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>
#pragma GCC optimize("O3")
#pragma GCC target("avx2,avx")
#pragma GCC optimize("unroll-loops")
using namespace std;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
int scan() { return getchar(); }
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(long double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T>
void scan(vector<T> &);
template <class T>
void scan(vector<T> &a) {
  for (auto &i : a) scan(i);
}
template <class T>
void scan(T &a) {
  cin >> a;
}
void IN() {}
template <class Head, class... Tail>
void IN(Head &head, Tail &...tail) {
  scan(head);
  IN(tail...);
}
string stin() {
  string s;
  cin >> s;
  return s;
}
template <class T, class S>
inline bool chmax(T &a, S b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T, class S>
inline bool chmin(T &a, S b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
vector<int> iota(int n) {
  vector<int> a(n);
  iota(begin(a), end(a), 0);
  return a;
}
template <class T>
void UNIQUE(vector<T> &x) {
  sort(begin(x), end(x));
  x.erase(unique(begin(x), end(x)), x.end());
}
int in() {
  int x;
  cin >> x;
  return x;
}
long long lin() {
  unsigned long long x;
  cin >> x;
  return x;
}
void print() { putchar(' '); }
void print(bool a) { cout << a; }
void print(int a) { cout << a; }
void print(long long a) { cout << a; }
void print(char a) { cout << a; }
void print(string &a) { cout << a; }
void print(double a) { cout << a; }
template <class T>
void print(const vector<T> &);
template <class T, size_t size>
void print(const array<T, size> &);
template <class T, class L>
void print(const pair<T, L> &p);
template <class T, size_t size>
void print(const T (&)[size]);
template <class T>
void print(const vector<T> &a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
  cout << endl;
}
template <class T>
void print(const deque<T> &a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, size_t size>
void print(const array<T, size> &a) {
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, class L>
void print(const pair<T, L> &p) {
  cout << '(';
  print(p.first);
  cout << ",";
  print(p.second);
  cout << ')';
}
template <class T>
void print(set<T> &x) {
  for (auto e : x) print(e), cout << " ";
  cout << endl;
}
template <class T>
void print(multiset<T> &x) {
  for (auto e : x) print(e), cout << " ";
  cout << endl;
}
template <class T, size_t size>
void print(const T (&a)[size]) {
  print(a[0]);
  for (auto i = a; ++i != end(a);) {
    cout << " ";
    print(*i);
  }
}
template <class T>
void print(const T &a) {
  cout << a;
}
int out() {
  putchar('\n');
  return 0;
}
template <class T>
int out(const T &t) {
  print(t);
  putchar('\n');
  return 0;
}
template <class Head, class... Tail>
int out(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
  return 0;
}
long long gcd(long long a, long long b) {
  while (b) {
    long long c = b;
    b = a % b;
    a = c;
  }
  return a;
}
long long lcm(long long a, long long b) {
  if (!a || !b) return 0;
  return a * b / gcd(a, b);
}
vector<pair<long long, long long>> factor(long long x) {
  vector<pair<long long, long long>> ans;
  for (long long i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back({i, 1});
      while ((x /= i) % i == 0) ans.back().second++;
    }
  if (x != 1) ans.push_back({x, 1});
  return ans;
}
template <class T>
vector<T> divisor(T x) {
  vector<T> ans;
  for (T i = 1; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back(i);
      if (i * i != x) ans.push_back(x / i);
    }
  return ans;
}
template <typename T>
void zip(vector<T> &x) {
  vector<T> y = x;
  sort(begin(y), end(y));
  for (int i = 0; i < x.size(); ++i) {
    x[i] = distance((y).begin(), lower_bound(begin(y), end(y), (x[i])));
  }
}
int popcount(long long x) { return __builtin_popcountll(x); }
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int n) { return uniform_int_distribution<int>(0, n - 1)(rng); }
long long rndll(long long n) {
  return uniform_int_distribution<long long>(0, n - 1)(rng);
}
template <typename T>
void shuffle(vector<T> &v) {
  for (long long i = v.size() - 1; i >= 1; --i) {
    swap(v[i], v[rnd(i)]);
  }
}
vector<string> YES{"NO", "YES"};
vector<string> Yes{"No", "Yes"};
vector<string> yes{"no", "yes"};
template <class... T>
void err(const T &...) {}
template <typename T>
struct edge {
  int from, to;
  T cost;
  int id;
  edge(int to, T cost) : from(-1), to(to), cost(cost) {}
  edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
  edge(int from, int to, T cost, int id)
      : from(from), to(to), cost(cost), id(id) {}
  edge &operator=(const int &x) {
    to = x;
    return *this;
  }
  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
struct Graph : vector<vector<int>> {
  using vector<vector<int>>::vector;
  Graph(int n, int m) : vector(n) { read(m); }
  inline void add(int a, int b, bool directed = false) {
    (*this)[a].emplace_back(b);
    if (!directed) (*this)[b].emplace_back(a);
  }
  void read(int n = -1, int offset = 1, bool directed = false) {
    if (n == -1) n = this->size() - 1;
    int a, b;
    while (n--) {
      cin >> a >> b;
      Graph::add(a - offset, b - offset, directed);
    }
  }
};
template <typename T>
struct WeightedGraph : vector<Edges<T>> {
  using vector<Edges<T>>::vector;
  inline void add(int a, int b, T c, bool directed = false) {
    (*this)[a].emplace_back(b, c);
    if (!directed) (*this)[b].emplace_back(a, c);
  }
  void read(int n = -1, int offset = 1) {
    if (n == -1) n = this->size() - 1;
    int a, b;
    T c;
    while (n--) {
      cin >> a >> b >> c;
      WeightedGraph::add(a - offset, b - offset, c);
    }
  }
};
struct Setup_io {
  Setup_io() {
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    cout << fixed << setprecision(15);
  }
} setup_io;
using Real = double;
using Point = complex<Real>;
const Real EPS = 1e-8, PI = acos(-1);
inline bool eq(Real a, Real b) { return fabs(b - a) < EPS; }
Point operator*(const Point &p, const Real &d) {
  return Point(real(p) * d, imag(p) * d);
}
istream &operator>>(istream &is, Point &p) {
  Real a, b;
  is >> a >> b;
  p = Point(a, b);
  return is;
}
ostream &operator<<(ostream &os, Point &p) {
  return os << fixed << setprecision(10) << p.real() << " " << p.imag();
}
Point rotate(Real theta, const Point &p) {
  return Point(cos(theta) * p.real() - sin(theta) * p.imag(),
               sin(theta) * p.real() + cos(theta) * p.imag());
}
Real radian_to_degree(Real r) { return (r * 180.0 / PI); }
Real degree_to_radian(Real d) { return (d * PI / 180.0); }
Real get_angle(const Point &a, const Point &b, const Point &c) {
  const Point v(b - a), w(c - b);
  Real alpha = atan2(v.imag(), v.real()), beta = atan2(w.imag(), w.real());
  if (alpha > beta) swap(alpha, beta);
  Real theta = (beta - alpha);
  return min(theta, 2 * acos(-1) - theta);
}
namespace std {
bool operator<(const Point &a, const Point &b) {
  return a.real() != b.real() ? a.real() < b.real() : a.imag() < b.imag();
}
}  // namespace std
struct Line {
  Point a, b;
  Line() = default;
  Line(Point a, Point b) : a(a), b(b) {}
  Line(Real A, Real B, Real C) {
    if (eq(A, 0))
      a = Point(0, C / B), b = Point(1, C / B);
    else if (eq(B, 0))
      b = Point(C / A, 0), b = Point(C / A, 1);
    else
      a = Point(0, C / B), b = Point(C / A, 0);
  }
  friend ostream &operator<<(ostream &os, Line &p) {
    return os << p.a << " to " << p.b;
  }
  friend istream &operator>>(istream &is, Line &a) { return is >> a.a >> a.b; }
};
struct Segment : Line {
  Segment() = default;
  Segment(Point a, Point b) : Line(a, b) {}
};
struct Circle {
  Point p;
  Real r;
  Circle() = default;
  Circle(Point p, Real r) : p(p), r(r) {}
};
using Points = vector<Point>;
using Polygon = vector<Point>;
using Segments = vector<Segment>;
using Lines = vector<Line>;
using Circles = vector<Circle>;
Real cross(const Point &a, const Point &b) {
  return real(a) * imag(b) - imag(a) * real(b);
}
Real dot(const Point &a, const Point &b) {
  return real(a) * real(b) + imag(a) * imag(b);
}
int ccw(const Point &a, Point b, Point c) {
  b = b - a, c = c - a;
  if (cross(b, c) > EPS) return +1;
  if (cross(b, c) < -EPS) return -1;
  if (dot(b, c) < 0) return +2;
  if (norm(b) < norm(c)) return -2;
  return 0;
}
bool parallel(const Line &a, const Line &b) {
  return eq(cross(a.b - a.a, b.b - b.a), 0.0);
}
bool orthogonal(const Line &a, const Line &b) {
  return eq(dot(a.a - a.b, b.a - b.b), 0.0);
}
Point projection(const Line &l, const Point &p) {
  double t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + (l.a - l.b) * t;
}
Point projection(const Segment &l, const Point &p) {
  double t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + (l.a - l.b) * t;
}
Point reflection(const Line &l, const Point &p) {
  return p + (projection(l, p) - p) * 2.0;
}
bool intersect(const Line &l, const Point &p) {
  return abs(ccw(l.a, l.b, p)) != 1;
}
bool intersect(const Line &l, const Line &m) {
  return abs(cross(l.b - l.a, m.b - m.a)) > EPS ||
         abs(cross(l.b - l.a, m.b - l.a)) < EPS;
}
bool intersect(const Segment &s, const Point &p) {
  return ccw(s.a, s.b, p) == 0;
}
bool intersect(const Line &l, const Segment &s) {
  return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < EPS;
}
Real distance(const Line &l, const Point &p);
bool intersect(const Circle &c, const Line &l) {
  return distance(l, c.p) <= c.r + EPS;
}
bool intersect(const Circle &c, const Point &p) {
  return abs(abs(p - c.p) - c.r) < EPS;
}
bool intersect(const Segment &s, const 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;
}
int intersect(const Circle &c, const Segment &l) {
  if (norm(projection(l, c.p) - c.p) - c.r * c.r > EPS) return 0;
  auto d1 = abs(c.p - l.a), d2 = abs(c.p - l.b);
  if (d1 < c.r + EPS && d2 < c.r + EPS) return 0;
  if (d1 < c.r - EPS && d2 > c.r + EPS || d1 > c.r + EPS && d2 < c.r - EPS)
    return 1;
  const Point h = projection(l, c.p);
  if (dot(l.a - h, l.b - h) < 0) return 2;
  return 0;
}
int intersect(Circle c1, Circle c2) {
  if (c1.r < c2.r) swap(c1, c2);
  Real d = abs(c1.p - c2.p);
  if (c1.r + c2.r < d) return 4;
  if (eq(c1.r + c2.r, d)) return 3;
  if (c1.r - c2.r < d) return 2;
  if (eq(c1.r - c2.r, d)) return 1;
  return 0;
}
Real distance(const Point &a, const Point &b) { return abs(a - b); }
Real distance(const Line &l, const Point &p) {
  return abs(p - projection(l, p));
}
Real distance(const Line &l, const Line &m) {
  return intersect(l, m) ? 0 : distance(l, m.a);
}
Real distance(const Segment &s, const Point &p) {
  Point r = projection(s, p);
  if (intersect(s, r)) return abs(r - p);
  return min(abs(s.a - p), abs(s.b - p));
}
Real distance(const Segment &a, const Segment &b) {
  if (intersect(a, b)) return 0;
  return min(
      {distance(a, b.a), distance(a, b.b), distance(b, a.a), distance(b, a.b)});
}
Real distance(const Line &l, const Segment &s) {
  if (intersect(l, s)) return 0;
  return min(distance(l, s.a), distance(l, s.b));
}
Point crosspoint(const Line &l, const Line &m) {
  Real A = cross(l.b - l.a, m.b - m.a);
  Real B = cross(l.b - l.a, l.b - m.a);
  if (eq(abs(A), 0.0) && eq(abs(B), 0.0)) return m.a;
  return m.a + (m.b - m.a) * B / A;
}
Point crosspoint(const Segment &l, const Segment &m) {
  return crosspoint(Line(l), Line(m));
}
pair<Point, Point> crosspoint(const Circle &c, const Line l) {
  Point pr = projection(l, c.p);
  Point e = (l.b - l.a) / abs(l.b - l.a);
  if (eq(distance(l, c.p), c.r)) return {pr, pr};
  double base = sqrt(c.r * c.r - norm(pr - c.p));
  return {pr - e * base, pr + e * base};
}
pair<Point, Point> crosspoint(const Circle &c, const Segment &l) {
  Line aa = Line(l.a, l.b);
  if (intersect(c, l) == 2) return crosspoint(c, aa);
  auto ret = crosspoint(c, aa);
  if (dot(l.a - ret.first, l.b - ret.first) < 0)
    ret.second = ret.first;
  else
    ret.first = ret.second;
  return ret;
}
pair<Point, Point> crosspoint(const Circle &c1, const Circle &c2) {
  Real d = abs(c1.p - c2.p);
  Real a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
  Real t = atan2(c2.p.imag() - c1.p.imag(), c2.p.real() - c1.p.real());
  Point p1 = c1.p + Point(cos(t + a) * c1.r, sin(t + a) * c1.r);
  Point p2 = c1.p + Point(cos(t - a) * c1.r, sin(t - a) * c1.r);
  return {p1, p2};
}
pair<Point, Point> tangent(const Circle &c1, const Point &p2) {
  return crosspoint(c1, Circle(p2, sqrt(norm(c1.p - p2) - c1.r * c1.r)));
}
Lines tangent(Circle c1, Circle c2) {
  Lines ret;
  if (c1.r < c2.r) swap(c1, c2);
  Real g = norm(c1.p - c2.p);
  if (eq(g, 0)) return ret;
  Point u = (c2.p - c1.p) / sqrt(g);
  Point v = rotate(PI * 0.5, u);
  for (int s : {-1, 1}) {
    Real h = (c1.r + s * c2.r) / sqrt(g);
    if (eq(1 - h * h, 0)) {
      ret.emplace_back(c1.p + u * c1.r, c1.p + (u + v) * c1.r);
    } else if (1 - h * h > 0) {
      Point uu = u * h, vv = v * sqrt(1 - h * h);
      ret.emplace_back(c1.p + (uu + vv) * c1.r, c2.p - (uu + vv) * c2.r * s);
      ret.emplace_back(c1.p + (uu - vv) * c1.r, c2.p - (uu - vv) * c2.r * s);
    }
  }
  return ret;
}
bool is_convex(const Polygon &p) {
  int n = (int)p.size();
  for (int i = 0; i < n; i++) {
    if (ccw(p[(i + n - 1) % n], p[i], p[(i + 1) % n]) == -1) return false;
  }
  return true;
}
Polygon convex_hull(Polygon &p) {
  int n = (int)p.size(), k = 0;
  if (n <= 2) return p;
  sort(p.begin(), p.end());
  vector<Point> ch(2 * n);
  for (int i = 0; i < n; ch[k++] = p[i++]) {
    while (k >= 2 && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < EPS) --k;
  }
  for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {
    while (k >= t && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < EPS) --k;
  }
  ch.resize(k - 1);
  return ch;
}
int main() {
  int n;
  IN(n);
  double mi = 1e16, ma = 0;
  Point p;
  cin >> p;
  Polygon P(n);
  for (long long i = 0; i < n; ++i) {
    cin >> P[i];
  }
  double pi = acos(-1);
  for (long long i = 0; i < n; ++i)
    chmin(mi, distance(p, P[i])), chmax(ma, distance(p, P[i]));
  for (long long i = 0; i < n; ++i)
    chmin(mi, distance(Segment(P[i], P[(i + 1) % n]), p)),
        chmax(ma, distance(Segment(P[i], P[(i + 1) % n]), p));
  cout << pi * (ma * ma - mi * mi) << '\n';
}