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:
#include <bits/stdc++.h>
using namespace std;

namespace geometry {
	// ???????????§??????
	
	typedef complex<double> Point;
	
	struct Segment {
		Point p1, p2;
		Segment(const Point &p1 = Point(), const Point &p2 = Point()): p1(p1), p2(p2){}
	};
	
	struct Circle {
		Point p;
		double r;
		Circle(const Point &p = Point(), double r = 0.0): p(p), r(r){}
	};
	
	typedef Point Vector;
	typedef Segment Line;
	typedef vector<Point> Polygon;
	
	
	// ??\??????
	
	inline istream & operator >> (istream &is, Point &p){
		double x, y;
		is >> x >> y;
		p.real(x), p.imag(y);
		return is;
	}
	
	inline istream & operator >> (istream &is, Segment &s){
		return is >> s.p1 >> s.p2;
	}
	
	inline istream & operator >> (istream &is, Circle &c){
		return is >> c.p >> c.r;
	}
	
	inline ostream & operator << (ostream &os, Segment &s){
		return os << "{" << s.p1 << ", " << s.p2 << "}";
	}
	
	inline ostream & operator << (ostream &os, Circle &c){
		return os << "{" << c.p << ", " << c.r << "}";
	}
	
	inline ostream & operator << (ostream &os, Polygon &g){
		os << "{";
		for (int i = 0; i < g.size(); i++){
			if (i) os << ", ";
			os << g[i];
		}
		return os << "}";
	}
	
	
	// ?????°, ??????
	
	const double PI = acos(-1);
	const double EPS = 1e-8;
	const double INF = 1e16;
	const int COUNTER_CLOCKWISE = 1;
	const int CLOCKWISE 		= -1;
	const int ONLINE_BACK		= 2;
	const int ONLINE_FRONT		= -2;
	const int ON_SEGMENT		= 0;
	const int OUT				= 0;
	const int ON				= 1;
	const int IN				= 2;
	
	inline double square(double a){return a * a;}
	inline bool equal(double a, double b){return abs(a - b) < EPS;}
	inline bool equalVector(const Vector &a, const Vector &b){return equal(a.real(), b.real()) && equal(a.imag(), b.imag());}
	inline double norm(const Point &a){return square(a.real()) + square(a.imag());}
	inline double dot(const Point &a, const Point &b){return (conj(a) * b).real();}
	inline double cross(const Point &a, const Point &b){return (conj(a) * b).imag();}
	inline double toDeg(double t){return t / PI * 180;}
	inline double toRad(double t){return t / 180 * PI;}
	
	#define curr(v, i) v[i]
	#define next(v, i) v[(i + 1) % v.size()]
	#define prev(v, i) v[(i - 1 + v.size()) % v.size()]
	
	
	// ????????¢??° (x ??§?¨?, y ??§?¨?, ????§?)
	// ????§?????????????????????? Point rp ?????£??\????????????
	
	bool cmpx(const Point &a, const Point &b){
		if (!equal(a.real(), b.real())) return a.real() < b.real();
		return b.imag() < b.imag();
	}
	
	bool cmpy(const Point &a, const Point &b){
		if (!equal(a.imag(), b.imag())) return a.imag() < b.imag();
		return a.real() < b.real();
	}
	
	Point rp;
	bool cmparg(const Point &a, const Point &b){
		double rada = arg(a - rp); if (rada < 0.0) rada += 2 * PI;
		double radb = arg(b - rp); if (radb < 0.0) radb += 2 * PI;
		if (!equal(rada, radb)) return rada < radb;
		return norm(a) < norm(b);
	}
	
	
	// ??´???, ??????
	
	bool orthgonal(const Vector &a, const Vector &b){
		return equal(dot(a, b), 0.0);
	}
	
	bool parallel(const Vector &a, const Vector &b){
		return equal(cross(a, b), 0.0);
	}
	
	
	// ????°?, ?°???±
	
	Point project(const Segment &s, const Point &p){
		Vector base = s.p2 - s.p1;
		double r = dot(p - s.p1, base) / norm(base);
		return s.p1 + base * r;
	}
	
	Point reflect(const Segment &s, const Point &p){
		return p + (project(s, p) - p) * 2.0;
	}
	
	
	// ??????????????????
	
	int ccw(const Point &p0, const Point &p1, const Point &p2){
		Vector a = p1 - p0;
		Vector b = p2 - p0;
		if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;
		if (cross(a, b) < -EPS) return CLOCKWISE;
		if (dot(a, b) < -EPS) return ONLINE_BACK;
		if (norm(a) > norm(b)) return ONLINE_FRONT;
		return ON_SEGMENT;
	}
	
	
	// ?????¢
	
	double distanceLP(const Line &l, const Point &p){
		return abs(cross(l.p2 - l.p1, p - l.p1) / abs(l.p2 - l.p1));
	}
	
	double distanceSP(const Segment &s, const Point &p){
		if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return abs(p - s.p1);
		if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return abs(p - s.p2);
		return distanceLP(s, p);
	}
	
	bool intersect(const Segment &s1, const Segment &s2);
	double distance(const Segment &s1, const Segment &s2){
		if (intersect(s1, s2)) return 0.0;
		return min(
			min(distanceSP(s1, s2.p1), distance(s1, s2.p2)),
			min(distanceSP(s2, s1.p1), distance(s2, s1.p2))
		);
	}
	
	
	// ????????????
	
	bool intersect(const Segment &s1, const Segment &s2){
		return ccw(s1.p1, s1.p2, s2.p1) * ccw(s1.p1, s1.p2, s2.p2) <= 0 &&
			ccw(s2.p1, s2.p2, s1.p1) * ccw(s2.p1, s2.p2, s1.p2) <= 0;
	}
	
	int intersect(const Circle &c, const Segment &s){
		// ???????????° (0 ~ 2) ?????????
		double dist = distanceSP(s, c.p) - c.r;
		if (equal(dist, 0.0)) return 1;
		if (dist < 0.0) return 2;
		return 0;
	}
	
	int intersect(const Circle &c1, const Circle &c2){
		// ???????????° (0 ~ 2) ?????????
		double dist = abs(c1.p - c2.p) - (c1.r + c2.r);
		if (equal(dist, 0.0)) return 1;
		if (dist < 0.0) return 2;
		return 0;
	}
	
	
	// ??????
	
	Point crossPoint(const Segment &s1, const Segment &s2){
		Vector base = s2.p2 - s2.p1;
		double d1 = abs(cross(base, s1.p1 - s2.p1));
		double d2 = abs(cross(base, s1.p2 - s2.p1));
		
		// !! ????????´?????¶????????????????????\????????¨ 0 ?????? !!
		assert(!equal(d1 + d2, 0.0));
		
		double t = d1 / (d1 + d2);
		return s1.p1 + (s1.p2 - s1.p1) * t;
	}
	
	vector<Point> crossPoints(const Circle &c, const Line &l){
		vector<Point> res;
		if (!intersect(c, l)) return res;
		
		Vector pr = project(l, c.p);
		Vector e = (l.p2 - l.p1) / abs(l.p2 - l.p1);
		double base = sqrt(c.r * c.r - norm(pr - c.p));
		res.push_back(pr + e * base);
		res.push_back(pr - e * base);
		if (equalVector(res[0], res[1])) res.pop_back();
		return res;
	}
	
	vector<Point> crossPoints(const Circle &c1, const Circle &c2){
		vector<Point> res;
		if (!intersect(c1, c2)) return res;
		
		double d = abs(c1.p - c2.p);
		double a = acos(square(c1.r) + square(d) - square(c2.r) / (2 * c2.r * d));
		double t = arg(c2.p - c1.p);
		res.push_back(c1.p + polar(c1.r, t + a));
		res.push_back(c1.p + polar(c1.r, t - a));
		if (equalVector(res[0], res[1])) res.pop_back();
	}
	
	
	// ??????
	
	int contains(const Polygon &g, const Point &p){
		int n = g.size();
		bool res = false;
		for (int i = 0; i < n; i++){
			Point a = g[i] - p;
			Point b = g[(i + 1) % n] - p;
			if (abs(cross(a, b)) < EPS && dot(a, b) < EPS) return ON;
			if (a.imag() > b.imag()) swap(a, b);
			if (a.imag() < EPS && EPS < b.imag() && cross(a, b) > EPS) res = !res;
		}
		return res ? IN : OUT;
	}
	
	
	// ??????
	
	Polygon convexHull(vector<Point> s){
		Polygon u, l;
		if (s.size() < 3) return s;
		sort(s.begin(), s.end());
		u.push_back(s[0]);
		u.push_back(s[1]);
		l.push_back(s[s.size() - 1]);
		l.push_back(s[s.size() - 2]);
		
		for (int i = 2; i < s.size(); i++){
			int n = u.size();
			while (n >= 2 && ccw(u[n - 2], u[n - 1], s[i]) != CLOCKWISE){
				u.pop_back();
				n--;
			}
			u.push_back(s[i]);
		}
		
		for (int i = s.size() - 3; i >= 0; i--){
			int n = l.size();
			while (n >= 2 && ccw(l[n - 2], l[n - 1], s[i]) != CLOCKWISE){
				l.pop_back();
				n--;
			}
			l.push_back(s[i]);
		}
		
		reverse(l.begin(), l.end());
		for (int i = u.size() - 2; i >= 1; i--){
			l.push_back(u[i]);
		}
		
		return l;
	}
	
	
	// ???????§???¢??????
	
	Polygon convexCut(const Polygon &g, const Line &l){
		Polygon res;
		for (int i = 0; i < g.size(); i++){
			const Point &a = curr(g, i);
			const Point &b = next(g, i);
			if (ccw(l.p1, l.p2, a) != CLOCKWISE){
				res.push_back(a);
			}
			if (ccw(l.p1, l.p2, a) * ccw(l.p1, l.p2, b) < 0){
				res.push_back(crossPoint(Line(a, b), l));
			}
		}
		
		return res;
	}
}

namespace std {
	bool operator < (const geometry::Point &a, const geometry::Point &b){
		return geometry::cmpx(a, b);
	}
}



using namespace geometry;

double area(const Polygon &g){
	double res = 0.0;
	for (int i = 1; i + 1 < g.size(); i++){
		const Point &p1 = curr(g, i);
		const Point &p2 = next(g, i);
		res += cross(p1 - g[0], p2 - g[0]);
	}
	return res / 2;
}


int n;
double d, V;
Polygon g;

double solve()
{
	double res = 0.0;
	
	for (int i = 0; i < n; i++){
		Line l(curr(g, i), next(g, i));
		Vector t = l.p2 - l.p1;
		l.p2 += t * 1000.0;
		l.p1 -= t * 1000.0;
		Vector un = (l.p2 - l.p1) * Vector(0, 1) / abs(l.p2 - l.p1);
		
		double left = 0.0;
		double right = 0.0;
		for (int j = 0; j < n; j++){
			double height = distanceLP(l, g[j]);
			right = max(right, height);
		}
		
		for (int loop = 0; loop < 100; loop++){
			double mid = (left + right) / 2;
			Line cl(l.p2 + un * mid, l.p1 + un * mid);
			Polygon ccg = convexCut(g, cl);
			double ar = area(ccg);
			
			//cout << mid << endl;
			
			if (ar * d < V) left = mid;
			else right = mid;
		}
		
		res = max(res, left);
	}
	
	return res;
}

int main()
{
	while (cin >> n >> d >> V, n){
		g.resize(n);
		for (int i = 0; i < n; i++){
			cin >> g[i];
		}
		
		printf("%.8f\n", solve());
	}
	
	return 0;
}