Problem: Peter got a new snow blower as a New Year present. Of course, Peter decided to try it immediately. After reading the instructions he realized that it does not work like regular snow blowing machines. In order to make it work, you need to tie it to some point that it does not cover, and then switch it on. As a result it will go along a circle around this point and will remove all the snow from its path.

Formally, we assume that Peter's machine is a polygon on a plane. Then, after the machine is switched on, it will make a circle around the point to which Peter tied it (this point lies strictly outside the polygon). That is, each of the points lying within or on the border of the polygon will move along the circular trajectory, with the center of the circle at the point to which Peter tied his machine.

Peter decided to tie his car to point P and now he is wondering what is the area of ​​the region that will be cleared from snow. Help him.

Input

The first line of the input contains three integers — the number of vertices of the polygon n (<image>), and coordinates of point P.

Each of the next n lines contains two integers — coordinates of the vertices of the polygon in the clockwise or counterclockwise order. It is guaranteed that no three consecutive vertices lie on a common straight line.

All the numbers in the input are integers that do not exceed 1 000 000 in their absolute value.

Output

Print a single real value number — the area of the region that will be cleared. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6. 

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.

Examples

Input

3 0 0
0 1
-1 2
1 2


Output

12.566370614359172464


Input

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


Output

21.991148575128551812

Note

In the first sample snow will be removed from that area:

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int M = 1000000007, BIG = 0x3f3f3f3f;
const double PI = 3.14159265358979323846, EPS = 0.0000000001;
struct Point {
  double x, y;
  Point() {}
  Point(double x, double y) : x(x), y(y) {}
  Point Rotate(double theta) {
    double rad = theta * PI / 180.;
    return {x * cos(rad) - y * sin(rad), x * sin(rad) + y * cos(rad)};
  }
  Point Rotate_Around(double theta, const Point& axis) {
    double rad = theta * PI / 180.;
    return {(x - axis.x) * cos(rad) - (y - axis.y) * sin(rad) + axis.x,
            (x - axis.x) * sin(rad) + (y - axis.y) * cos(rad) + axis.y};
  }
};
bool operator==(const Point& p1, const Point& p2) {
  return (fabs(p1.x - p2.x) < EPS) && (fabs(p1.y - p2.y) < EPS);
}
istream& operator>>(istream& is, Point& _a) {
  is >> _a.x >> _a.y;
  return is;
}
ostream& operator<<(ostream& os, Point& _a) {
  os << _a.x << " " << _a.y;
  return os;
}
double Euclidean_Distance(const Point& _a, const Point& _b) {
  return hypot(_a.x - _b.x, _a.y - _b.y);
}
struct Line {
  double a, b, c;
  Line() {}
  Line(double a, double b, double c) : a(a), b(b), c(c) {}
  Line(const Point& _a, const Point& _b) {
    if (fabs(_a.x - _b.x) < EPS) {
      a = 1;
      b = 0;
      c = -_a.x;
    } else {
      a = -(_a.y - _b.y) / (_a.x - _b.x);
      b = 1.;
      c = -(a * _a.x) - _a.y;
    }
  }
};
Line Perpendicular_Line(const Line& _a, const Point& _p) {
  double sl = 1. / (_a.a / _a.b);
  double cc = _p.y - sl * _p.x;
  return Line(-sl, 1, -cc);
}
bool Parallel_Lines(const Line& _a, const Line& _b) {
  return (fabs(_a.a - _b.a) < EPS) && (fabs(_a.b - _b.b) < EPS);
}
bool operator==(const Line& _a, const Line& _b) {
  return Parallel_Lines(_a, _b) && (fabs(_a.c - _b.c) < EPS);
}
Point Intersection(const Line& _a, const Line& _b) {
  double w = _a.a * _b.b - _b.a * _a.b;
  if (fabs(w) < EPS) {
    cout << "Division by zero\n";
    exit(0);
  }
  return {(_a.b * _b.c - _b.b * _a.c) / w, (_b.a * _a.c - _a.a * _b.c) / w};
}
struct Vec {
  double x, y;
  Vec() {}
  Vec(double x, double y) : x(x), y(y) {}
  Vec(const Point& _a, const Point& _b) : x(_b.x - _a.x), y(_b.y - _a.y) {}
  Vec Scale(double _s) const { return {x * _s, y * _s}; }
  double Squared_Norm() { return x * x + y * y; }
};
double operator*(const Vec& _a, const Vec& _b) {
  return _a.x * _b.x + _a.y * _b.y;
}
double Cross_Product(const Vec& _a, const Vec& _b) {
  return _a.x * _b.y - _a.y * _b.x;
}
double Cross_Product(const Point& _a, const Point& _b) {
  return _a.x * _b.y - _a.y * _b.x;
}
Point Translate(const Point& _p, const Vec& _v) {
  return {_p.x + _v.x, _p.y + _v.y};
}
Point Closest_Point_In_Line(const Point& _p, const Point& _a, const Point& _b) {
  Vec ap(_a, _p), ab(_a, _b);
  double u = ap * ab / ab.Squared_Norm();
  return Translate(_a, ab.Scale(u));
}
double Distance_To_Line(const Point& _p, const Point& _a, const Point& _b) {
  return Euclidean_Distance(_p, Closest_Point_In_Line(_p, _a, _b));
}
Point Closest_Point_In_Line_Segment(const Point& _p, const Point& _a,
                                    const Point& _b) {
  Vec ap(_a, _p), ab(_a, _b);
  double u = ap * ab / ab.Squared_Norm();
  if (u < 0.0) return {_a.x, _a.y};
  if (u > 1.0) return {_b.x, _b.y};
  return Translate(_a, ab.Scale(u));
}
double Distance_To_Line_Segment(const Point& _p, const Point& _a,
                                const Point& _b) {
  return Euclidean_Distance(_p, Closest_Point_In_Line_Segment(_p, _a, _b));
}
double Angle(const Point& _a, const Point& _o, const Point& _b) {
  Vec oa(_o, _a), ob(_o, _b);
  return acos(oa * ob / sqrt(oa.Squared_Norm() * ob.Squared_Norm()));
}
double Angle_CCW_From_X_Axis(const Point& _a) {
  if (fabs(_a.x) < EPS) {
    if (fabs(_a.y) < EPS) return 0;
    if (_a.y > 0) return PI / 2.;
    return 3. * PI / 2.;
  } else if (fabs(_a.y) < EPS) {
    if (_a.x > 0) return 0;
    return PI;
  }
  double ans = atan(_a.y / _a.x);
  if (_a.y < 0) ans += PI;
  return ans;
}
bool Left_Of_Line(const Point& _p, const Point& _a, const Point& _b) {
  return Cross_Product(Vec(_a, _b), Vec(_a, _p)) > 0;
}
bool Collinear(const Point& _p, const Point& _a, const Point& _b) {
  return fabs(Cross_Product(Vec(_a, _b), Vec(_a, _p))) < EPS;
}
struct Circle {
  double radius, area, circumference;
  Point possible_center1, possible_center2;
  Circle(double radius) : radius(radius) {}
  void Init() {
    area = PI * radius * radius;
    circumference = 2. * PI * radius;
  }
  bool Get_Center(const Point& p1, const Point& p2) {
    double dSq = (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
    double det = radius * radius / dSq - 0.25;
    if (det < 0.) return 0;
    double h = sqrt(det);
    possible_center1.x = (p1.x + p2.x) * .5 + (p1.y - p2.y) * h;
    possible_center1.y = (p1.y + p2.y) * .5 + (p2.x - p1.x) * h;
    possible_center2.x = (p1.x + p2.x) * .5 + (p2.y - p1.y) * h;
    possible_center2.y = (p1.y + p2.y) * .5 + (p1.x - p2.x) * h;
    return 1;
  }
};
struct Triangle {
  Point p1, p2, p3;
  double area, s1, s2, s3, semip;
  void Init() {
    semip = (s1 + s2 + s3) / 2;
    area = sqrt(semip * (semip - s1) * (semip - s2) * (semip - s3));
  }
  Triangle(double s1, double s2, double s3) : s1(s1), s2(s2), s3(s3) { Init(); }
  Triangle(const Point& p1, const Point& p2, const Point& p3)
      : p1(p1), p2(p2), p3(p3) {
    s1 = Euclidean_Distance(p1, p2);
    s2 = Euclidean_Distance(p2, p3);
    s3 = Euclidean_Distance(p1, p3);
    Init();
  }
  double Incircle_Radius() { return area / semip; }
  double Circumcircle_Radius() { return s1 * s2 * s3 / (4. * area); }
  Point Circumcircle_Center() {
    Point ans;
    Point mid1 = Point((p1.x + p2.x) / 2, (p1.y + p2.y) / 2);
    Point mid2 = Point((p2.x + p3.x) / 2, (p2.y + p3.y) / 2);
    Line per1 = Perpendicular_Line(Line(p1, p2), mid1);
    Line per2 = Perpendicular_Line(Line(p2, p3), mid2);
    return Intersection(per1, per2);
  }
  Point Incircle_Center() {
    double ratio = s1 / s3;
    Point p = Translate(p2, Vec(p2, p3).Scale(ratio / (1 + ratio)));
    ratio = s1 / s2;
    p = Translate(p1, Vec(p1, p3).Scale(ratio / (1 + ratio)));
    return Intersection(Line(p1, p), Line(p2, p));
  }
};
struct Polygon {
  vector<Point> vp;
  Polygon() {}
  void Add(const Point& _p) { vp.push_back(_p); }
  double Perimeter() {
    double ans = 0.0;
    for (int i = 0; i < (int)vp.size() - 1; i++)
      ans += Euclidean_Distance(vp[i], vp[i + 1]);
    return ans;
  }
  double Area() {
    double ans = 0.0, x1, y1, x2, y2;
    for (int i = 0; i < (int)vp.size() - 1; i++) {
      x1 = vp[i].x;
      x2 = vp[i + 1].x;
      y1 = vp[i].y;
      y2 = vp[i + 1].y;
      ans += (x1 * y2 - x2 * y1);
    }
    return fabs(ans) / 2.0;
  }
  bool Convex() {
    int sz = (int)vp.size();
    if (sz <= 3) return 0;
    bool isLeft = Left_Of_Line(vp[2], vp[0], vp[1]);
    for (int i = 1; i < sz - 1; i++)
      if (Left_Of_Line(vp[(i + 2) == sz ? 1 : i + 2], vp[i], vp[i + 1]) !=
          isLeft)
        return 0;
    return 1;
  }
  bool Contains_Point(const Point& _p) {
    if ((int)vp.size() == 0) return 0;
    double sum = 0;
    for (int i = 0; i < (int)vp.size() - 1; i++) {
      if (Left_Of_Line(vp[i + 1], _p, vp[i]))
        sum += Angle(vp[i], _p, vp[i + 1]);
      else
        sum -= Angle(vp[i], _p, vp[i + 1]);
    }
    return fabs(fabs(sum) - 2. * PI) < EPS;
  }
  Point Line_Intersect_Seg(const Point& _p, const Point& _q, const Point& _A,
                           const Point& _B) {
    double a, b, c, u, v;
    a = _B.y - _A.y;
    b = _A.x - _B.x;
    c = _B.x * _A.y - _A.x * _B.y;
    u = fabs(a * _p.x + b * _p.y + c);
    v = fabs(a * _q.x + b * _q.y + c);
    return Point((_p.x * v + _q.x * u) / (u + v),
                 (_p.y * v + _q.y * u) / (u + v));
  }
  Polygon Cut_Polygon(const Point& _a, const Point& _b) {
    Polygon ans;
    for (int i = 0; i < (int)vp.size(); i++) {
      double left1 = Cross_Product(Vec(_a, _b), Vec(_a, vp[i])), left2 = 0;
      if (i != (int)vp.size() - 1)
        left2 = Cross_Product(Vec(_a, _b), Vec(_a, vp[i + 1]));
      if (left1 > -EPS) ans.Add(vp[i]);
      if (left1 * left2 < -EPS)
        ans.Add(Line_Intersect_Seg(vp[i], vp[i + 1], _a, _b));
    }
    if (!ans.vp.empty() && !(ans.vp.back() == ans.vp.front()))
      ans.Add(ans.vp.front());
    return ans;
  }
};
vector<Point> Convex_Hull(vector<Point> vp) {
  int i, j, n = (int)vp.size();
  if (n <= 3) {
    if (!(vp[0] == vp[n - 1])) vp.push_back(vp[0]);
    return vp;
  }
  int P0 = 0;
  for (i = 1; i < n; i++)
    if (vp[i].y < vp[P0].y || (vp[i].y == vp[P0].y && vp[i].x > vp[P0].x))
      P0 = i;
  swap(vp[0], vp[P0]);
  sort(vp.begin() + 1, vp.end(), [vp](const Point& _a, const Point& _b) {
    if (Collinear(vp[0], _a, _b))
      return Euclidean_Distance(vp[0], _a) < Euclidean_Distance(vp[0], _b);
    double d1x = _a.x - vp[0].x, d1y = _a.y - vp[0].y;
    double d2x = _b.x - vp[0].x, d2y = _b.y - vp[0].y;
    return (atan2(d1y, d1x) - atan2(d2y, d2x)) < 0;
  });
  vector<Point> ans;
  ans.push_back(vp[n - 1]);
  ans.push_back(vp[0]);
  ans.push_back(vp[1]);
  i = 2;
  while (i < n) {
    j = (int)ans.size() - 1;
    if (Left_Of_Line(vp[i], ans[j - 1], ans[j]))
      ans.push_back(vp[i++]);
    else
      ans.pop_back();
  }
  return ans;
}
double Area_Of_Polygon(const vector<Point> vertices) {
  double sum = 0.;
  for (int i = 0; i < vertices.size(); i++)
    sum += Cross_Product(vertices[i], vertices[(i + 1) % vertices.size()]);
  return abs(sum) / 2.0;
}
int n;
Point P;
vector<Point> p;
double Process() {
  double R = 0, r = Distance_To_Line_Segment(P, p[0], p.back());
  for (auto x : p) R = max(R, Euclidean_Distance(x, P));
  for (int i = 1; i < n; i++)
    r = min(r, Distance_To_Line_Segment(P, p[i - 1], p[i]));
  return PI * (R * R - r * r);
}
void Output() {
  double ans = Process();
  cout << fixed << setprecision(12) << ans << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  while (cin >> n) {
    cin >> P;
    p.resize(n);
    for (int i = 0; i < n; i++) cin >> p[i];
    Output();
  }
  return 0;
}