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;
template <typename T, typename U>
std::istream &operator>>(std::istream &i, pair<T, U> &p) {
  i >> p.first >> p.second;
  return i;
}
template <typename T>
std::istream &operator>>(std::istream &i, vector<T> &t) {
  for (auto &v : t) {
    i >> v;
  }
  return i;
}
template <typename T>
std::ostream &operator<<(std::ostream &o, const vector<T> &t) {
  if (t.empty()) o << '\n';
  for (size_t i = 0; i < t.size(); ++i) {
    o << t[i] << " \n"[i == t.size() - 1];
  }
  return o;
}
template <typename T, typename U>
std::ostream &operator<<(std::ostream &o, pair<T, U> &p) {
  o << p.first << ' ' << p.second;
  return o;
}
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T, vector<T>, less<T>>;
template <typename T>
bool in(T a, T b, T c) {
  return a <= b && b < c;
}
unsigned int logceil(int first) {
  return 8 * sizeof(int) - __builtin_clz(first);
}
namespace std {
template <typename T, typename U>
struct hash<pair<T, U>> {
  hash<T> t;
  hash<U> u;
  size_t operator()(const pair<T, U> &p) const {
    return t(p.first) ^ (u(p.second) << 7);
  }
};
}  // namespace std
template <typename T, typename F>
T bsh(T l, T h, const F &f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      l = m + 1;
      r = m;
    } else {
      h = m - 1;
    }
  }
  return r;
}
template <typename F>
double bshd(double l, double h, const F &f, double p = 1e-9) {
  unsigned int r = 3 + (unsigned int)log2((h - l) / p);
  while (r--) {
    double m = (l + h) / 2;
    if (f(m)) {
      l = m;
    } else {
      h = m;
    }
  }
  return (l + h) / 2;
}
template <typename T, typename F>
T bsl(T l, T h, const F &f) {
  T r = -1, m;
  while (l <= h) {
    m = (l + h) / 2;
    if (f(m)) {
      h = m - 1;
      r = m;
    } else {
      l = m + 1;
    }
  }
  return r;
}
template <typename F>
double bsld(double l, double h, const F &f, double p = 1e-9) {
  unsigned int r = 3 + (unsigned int)log2((h - l) / p);
  while (r--) {
    double m = (l + h) / 2;
    if (f(m)) {
      h = m;
    } else {
      l = m;
    }
  }
  return (l + h) / 2;
}
template <typename T>
T gcd(T a, T b) {
  if (a < b) swap(a, b);
  return b ? gcd(b, a % b) : a;
}
template <typename T>
class vector2 : public vector<vector<T>> {
 public:
  vector2() {}
  vector2(size_t a, size_t b, T t = T())
      : vector<vector<T>>(a, vector<T>(b, t)) {}
};
template <typename T>
class vector3 : public vector<vector2<T>> {
 public:
  vector3() {}
  vector3(size_t a, size_t b, size_t c, T t = T())
      : vector<vector2<T>>(a, vector2<T>(b, c, t)) {}
};
template <typename T>
class vector4 : public vector<vector3<T>> {
 public:
  vector4() {}
  vector4(size_t a, size_t b, size_t c, size_t d, T t = T())
      : vector<vector3<T>>(a, vector3<T>(b, c, d, t)) {}
};
template <typename T>
class vector5 : public vector<vector4<T>> {
 public:
  vector5() {}
  vector5(size_t a, size_t b, size_t c, size_t d, size_t e, T t = T())
      : vector<vector4<T>>(a, vector4<T>(b, c, d, e, t)) {}
};
template <typename T>
struct bounded_priority_queue {
  inline bounded_priority_queue(unsigned int X) : A(X), B(0), s(0) {}
  inline void push(unsigned int L, T V) {
    B = max(B, L);
    A[L].push(V);
    ++s;
  }
  inline const T &top() const { return A[B].front(); }
  inline void pop() {
    --s;
    A[B].pop();
    while (B > 0 && A[B].empty()) --B;
  }
  inline bool empty() const { return A[B].empty(); }
  inline void clear() {
    s = B = 0;
    for (auto &a : A) a = queue<T>();
  }
  inline unsigned int size() const { return s; }

 private:
  vector<queue<T>> A;
  unsigned int B;
  int s;
};
constexpr double PI = 3.14159265358979323846;
template <typename T>
struct Segment;
template <typename T>
struct Point : public pair<T, T> {
  Point(T a = 0, T b = 0) : pair<T, T>(a, b) {}
  Point(const pair<T, T> &p) : pair<T, T>(p.first, p.second) {}
  Point(const Point<T> &p) = default;
  Point<T> &operator=(const Point<T> &p) = default;
  T squaredDistance(const Point<T> &o) const {
    return Segment<T>{*this, o}.squaredLength();
  }
  double distance(const Point<T> &o) const {
    return Segment<T>{*this, o}.length();
  }
};
template <typename T>
ostream &operator<<(ostream &o, const Point<T> &p) {
  o << p.first << ' ' << p.second;
  return o;
}
template <typename T>
T ccw(const Point<T> &a, const Point<T> &b, const Point<T> &c) {
  return (b.first - a.first) * (c.second - a.second) -
         (b.second - a.second) * (c.first - a.first);
}
template <typename T>
T area(const Point<T> &a, const Point<T> &b, const Point<T> &c) {
  return abs(ccw(a, b, c));
}
template <typename T>
double cosangle(const Point<T> &a, const Point<T> &b, const Point<T> &c) {
  return ((b.first - a.first) * (c.first - a.first) +
          (b.second - a.second) * (c.second - a.second)) /
         a.distance(b) / a.distance(c);
}
template <typename T>
double angle(const Point<T> &a, const Point<T> &b, const Point<T> &c) {
  return acos(cosangle(a, b, c));
}
template <typename T>
int orientation(const Point<T> &a, const Point<T> &b, const Point<T> &c) {
  auto o = ccw(a, b, c);
  return (o > 1e-6) - (o < -1e-6);
}
template <typename T>
bool collinear(const Point<T> &a, const Point<T> &b, const Point<T> &c) {
  return orientation(a, b, c) == 0;
}
template <typename T>
struct Segment : public pair<Point<T>, Point<T>> {
  using pair<Point<T>, Point<T>>::first;
  using pair<Point<T>, Point<T>>::second;
  explicit Segment(Point<T> a = {0, 0}, Point<T> b = {0, 0})
      : pair<Point<T>, Point<T>>(a, b) {}
  Segment(const Segment<T> &) = default;
  Segment<T> &operator=(const Segment<T> &) = default;
  inline T dx() const { return first.first - second.first; }
  inline T dy() const { return first.second - second.second; }
  T squaredLength() const { return dx() * dx() + dy() * dy(); }
  double length() const { return sqrt(squaredLength()); }
  bool contains(const Point<T> &q) const {
    return collinear(first, q, second) &&
           ((q.first <= max(first.first, second.first) &&
             q.first >= min(first.first, second.first)) ||
            (q.second <= max(first.second, second.second) &&
             q.second >= min(first.second, second.second)));
  }
  double distance(const Point<T> &p) const {
    double u =
        ((p.first - second.first) * dx() + (p.second - second.second) * dy()) /
        double(dx() * dx() + dy() * dy());
    if (u > 1) u = 1;
    if (u < 0) u = 0;
    return Point<double>(p.first, p.second)
        .distance({second.first + u * dx(), second.second + u * dy()});
  }
  bool intersect(const Segment<T> &s) const {
    return (orientation(first, second, s.first) !=
                orientation(first, second, s.second) &&
            orientation(s.first, s.second, first) !=
                orientation(s.first, s.second, second)) ||
           contains(s.first) || contains(s.second) || s.contains(first) ||
           s.contains(second);
  }
};
template <typename T>
struct Line : public pair<Point<T>, Point<T>> {
  using pair<Point<T>, Point<T>>::first;
  using pair<Point<T>, Point<T>>::second;
  Line(Point<T> a = {0, 0}, Point<T> b = {0, 0})
      : pair<Point<T>, Point<T>>(a, b) {}
  explicit Line(const Segment<T> &s)
      : pair<Point<T>, Point<T>>(s.first, s.second) {}
  Line(const Line<T> &p) = default;
  Line<T> &operator=(const Line<T> &p) = default;
  inline T dx() const { return first.first - second.first; }
  inline T dy() const { return first.second - second.second; }
  inline T c() const {
    return first.second * second.first - first.first * second.second;
  }
  double distance(const Point<T> &p) const {
    long long px = dx(), py = dy(), dL = px * px + py * py;
    return abs(py * p.first - px * p.second + second.first * first.second -
               second.second * first.first) /
           sqrt(dL);
  }
  Point<double> project(const Point<T> &p) const {
    double u =
        ((p.first - second.first) * dx() + (p.second - second.second) * dy()) /
        double(dx() * dx() + dy() * dy());
    return {second.first + u * dx(), second.second + u * dy()};
  }
  bool parallel(const Line<T> &l) const {
    return abs(l.dx() * dy() - l.dy() * dx()) < 1e-6;
  }
  Point<double> intersection(const Line<T> &l) {
    double det = l.dx() * dy() - l.dy() * dx();
    if (abs(det) < 1e-6)
      return {1e300, 1e300};
    else {
      double c1 = c(), c2 = l.c();
      double first = -(c2 * dx() - l.dx() * c1) / det;
      double second = -(-l.dy() * c1 + c2 * dy()) / det;
      return {first, second};
    }
  };
};
template <typename T>
struct Circle {
  Point<T> center;
  T radius;
  bool intersect(const Circle<T> &o) const {
    return o.center.squaredDistance(center) <=
           (radius + o.radius) * (radius + o.radius);
  }
  bool contains(const Point<T> &p) const {
    return p.squaredDistance(center) <= radius * radius;
  }
  bool contains(const Circle<T> &o) const {
    return radius >= o.radius && center.squaredDistance(center) <=
                                     (radius - o.radius) * (radius - o.radius);
  }
  bool touches(const Circle<T> &o) const {
    T dist = center.squaredDistance(center);
    return dist == (radius - o.radius) * (radius - o.radius) ||
           dist == (radius + o.radius) * (radius + o.radius);
  }
};
template <typename T>
struct Polygon : public vector<Point<T>> {
  using vector<Point<T>>::vector;
  using vector<Point<T>>::at;
  using vector<Point<T>>::front;
  using vector<Point<T>>::back;
  T doubleSignedArea() const {
    if (this->empty()) return T(0);
    T area = back().first * front().second - back().second * front().first;
    for (int i = 0; i < this->size() - 1; ++i)
      area += (at(i).first * at(i + 1).second - at(i + 1).first * at(i).second);
    return area;
  }
  double circumference() const {
    if (this->empty()) return T(0);
    T res = back().distance(front());
    for (int i = 0; i < this->size() - 1; ++i) res += at(i).distance(at(i + 1));
    return res;
  }
};
template <typename T>
Polygon<T> convexhull(const vector<Point<T>> &v) {
  unsigned int N = (unsigned int)v.size();
  vector<Point<T>> w(N + 1);
  int lo = 0;
  for (int i = 0; i < N; ++i)
    if (v[i].second < v[lo].second) lo = i;
  Point<T> o = v[lo];
  for (int i = 0; i < N; ++i)
    w[i + 1] = {v[i].first - o.first, v[i].second - o.second};
  swap(w[1], w[lo + 1]);
  sort(w.begin() + 2, w.end(), [](Point<T> &a, Point<T> &b) {
    if (a.second == 0 && a.first > 0) return true;
    if (b.second == 0 && b.first > 0) return false;
    if (a.second > 0 && b.second < 0) return true;
    return !(a.second < 0 && b.second > 0) &&
           (a.first * b.second - a.second * b.first) > 1e-6;
  });
  w[0] = w[N];
  unsigned int M = 1;
  for (int i = 2; i <= N; ++i) {
    while (ccw(w[M - 1], w[M], w[i]) <= 0)
      if (M > 1)
        --M;
      else if (i == N)
        break;
      else
        ++i;
    ++M;
    swap(w[M], w[i]);
  }
  Polygon<T> res(M);
  for (int i = 0; i < M; ++i)
    res[i] = {w[i + 1].first + o.first, w[i + 1].second + o.second};
  return res;
}
class TaskA {
 public:
  void solve(istream &cin, ostream &cout) {
    int N;
    cin >> N;
    double lo = 1e12;
    double hi = 0;
    Point<long long> P;
    cin >> P;
    vector<Point<long long>> R(N);
    cin >> R;
    for (int i = 0; i < N; ++i) {
      double dist = R[i].distance(P);
      lo = min(lo, dist);
      hi = max(hi, dist);
    }
    for (int i = 0; i < N; ++i) {
      auto a = R[i];
      auto b = R[(i + 1) % N];
      Segment<long long> S{a, b};
      double dist = S.distance(P);
      lo = min(lo, dist);
      hi = max(hi, dist);
    }
    double ans = PI * (hi * hi - lo * lo);
    cout << fixed << setprecision(10) << ans << endl;
  }
};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  TaskA solver;
  std::istream &in(std::cin);
  std::ostream &out(std::cout);
  solver.solve(in, out);
  return 0;
}