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;
#define rep(i,n) for (int i=0; i < (n); i++)
typedef double D;      // 座標値の型。doubleかlong doubleを想定
typedef complex<D> P;  // Point
typedef pair<P, P> L;  // Line
typedef vector<P> VP;
typedef vector<VP> Vcon;
const D EPS = 1e-10;    // 許容誤差。問題によって変える
#define X real()
#define Y imag()
#define LE(n,m) ((n) < (m) + EPS)
#define GE(n,m) ((n) + EPS > (m))
#define EQ(n,m) (abs((n)-(m)) < EPS)
 
// 内積　dot(a,b) = |a||b|cosθ
D dot(P a, P b) {return (conj(a)*b).X; }
 
// 外積　cross(a,b) = |a||b|sinθ
D cross(P a, P b) {  return (conj(a)*b).Y;}
 
// 点の進行方向
int ccw(P a, P b, P c) {
  b -= a;  c -= a;
  if (cross(b,c) >  EPS) return +1;  // counter clockwise
  if (cross(b,c) < -EPS) return -1;  // clockwise
  if (dot(b,c)   < -EPS) return +2;  // c--a--b on line
  if (norm(b) < norm(c)) return -2;  // a--b--c on line or a==b
  return 0;                          // a--c--b on line or a==c or b==c
}

bool isparallel(L a,L b){
  return cross(a.first-a.second,b.first-b.second) == 0.0 ;
}
 
/* 交差判定　直線・線分は縮退してはならない。接する場合は交差するとみなす。isecはintersectの略 */
 
// 直線と点
bool isecLP(P a1, P a2, P b) {
  return abs(ccw(a1, a2, b)) != 1;  // return EQ(cross(a2-a1, b-a1), 0); と等価
}
 
// 直線と直線
bool isecLL(P a1, P a2, P b1, P b2) {
  return !isecLP(a2-a1, b2-b1, 0) || isecLP(a1, b1, b2);
}
 
// 直線と線分
bool isecLS(P a1, P a2, P b1, P b2) {
  return cross(a2-a1, b1-a1) * cross(a2-a1, b2-a1) < EPS;
}
 
// 線分と線分
bool isecSS(P a1, P a2, P b1, P b2) {
  return ccw(a1, a2, b1)*ccw(a1, a2, b2) <= 0 &&
         ccw(b1, b2, a1)*ccw(b1, b2, a2) <= 0;
}
 
// 線分と点
bool isecSP(P a1, P a2, P b) {
  //return !ccw(a1, a2, b);
   return abs(a1 - b) + abs(a2 - b) - abs(a2 - a1) < EPS;  //Perfective
}
 
 
/* 距離　各直線・線分は縮退してはならない */
 
// 点pの直線aへの射影点を返す
P proj(P a1, P a2, P p) {
  return a1 + dot(a2-a1, p-a1)/norm(a2-a1) * (a2-a1);
}
 
// 点pの直線aへの反射点を返す
P reflection(P a1, P a2, P p) {
  return 2.0*proj(a1, a2, p) - p;
}
 
D distLP(P a1, P a2, P p) {
  return abs(proj(a1, a2, p) - p);
}
 
D distLL(P a1, P a2, P b1, P b2) {
  return isecLL(a1, a2, b1, b2) ? 0 : distLP(a1, a2, b1);
}
 
D distLS(P a1, P a2, P b1, P b2) {
  return isecLS(a1, a2, b1, b2) ? 0 : min(distLP(a1, a2, b1), distLP(a1, a2, b2));
}
 
D distSP(P a1, P a2, P p) {
  P r = proj(a1, a2, p);
  if (isecSP(a1, a2, r)) return abs(r-p);
  return min(abs(a1-p), abs(a2-p));
}
 
D distSS(P a1, P a2, P b1, P b2) {
  if (isecSS(a1, a2, b1, b2)) return 0;
  return min(min(distSP(a1, a2, b1), distSP(a1, a2, b2)),
             min(distSP(b1, b2, a1), distSP(b1, b2, a2)));
}
 
// 2直線の交点
P crosspointLL(P a1, P a2, P b1, P b2) {
  D d1 = cross(b2-b1, b1-a1);
  D d2 = cross(b2-b1, a2-a1);
  if (EQ(d1, 0) && EQ(d2, 0)) return a1;  // same line
  if (EQ(d2, 0)) throw "kouten ga nai";   // 交点がない
  return a1 + d1/d2 * (a2-a1);
}
 
 
/* 円 */
 
D distLC(P a1, P a2, P c, D r) {
  return max(distLP(a1, a2, c) - r, 0.0);
}
 
D distSC(P a1, P a2, P c, D r) {
  D dSqr1 = norm(c-a1), dSqr2 = norm(c-a2);
  if (dSqr1 < r*r ^ dSqr2 < r*r) return 0;  // 円が線分を包含するとき距離0ならここをORに変える
  if (dSqr1 < r*r & dSqr2 < r*r) return r - sqrt(max(dSqr1, dSqr2));
  return max(distSP(a1, a2, c) - r, 0.0);
}
 
VP crosspointLC(P a1, P a2, P c, D r) {
  VP ps;
  P ft = proj(a1, a2, c);
  if (!GE(r*r, norm(ft-c))) return ps;
 
  P dir = sqrt(max(r*r - norm(ft-c), 0.0)) / abs(a2-a1) * (a2-a1);
  ps.push_back(ft + dir);
  if (!EQ(r*r, norm(ft-c))) ps.push_back(ft - dir);
  return ps;
}
 
D distCC(P a, D ar, P b, D br) {
  D d = abs(a-b);
  return GE(d, abs(ar-br)) ? max(d-ar-br, 0.0) : abs(ar-br) - d;
}
 
// 2円の交点
VP crosspointCC(P a, D ar, P b, D br) {
  VP ps;
  P ab = b-a;
  D d = abs(ab);
  D crL = (norm(ab) + ar*ar - br*br) / (2*d);
  if (EQ(d, 0) || ar < abs(crL)) return ps;
 
  P abN = ab * P(0, sqrt(ar*ar - crL*crL) / d);
  P cp = a + crL/d * ab;
  ps.push_back(cp + abN);
  if (!EQ(norm(abN), 0)) ps.push_back(cp - abN);
  return ps;
}
 
// 点pから円aへの接線の接点
VP tangentPoints(P a, D ar, P p) {
  VP ps;
  D sin = ar / abs(p-a);
  if (!LE(sin, 1)) return ps;  // ここでNaNも弾かれる
  D t = M_PI_2 - asin(min(sin, 1.0));
  ps.push_back(                 a + (p-a)*polar(sin, t));
  if (!EQ(sin, 1)) ps.push_back(a + (p-a)*polar(sin, -t));
  return ps;
}
 
// 2円の共通接線。返される各直線に含まれる頂点は円との接点となる
vector<L> tangentLines(P a, D ar, P b, D br) {
  vector<L> ls;
  D d = abs(b-a);
  rep (i,2) {
    D sin = (ar - (1-i*2)*br) / d;
    if (!LE(sin*sin, 1)) break;
    D cos = sqrt(max(1 - sin*sin, 0.0));
    rep (j,2) {
      P n = (b-a) * P(sin, (1-j*2)*cos) / d;
      ls.push_back(L(a + ar*n, b + (1-i*2)*br*n));
      if (cos < EPS) break;  // 重複する接線を無視（重複していいならこの行不要）
    }
  }
  return ls;
}
 
// 三角形の外心。点a,b,cは同一線上にあってはならない
P circumcenter(P a, P b, P c) {
  a = (a-c)*0.5;
  b = (b-c)*0.5;
  return c + crosspointLL(a, a*P(1,1), b, b*P(1,1));
}
 
// 点aと点bを通り、半径がrの円の中心を返す
VP circlesPointsRadius(P a, P b, D r) {
  VP cs;
  P abH = (b-a)*0.5;
  D d = abs(abH);
  if (d == 0 || d > r) return cs;  // 必要なら !LE(d,r) として円1つになる側へ丸める
  D dN = sqrt(r*r - d*d);          // 必要なら max(r*r - d*d, 0) とする
  P n = abH * P(0,1) * (dN / d);
  cs.push_back(a + abH + n);
  if (dN > 0) cs.push_back(a + abH - n);
  return cs;
}
 
// 点aと点bを通り、直線lに接する円の中心
VP circlesPointsTangent(P a, P b, P l1, P l2) {
  P n = (l2-l1) * P(0,1);
  P m = (b-a) * P(0,0.5);
  D rC = dot((a+b)*0.5-l1, n);
  D qa = norm(n)*norm(m) - dot(n,m)*dot(n,m);
  D qb = -rC * dot(n,m);
  D qc = norm(n)*norm(m) - rC*rC;
  D qd = qb*qb - qa*qc;  // qa*k^2 + 2*qb*k + qc = 0
 
  VP cs;
  if (qd < -EPS) return cs;
  if (EQ(qa, 0)) {
    if (!EQ(qb, 0)) cs.push_back((a+b)*0.5 - m * (qc/qb/2));
    return cs;
  }
  D t = -qb/qa;
  cs.push_back(              (a+b)*0.5 + m * (t + sqrt(max(qd, 0.0))/qa));
  if (qd > EPS) cs.push_back((a+b)*0.5 + m * (t - sqrt(max(qd, 0.0))/qa));
  return cs;
}
 
// 点集合を含む最小の円の中心
P minEnclosingCircle(const VP& ps) {
  P c;
  double move = 0.5;
  rep(i,39) {  // 2^(-39-1) \approx 0.9e-12
    rep(t,50) {
      D max = 0;
      int k = 0;
      rep (j, ps.size()) if (max < norm(ps[j]-c)) {
        max = norm(ps[j]-c);
        k = j;
      }
      c += (ps[k]-c) * move;
    }
    move /= 2;
  }
  return c;
}


/*
D degree_to_radi(D a){
  return a * M_PI /1 80.0;
}

D radi_to_degree(D a){
  return a * 180.0 / M_PI;
}

// p1を基準にpをa度回転
P rot(P p,double a,P p1){
  a = a * M_PI / 180.0;
  p -= p1;
  D x = p.X*cos( a )+p.Y * (-sin( a ))+p1.X;
  D y = p.X*sin( a )+p.Y * cos( a )+p1.Y;
  return P(x,y);
}

// ベクトル a b のなす角
D deg_cal(P a,P b){
  double p=(a.X*b.X+a.Y*b.Y) / (sqrt(a1*a1+a2*a2)*sqrt(b1*b1+b2*b2));
  p=acos(p);
  p=p*180.0/M_PI;
  return p;
}
 */


// 角度計算
// p1を原点とした時にpをcounter clockwiseで回転させた座標
// D radi=acos((a*a+b*b-c*c)/(2*a*b));
// radi=radi/M_PI*180;   /---これ忘れないで---/
/*
P rot(P p, double a,P p1){
  a=a*M_PI/180.0;
  p-=p1;
  return P(p.X*cos(a)+p.Y*(-sin(a))+x,p.X*sin(a)+p.Y*cos(a)+y);
}
*/
// (a*a+b*b-c*c)/(2*a*b) = cos X 余弦定理
// acos(X) = ラジアンー＞角度

/* 多角形 */

P mae_syori(P p1, P p2, P Q){
  double xa,ya,xb,yb,t1,t2;
  P R;
  xa=Q.X-p1.X,ya=Q.Y-p1.Y;
  xb=p2.X-p1.X,yb=p2.Y-p1.Y;
  t1=xa*xb+ya*yb,t2=xb*xb+yb*yb;
  R=P(2*(p1.X+xb*t1/t2)-Q.X,2*(p1.Y+yb*t1/t2)-Q.Y);
  return R;
}
// 直線abから左側にh離れた直線
L parallel_line(P a,P b,double h){
    double t = atan((a.Y-b.Y)/(a.X-b.X));
    P a_=P(a.X + h*cos(t+M_PI/2), a.Y + h*sin(t+M_PI/2));
    P b_=P(b.X + h*cos(t+M_PI/2), b.Y + h*sin(t+M_PI/2));
    if(ccw(a,b,a_)==-1)a_=mae_syori(a,b,a_),b_=mae_syori(a,b,b_);  // -1ならabを左側にhだけ移動
    return make_pair(a_,b_);
}
 
// 頂点の順序（sortやmax_elementに必要）
namespace std {
  bool operator<(const P a, const P b) {
    return a.X != b.X ? a.X < b.X : a.Y < b.Y;
  }
}
 
// 凸包
VP convexHull(VP ps) {  // 元の点集合がソートされていいならVP&に
  int n = ps.size(), k = 0;
  sort(ps.begin(), ps.end());
  VP ch(2*n);
  for (int i = 0; i < n; ch[k++] = ps[i++]) // lower-hull
    while (k >= 2 && ccw(ch[k-2], ch[k-1], ps[i]) <= 0) --k;  // 余計な点も含むなら == -1 とする
  for (int i = n-2, t = k+1; i >= 0; ch[k++] = ps[i--]) // upper-hull
    while (k >= t && ccw(ch[k-2], ch[k-1], ps[i]) <= 0) --k;
  ch.resize(k-1);
  return ch;
}
 
// 凸判定。縮退を認めないならccwの判定部分を != 1 とする
bool isCcwConvex(const VP& ps) {
  int n = ps.size();
  rep (i, n) if (ccw(ps[i], ps[(i+1) % n], ps[(i+2) % n]) == -1) return false;
  return true;
}
 
// 凸多角形の内部判定　O(n)
// 点が領域内部なら1、境界上なら2、外部なら0を返す
int inConvex(P p, const VP& ps) {
  int n = ps.size();
  int dir = ccw(ps[0], ps[1], p);
  rep (i, n) {
    int ccwc = ccw(ps[i], ps[(i + 1) % n], p);
    if (!ccwc) return 2;  // 線分上に存在
    if (ccwc != dir) return 0;
  }
  return 1;
}
 
// 凸多角形の内部判定　O(logn)
// 点が領域内部なら1、境界上なら2、外部なら0を返す
int inCcwConvex(const VP& ps, P p) {
  int n = ps.size();
  P g = (ps[0] + ps[n / 3] + ps[n*2 / 3]) / 3.0;
  if (g == p) return 1;
  P gp = p - g;
 
  int l = 0, r = n;
  while (l + 1 < r) {
    int mid = (l + r) / 2;
    P gl = ps[l] - g;
    P gm = ps[mid] - g;
    if (cross(gl, gm) > 0) {
      if (cross(gl, gp) >= 0 && cross(gm, gp) <= 0) r = mid;
      else l = mid;
    }
    else {
      if (cross(gl, gp) <= 0 && cross(gm, gp) >= 0) l = mid;
      else r = mid;
    }
  }
  r %= n;
  D cr = cross(ps[l] - p, ps[r] - p);
  return EQ(cr, 0) ? 2 : cr < 0 ? 0 : 1;
}
 
// 多角形の内部判定
// 点が領域内部なら1、境界上なら2、外部なら0を返す
int inPolygon(const VP& ps, P p) {
  int n = ps.size();
  bool in = false;
  rep (i, n) {
    P a = ps[i] - p;
    P b = ps[(i + 1) % n] - p;
    if (EQ(cross(a,b), 0) && LE(dot(a,b), 0)) return 2;
    if (a.Y > b.Y) swap(a,b);
    if ((a.Y*b.Y < 0 || (a.Y*b.Y < EPS && b.Y > EPS)) && LE(cross(a, b), 0)) in = !in;
  }
  return in;
}
 
// 凸多角形クリッピング
VP convexCut(const VP& ps, P a1, P a2) {
  int n = ps.size();
  VP ret;
  rep(i,n) {
    int ccwc = ccw(a1, a2, ps[i]);
    if (ccwc != -1) ret.push_back(ps[i]);
    int ccwn = ccw(a1, a2, ps[(i + 1) % n]);
    if (ccwc * ccwn == -1) ret.push_back(crosspointLL(a1, a2, ps[i], ps[(i + 1) % n]));
  }
  return ret;
}
D area(const VP&);
D area(const VP& ps) {
  D a = 0;
  rep (i, ps.size()) a += cross(ps[i], ps[(i+1) % ps.size()]);
  return a / 2;
}

signed main(){
  int n;
  double d,V;
  while(cin>>n>>d>>V,n){
    V/=d;
    vector<P>v;
    rep(i,n){
      double a,b;
      cin>>a>>b;
      v.push_back(P(a,b));
    }
    double ans=0;
    rep(i,n){
      P a=v[i];
      P b=v[(i+1)%n];
      double l=0,r=1000000;
      rep(j,50){
        double mid=(l+r)/2;
        L t=parallel_line(a,b,mid);
        VP x=convexCut(v,t.second,t.first);
       // cout<<area(x)<<endl;
        if( area(x) > V || abs(area(x)-area(v)) < EPS )r=mid;
        else l=mid;
        //cout<<l<<' '<<r<<endl;
      }
      //cout<<endl;
      //cout<<l<<endl;
      ans=max(ans,l);
    }
    printf("%.9f\n",ans);
  }
}