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 <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <numeric>
#include <bitset>
#include <cmath>

static const int MOD = 1000000007;
using ll = long long;
using u32 = unsigned;
using u64 = unsigned long long;
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max()/32*15+208;

using real = double;
static constexpr real EPS = 1e-10;
struct Point {
    real x, y;
    Point& operator+=(const Point a) { x += a.x; y += a.y;  return *this; }
    Point& operator-=(const Point a) { x -= a.x; y -= a.y;  return *this; }
    Point& operator*=(const real k) { x *= k; y *= k;  return *this; }
    Point& operator/=(const real k) { x /= k; y /= k;  return *this; }
    Point operator+(const Point a) const {return Point(*this) += a; }
    Point operator-(const Point a) const {return Point(*this) -= a; }
    Point operator*(const real k) const {return Point(*this) *= k; }
    Point operator/(const real k) const {return Point(*this) /= k; }
    bool operator<(const Point &a) const { return (x != a.x ? x < a.x : y < a.y); }
    explicit Point(real a = 0, real b = 0) : x(a), y(b) {};
};

bool sorty(Point a, Point b){
    return (a.y != b.y ? a.y < b.y : a.x < b.x);
}

istream& operator>> (istream& s, Point& P){
    s >> P.x >> P.y;
    return s;
}

inline real dot(Point a, Point b){ return a.x*b.x + a.y*b.y; }
inline real cross(Point a, Point b){ return a.x*b.y - a.y*b.x; }
inline real abs(Point a){ return sqrt(dot(a, a)); }


real angle(Point A, Point B){
    return acos(dot(A, B)/abs(A)/abs(B));
}



static constexpr int COUNTER_CLOCKWISE = 1;
static constexpr int CLOCKWISE = -1;
static constexpr int ONLINE_BACK = 2;
static constexpr int ONLINE_FRONT = -2;
static constexpr int ON_SEGMENT = 0;

int ccw(Point a, Point b, Point c){
    b -= a; c -= a;
    if(cross(b, c) > EPS) return COUNTER_CLOCKWISE;
    if(cross(b, c) < -EPS) return CLOCKWISE;
    if(dot(b, c) < 0) return ONLINE_BACK;
    if(abs(b) < abs(c)) return ONLINE_FRONT;
    return ON_SEGMENT;
}
struct Segment {
    Point a, b;
    Segment(Point x, Point y) : a(x), b(y) {};
};

struct Line {
    Point a, b;
    Line(Point x, Point y) : a(x), b(y) {};
};

struct Circle{
    Point c; real r;
    Circle(Point c, real r): c(c), r(r) {};
};

using Polygon = vector<Point>;

bool intersect(Segment s, Segment t){
    return (ccw(s.a, s.b, t.a)*ccw(s.a, s.b, t.b) <= 0 &&
            ccw(t.a, t.b, s.a)*ccw(t.a, t.b, s.b) <= 0);
}

bool intersect(Segment s, Line t){
    int a = ccw(t.a, t.b, s.a), b = ccw(t.a, t.b, s.b);
    return (!(a&1) || !(b&1) || a != b);
}

Point polar(double r, double t){
    return Point(r*cos(t), r*sin(t));
}

double arg(Point p){
    return atan2(p.y, p.x);
}

static constexpr int CONTAIN = 0;
static constexpr int INSCRIBE = 1;
static constexpr int INTERSECT = 2;
static constexpr int CIRCUMSCRIBED = 3;
static constexpr int SEPARATE = 4;

int intersect(Circle c1, Circle c2){
    if(c1.r < c2.r) swap(c1, c2);
    real d = abs(c1.c-c2.c);
    real r = c1.r + c2.r;
    if(fabs(d-r) < EPS) return CIRCUMSCRIBED;
    if(d > r) return SEPARATE;
    if(fabs(d+c2.r-c1.r) < EPS) return INSCRIBE;
    if(d+c2.r < c1.r) return CONTAIN;
    return INTERSECT;
}

real distance(Line l, Point c){
    return abs(cross(l.b-l.a, c-l.a)/abs(l.b-l.a));
}


real distance(Segment s, Point c){
    if(dot(s.b-s.a, c-s.a) < EPS) return abs(c-s.a);
    if(dot(s.a-s.b, c-s.b) < EPS) return abs(c-s.b);
    return abs(cross(s.b-s.a, c-s.a)) / abs(s.a-s.b);
}

real distance(Segment s, Segment t){
    if(intersect(s, t)) return 0.0;
    return min({distance(s, t.a), distance(s, t.b),
                distance(t, s.a), distance(t, s.b)});
}


Point project(Line l, Point p){
    Point Q = l.b-l.a;
    return l.a + Q*(dot(p-l.a, Q) / dot(Q, Q));
}


Point project(Segment s, Point p){
    Point Q = s.b-s.a;
    return s.a + Q*(dot(p-s.a, Q) / dot(Q, Q));
}

Point refrect(Segment s, Point p){
    Point Q = project(s, p);
    return Q*2-p;
}

bool isOrthogonal(Segment s, Segment t){
    return fabs(dot(s.b-s.a, t.b-t.a)) < EPS;
}

bool isparallel(Segment s, Segment t){
    return fabs(cross(s.b-s.a, t.b-t.a)) < EPS;
}


Point crossPoint(Segment s, Segment t){
    real d1 = cross(s.b-s.a, t.b-t.a);
    real d2 = cross(s.b-s.a, s.b-t.a);
    if(fabs(d1) < EPS && fabs(d2) < EPS) return t.a;
    return t.a+(t.b-t.a)*d2/d1;
}

Point crossPoint(Line s, Line t){
    real d1 = cross(s.b-s.a, t.b-t.a);
    real d2 = cross(s.b-s.a, s.b-t.a);
    if(fabs(d1) < EPS && fabs(d2) < EPS) return t.a;
    return t.a+(t.b-t.a)*d2/d1;
}

Polygon crossPoint(Circle c, Line l){
    Point p = project(l, c.c), q = (l.b-l.a)/abs(l.b-l.a);
    if(abs(distance(l, c.c)-c.r) < EPS){
        return {p};
    }
    double k = sqrt(c.r*c.r-dot(p-c.c, p-c.c));
    return {p-q*k, p+q*k};
}

Polygon crossPoint(Circle c, Segment s){
    auto tmp = crossPoint(c, Line(s.a, s.b));
    Polygon ret;
    for (auto &&i : tmp) {
        if(distance(s, i) < EPS) ret.emplace_back(i);
    }
    return ret;
}


Polygon crossPoint(Circle c1, Circle c2){
    double d = abs(c1.c-c2.c);
    double a = acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d));
    double t = arg(c2.c-c1.c);
    return {c1.c+polar(c1.r, t+a), c1.c+polar(c1.r, t-a)};
}

Polygon tangent(Circle c1, Point p){
    Circle c2 = Circle(p, sqrt(dot(c1.c-p, c1.c-p)-c1.r*c1.r));
    return crossPoint(c1, c2);
}
vector<Line> tangent(Circle c1, Circle c2){
    vector<Line> ret;
    if(c1.r < c2.r) swap(c1, c2);
    double k = dot(c1.c-c2.c, c1.c-c2.c);
    if(abs(k) < EPS) return {};
    Point u = (c2.c-c1.c)/sqrt(k);
    Point v(-u.y, u.x);
    for (auto &&i : {-1, 1}) {
        double h = (c1.r+i*c2.r)/sqrt(k);
        if(abs(h*h-1) < EPS){
            ret.emplace_back(c1.c+u*c1.r, c1.c+(u+v)*c1.r);
        }else if(h*h < 1){
            Point u2 = u*h, v2 = v*sqrt(1-h*h);
            ret.emplace_back(c1.c+(u2+v2)*c1.r, c2.c-(u2+v2)*c2.r*i);
            ret.emplace_back(c1.c+(u2-v2)*c1.r, c2.c-(u2-v2)*c2.r*i);
        }
    }
    return ret;
}

real area(Polygon v){
    if(v.size() < 3) return 0.0;
    real ans = 0.0;
    for (int i = 0; i < v.size(); ++i) {
        ans += cross(v[i], v[(i+1)%v.size()]);
    }
    return ans/2;
}

real area(Circle c, Polygon &v){
    int n = v.size();
    real ans = 0.0;
    Polygon u;
    for (int i = 0; i < n; ++i) {
        u.emplace_back(v[i]);
        auto q = crossPoint(c, Segment(v[i], v[(i+1)%n]));
        for (auto &&j : q) {
            u.emplace_back(j);
        }
    }
    for (int i = 0; i < u.size(); ++i) {
        Point A = u[i]-c.c, B = u[(i+1)%u.size()]-c.c;
        if(abs(A) >= c.r+EPS || abs(B) >= c.r+EPS){
            Point C = polar(1, arg(B)-arg(A));
            ans += c.r*c.r*arg(C)/2;
        }else {
            ans += cross(A, B)/2;
        }
    }
    return ans;
}

Polygon convex_hull(Polygon v){
    int n = v.size();
    sort(v.begin(),v.end(), sorty);
    int k = 0;
    Polygon ret(n*2);
    for (int i = 0; i < n; ++i) {
        while(k > 1 && cross(ret[k-1]-ret[k-2], v[i]-ret[k-1]) < 0) k--;
        ret[k++] = v[i];
    }
    for(int i = n-2, t=k; i >= 0; i--){
        while(k > t && cross(ret[k-1]-ret[k-2], v[i]-ret[k-1]) < 0) k--;
        ret[k++] = v[i];
    }
    ret.resize(k-1);
    return ret;
}

bool isconvex(Polygon v){
    int n = v.size();
    for (int i = 0; i < n; ++i) {
        if(ccw(v[(i+n-1)%n], v[i], v[(i+1)%n]) == CLOCKWISE) return false;
    }
    return true;
}

int contains(Polygon v, Point p){
    int n = v.size();
    bool x = false;
    static constexpr int IN = 2;
    static constexpr int ON = 1;
    static constexpr int OUT = 0;
    for (int i = 0; i < n; ++i) {
        Point a = v[i]-p, b = v[(i+1)%n]-p;
        if(fabs(cross(a, b)) < EPS && dot(a, b) < EPS) return ON;
        if(a.y > b.y) swap(a, b);
        if(a.y < EPS && EPS < b.y && cross(a, b) > EPS) x = !x;
    }
    return (x?IN:OUT);
}

real diameter(Polygon v){
    int n = v.size();
    if(n == 2) return abs(v[0]-v[1]);
    int i = 0, j = 0;
    for (int k = 0; k < n; ++k) {
        if(v[i] < v[k]) i = k;
        if(!(v[j] < v[k])) j = k;
    }
    real ret = 0;
    int si = i, sj = j;
    while(i != sj || j != si){
        ret = max(ret, abs(v[i]-v[j]));
        if(cross(v[(i+1)%n]-v[i], v[(j+1)%n]-v[j]) < 0.0) i = (i+1)%n;
        else j = (j+1)%n;
    }
    return ret;
}

Polygon convexCut(Polygon v, Line l){
    Polygon q;
    int n = v.size();
    for (int i = 0; i < n; ++i) {
        Point a = v[i], b = v[(i+1)%n];
        if(ccw(l.a, l.b, a) != -1) q.push_back(a);
        if(ccw(l.a, l.b, a)*ccw(l.a, l.b, b) < 0){
            q.push_back(crossPoint(Line(a, b), l));
        }
    }
    return q;
}

real closest_pair(Polygon &v, int l = 0, int r = -1){
    if(!(~r)){
        r = v.size();
        sort(v.begin(),v.end());
    }
    if(r - l < 2) {
        return abs(v.front()-v.back());
    }
    int mid = (l+r)/2;
    real p = v[mid].x;
    real d = min(closest_pair(v, l, mid), closest_pair(v, mid, r));
    inplace_merge(v.begin()+l, v.begin()+mid, v.begin()+r, sorty);
    Polygon u;
    for (int i = l; i < r; ++i) {
        if(fabs(v[i].x-p) >= d) continue;
        for (int j = 0; j < u.size(); ++j) {
            real dy = v[i].y-next(u.rbegin(), j)->y;
            if(dy >= d) break;
            d = min(d, abs(v[i]-*next(u.rbegin(), j)));
        }
        u.emplace_back(v[i]);
    }
    return d;
}

void solve(int n, int d, int v){
    Polygon p(n);
    for (auto &&i : p) cin >> i;
    vector<Segment> S;
    for (int i = 0; i < n; ++i) {
        S.emplace_back(p[i], p[(i+1)%n]);
    }
    double ans = 0;
    for (int i = 0; i < n; ++i) {
        Point A(-(p[(i+1)%n]-p[i]).y, (p[(i+1)%n]-p[i]).x);
        A /= abs(A);
        double ok = 0, ng = 3000;
        for (int j = 0; j < 100; ++j) {
            double mid = (ok+ng)/2;
            Line x(p[(i+1)%n]+A*mid, p[i]+A*mid);
            int good = 0;
            for (int k = 0; k < n; ++k) {
                if(intersect(S[k], x)) good = 1;
            }
            if(!good){
                ng = mid;
                continue;
            }
            if(area(convexCut(p, x))*d <= v) ok = mid;
            else ng = mid;
        }
        ans = max(ans, ok);
    }
    printf("%.10lf\n", ans);
}


int main() {
    int n, d, v;
    while(cin >> n >> d >> v, n){
        solve(n, d, v);
    }
    return 0;
}