const Point& rhs) {return !(lhs == rhs);}
bool operator<=(const Point& lhs, const Point& rhs) {return !(lhs > rhs);}
bool operator>=(const Point& lhs, const Point& rhs) {return !(lhs < rhs);}
const Point operator+(const Point& lhs, const Point& rhs) {return Point(lhs.x + rhs.x, lhs.y + rhs.y);}
const Point operator-(const Point& lhs, const Point& rhs) {return Point(lhs.x - rhs.x, lhs.y - rhs.y);}
const Point operator*(const Point& lhs, const Point& rhs) {return Point(lhs.x * rhs.x, lhs.y * rhs.y);}
const Point operator/(const Point& lhs, const Point& rhs) {return Point(lhs.x / rhs.x, lhs.y / rhs.y);}
const Point operator-(const Point& p) {return Point(-p.x, -p.y);}
// ???
double abs(const Point& p) {return std::hypot(p.x, p.y);}
double norm(const Point& p) {return p.x * p.x + p.y * p.y;}
double dot(const Point& a, const Point& b) {return a.x * b.x + a.y * b.y;}
double cross(const Point& a, const Point& b) {return a.x * b.y - a.y * b.x;}
const Point normalize(const Point& p) {return p / abs(p);}
// ??????
// Segment shrink(const Segment& s, const double d = EPS) {
//   Point p = (s.terminal - s.initial) * d;
//   return Segment(s.initial + p, s.terminal - p);
// }
// ???
bool parallel(const Line& l1, const Line& l2) {return std::abs(cross(l2.terminal - l2.initial, l1.terminal - l1.initial)) < EPS;}
bool orthogonal(const Line& l1, const Line& l2) {return std::abs(dot(l2.terminal - l2.initial, l1.terminal - l1.initial)) < EPS;}
// ??????????????¢???
enum POSITION {ONLINE_FRONT = -2, CLOCKWISE, ON_SEGMENT, COUNTER_CLOCKWISE, ONLINE_BACK}; 
POSITION ccw(const Point& a, const Point& b, const Point& p) {
  Point v1 = b - a;
  Point v2 = p - a;
  if(cross(v1, v2) >= EPS) return COUNTER_CLOCKWISE;
  if(cross(v1, v2) <= -EPS) return CLOCKWISE;
  if(dot(v1, v2) <= -EPS) return ONLINE_BACK;
  if(norm(v1) < norm(v2)) return ONLINE_FRONT;              // ????????????: norm(v1)<norm(v2)+EPS?????¨WrongAnswer
  return ON_SEGMENT;
}
// ????????????
bool intersect(const Point& p1, const Point& p2) {return p1 == p2;}
bool intersect(const Point& p, const Segment& s) {return abs(p - s.initial) + abs(p - s.terminal) - abs(s.initial - s.terminal) <= EPS;}
bool intersect(const Segment& s, const Point& p) {return intersect(p, s);}
bool intersect(const Point& p, const Line& l) {return !parallel(Line(p, l.initial), Line(p, l.terminal));}
bool intersect(const Line& l, const Point& p) {return intersect(p, l);}
bool intersect(const Segment& s1, const Segment& s2) {
  return ccw(s1.initial, s1.terminal, s2.initial) * ccw(s1.initial, s1.terminal, s2.terminal) <= 0
      && ccw(s2.initial, s2.terminal, s1.initial) * ccw(s2.initial, s2.terminal, s1.terminal) <= 0;
}
bool intersect(const Segment& s, const Line& l) {
  auto v1 = l.terminal - l.initial;
  auto v2 = s.initial  - l.initial;
  auto v3 = s.terminal - l.initial;
  return cross(v1, v2) * cross(v1, v3) <= EPS;
}
bool intersect(const Line& l, const Segment& s) {return intersect(s, l);}
bool intersect(const Line& l1, const Line& l2) {return !parallel(l1, l2) || intersect(l1.initial, l2);}
// ???????§????
Point projection(const Point& p, const Line& l) {
  auto v = l.initial - l.terminal;
  return l.initial + dot(p - l.initial, v) / norm(v) * v;
}
Point projection(const Line& l, const Point& p) {return projection(p, l);}
Point reflection(const Point& p, const Line& l) {return p + 2 * (projection(p, l) - p);}
Point reflection(const Line& l, const Point& p) {return reflection(p, l);}
// ?????¢
double distance(const Point& p1, const Point& p2) {
  auto p = p1 - p2;
  return hypot(p.x, p.y);
}
double distance(const Point& p, const Segment& s) {
  auto r = projection(s, p);
  return intersect(r, s) ? distance(p, r) : std::min(distance(p, s.initial), distance(p, s.terminal));
}
double distance(const Segment& s, const Point& p) {return distance(p, s);}
double distance(const Point& p, const Line& l) {return distance(p, projection(p, l));}
double distance(const Line& l, const Point& p) {return distance(p, l);}
double distance(const Segment& s1, const Segment& s2) {
  return intersect(s1, s2) ? 0.0 : std::min({distance(s1, s2.initial), distance(s1, s2.terminal), distance(s2, s1.initial), distance(s2, s1.terminal)});
}
double distance(const Segment& s, const Line& l) {return intersect(s, l) ? 0.0 : std::min(distance(s.initial, l), distance(s.terminal, l));}
double distance(const Line& l,const Segment& s) {return distance(s, l);}
double distance(const Line& l1, const Line& l2) {return intersect(l1, l2) ? 0.0 : distance(l1.initial, l2);}
// ??????
const Point crosspoint(const Line& l1, const Line& l2) {
  assert(intersect(l1, l2));
  if(parallel(l1, l2)) return l1.initial;                   // ???????????¨???l1????§?????????????
  double A = cross(l1.terminal - l1.initial, l2.terminal - l2.initial);
  double B = cross(l1.terminal - l1.initial, l1.terminal - l2.initial);
  return l2.initial + B / A * (l2.terminal - l2.initial);
}
const Point crosspoint(const Segment& s, const Line& l) {
  assert(intersect(s, l));
  if(parallel(s, l)) return s.initial;
  Point cp = crosspoint(Line(s), l);
//   assert(intersect(s, cp));
  return cp;
}
const Point crosspoint(const Line& l, const Segment& s) {return crosspoint(s, l);}
const Point crosspoint(const Segment& s1, const Segment& s2) {
  assert(intersect(s1, s2));
  if(parallel(s1, s2)) {                                    // ???????????¨?????????????????????????????????
    if(intersect(s1.initial,  s2)) return s1.initial;
    if(intersect(s1.terminal, s2)) return s1.terminal;
    if(intersect(s2.initial,  s1)) return s2.initial;
    if(intersect(s2.terminal, s1)) return s2.terminal;
  }
  return crosspoint(Line(s1), Line(s2));
}
// ???????????°??¨
// #include<bits/stdc++.h>
// using namespace std;
// ostream& operator<<(ostream& os, const Point& p) {os<<"point: "; os<<"("<<p.x<<","<<p.y<<")"; return os;}
// ostream& operator<<(ostream& os, const Segment& s) {os<<"segment: "; os<<s.initial<<" - "<<s.terminal; return os;}
// ostream& operator<<(ostream& os, const Line& l) {os<<"line: "; os<<l.initial<<" - "<<l.terminal; return os;}
////////////////////////////////////////////////////////////////////////////////
// ????§???¢
//   ????????????????????°????????????????????¢???????´????edge(void)???O(????????°)???edge().begin()????????£????????????????????????????????????????????????
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
class Polygon {
public:
  // ??¨???
  void add(const Point& p);
  void clear();
  // ?????±
  int size() const;
  Point vertex(const int n) const;
  Segment edge(const int n) const;
  const std::vector<Point>& vertex() const;
  const std::vector<Segment>& edge() const;
  // ??????
  bool touch(const Point& p) const;
  bool intersect(const Point& p) const;
  double area() const;
  bool convex() const;
  // ???????§???¢
  const Polygon convex_hull() const;
  double convex_diameter() const;
  const Polygon convex_cut(const Line& l) const;
private:
  std::vector<Point> vertex_;
  std::vector<Segment> edge_;
};
// ??¨???
void Polygon::add(const Point& p) {
  if(!vertex_.empty()) {
    if(!edge_.empty()) edge_.pop_back();
    edge_.push_back(Segment(vertex_.back(), p));
    edge_.push_back(Segment(p, vertex_.front()));
  }
  vertex_.push_back(p);
}
void Polygon::clear() {
  vertex_.clear();
  edge_.clear();
};
// ?????±
int Polygon::size() const {return vertex_.size();}
Point Polygon::vertex(const int n) const {return vertex_.at(n);}
Segment Polygon::edge(const int n) const {return edge_.at(n);}
const std::vector<Point>& Polygon::vertex() const {return vertex_;}
const std::vector<Segment>& Polygon::edge() const {return edge_;}
// ??????
bool Polygon::touch(const Point& p) const {
  return std::any_of(std::begin(edge()), std::end(edge()), [=](const Segment& s) {return ccw(s.initial, s.terminal, p) == ON_SEGMENT;});
}
bool Polygon::intersect(const Point& p) const {
  bool in = false;                    // p=(x,y)??????(INF,y)???????????´?????¨????§???¢??¨????????????????????° mod 2
  for(const auto& e: edge()) {
    if(::intersect(p, e)) return true;
    Point a = e.initial  - p;
    Point b = e.terminal - p;
    if(a.y > b.y) std::swap(a, b);
    if(a.y < EPS && EPS <= b.y && cross(a, b) < EPS) in = !in;
  }
  return in;
}
double Polygon::area() const {
  return std::abs(std::accumulate(std::begin(edge()), std::end(edge()), 0.0, [=](const double sum, const Segment& e){return sum + cross(e.initial, e.terminal);})) / 2.0;
}
bool Polygon::convex() const {
  bool positive = false;
  bool negative = false;
  for(int i = 0; i < size(); ++i) {
    auto position = ccw(vertex(i), vertex((i + 1) % size()), vertex((i + 2) % size()));
    positive |= position == CLOCKWISE;
    negative |= position == COUNTER_CLOCKWISE;
    if(negative && positive) return false;
  }
  return true;
}
// ??????
// Andrew's Monotone Chain
const Polygon Polygon::convex_hull() const {
  auto original = vertex();
  std::sort(std::begin(original), std::end(original));
  original.insert(std::end(original), original.rbegin() + 1, original.rend());
  std::vector<Point> point;
  for(const auto& p: original) {
    while(point.size() >= 2 && ccw(point[point.size() - 2], point.back(), p) == CLOCKWISE) point.pop_back();
    point.push_back(p);
  }
  Polygon convex_hull;
  point.pop_back();
  for(const auto& p: point) convex_hull.add(p);
  return convex_hull;
}
// Rotating calipers
double Polygon::convex_diameter() const {
  auto point = vertex();
  int p, q, start_p, start_q, max_p, max_q;
  p = start_p = max_p = std::min_element(std::begin(point), std::end(point)) - std::begin(point);
  q = start_q = max_q = std::max_element(std::begin(point), std::end(point)) - std::begin(point);
  double max_d = norm(vertex(p) - vertex(q));
  do {
    if(cross(vertex((p + 1) % size()) - vertex(p), vertex((q + 1) % size()) - vertex(q)) >= 0) q = (q + 1) % size();
    else p = (p + 1) % size();
    if(norm(vertex(p) - vertex(q)) > max_d) {
      max_d = norm(vertex(p) - vertex(q));
      max_p = p;
      max_q = q;
    }
  } while(start_p != q || start_q != p);
  return std::sqrt(max_d);
}
const Polygon Polygon::convex_cut(const Line& l) const {
  Polygon result;
  for(const auto& e: edge()) {
    if(ccw(l.initial, l.terminal, e.initial) == COUNTER_CLOCKWISE) result.add(e.initial);
    if(::intersect(e, l)) result.add(crosspoint(e, l));
  }
  return result;
}
////////////////////////////////////////////////////////////////////////////////
#include<bits/stdc++.h>
using namespace std;
int main() {
  int n;
  double d, V;
  while(cin >> n >> d >> V, n + d + V) {
    vector<Point> point;
    for(int i = 0; i < n; ++i) {
      int x, y;
      cin >> x >> y;
      point.emplace_back(x, y);
    }
    Polygon polygon;
    for(const auto& p: point) polygon.add(p);
    double answer = 0.0;
    for(const auto& e: polygon.edge()) {
      Point p = e.terminal - e.initial;
      Point n = normalize(Point(-p.y, p.x));
      double low = 0.0;
      double high = 4000.0;
      while(high - low > EPS) {
        double middle = (low + high) / 2.0;
        double area = polygon.convex_cut(Line(e.terminal + (n * middle), e.initial + (n * middle))).area();
        if(area * d < V) low = middle;
        else high = middle;
      }
      answer = max(answer, low);
    }
    cout << setprecision(10) << fixed << answer << endl;
  }
}