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;
inline namespace Infinity {
const char CR = '\n';
inline void write(const int n) { printf("%d", n); }
inline void write(const unsigned n) { printf("%u", n); }
inline void write(const long long n) { cout << n; }
inline void write(const unsigned long long n) { cout << n; }
inline void writef(const double a, const int n = 15) { printf("%.*f", n, a); }
inline void writef(const long double a, const int n = 18) {
  cout << setprecision(n) << fixed << a;
}
inline void write(const char c) { printf("%c", c); }
inline void write(const char s[] = "") { printf("%s", s); }
inline void write(const string &s) { cout << s; }
inline void write(const pair<int, int> &p) {
  printf("%d %d", p.first, p.second);
}
template <class T>
inline void write(const T a) {
  for (auto i : a) write(i);
}
inline void writeln() { write(CR); }
template <typename T>
inline void writeln(const T &a) {
  write(a);
  write(CR);
}
inline void writefln(const double a, int n) {
  printf("%.*f", n, a);
  write(CR);
}
inline void writefln(const long double a, int n = 18) {
  cout << setprecision(n) << fixed << a << endl;
}
inline void writesln(const int *a, const int l, const int r) {
  for (int i = l; i <= r; i++) printf("%d ", a[i]);
  writeln(CR);
}
template <class T>
inline void writelns(const T a) {
  for (__typeof a.begin() i = a.begin(); i != a.end(); i++) writeln(*i);
}
template <typename T, typename... types>
inline void write(const T &a, const types &...args) {
  write(a);
  write(args...);
}
template <typename... types>
inline void writeln(const types &...args) {
  write(args...);
  write(CR);
}
inline void writelnYN(bool b) { writeln(b ? "YES" : "NO"); }
inline void writelnyn(bool b) { writeln(b ? "Yes" : "No"); }
inline int read(int &n) { return scanf("%d", &n); }
inline int read(long long &n) { return cin >> n ? 1 : -1; }
template <typename T, typename... types>
inline int read(T &n, types &...args) {
  read(n);
  return read(args...);
}
inline char getcc() {
  char c;
  do c = getchar();
  while (c == ' ' || c == '\n');
  return c;
}
inline int getint() {
  int n;
  read(n);
  return n;
}
inline long long getll() {
  long long n;
  read(n);
  return n;
}
inline double getdouble() {
  double n;
  scanf("%lf", &n);
  return n;
}
inline vector<int> getints(int n) {
  vector<int> v(n);
  for (int i = 0; i < n; i++) v[i] = getint();
  return v;
}
inline vector<pair<int, int>> getpairs(int n) {
  vector<pair<int, int>> v(n);
  for (int i = 0; i < n; i++) {
    int a = getint(), b = getint();
    v[i] = pair<int, int>(a, b);
  }
  return v;
}
inline void read(string &str, const unsigned size) {
  char s[size];
  scanf("%s", s);
  str = string(s);
}
inline string getstr(const unsigned size = 1048576) {
  string s;
  read(s, size + 1);
  return s;
}
inline string getln(const unsigned size = 1048576) {
  char s[size + 1];
  scanf("%[^\n]", s);
  return string(s);
}
}  // namespace Infinity
inline namespace Infinity {
inline namespace Geometry {
class Point {
 public:
  Point(long double x = 0, long double y = 0) : x(x), y(y) {}
  Point(const pair<int, int> &p) : x(p.first), y(p.second) {}
  long double x, y;
};
class Line {
 public:
  Line(long double a, long double b, long double c) : a(a), b(b), c(c) {}
  Line(Point p1, Point p2) {
    assert(p1.x != p2.x || p1.y != p2.y);
    a = p2.y - p1.y;
    b = p1.x - p2.x;
    c = p1.y * (p2.x - p1.x) - p1.x * (p2.y - p1.y);
  }
  long double a, b, c;
};
const long double pi = acosl(-1);
const long double eps = 1e-15l;
long double sq(long double a) { return a * a; }
long double dist(Point a, Point b) {
  return sqrtl(sq(a.x - b.x) + sq(a.y - b.y));
}
bool parallel(Line l1, Line l2) { return l1.a * l2.b - l1.b * l2.a == 0; }
Point intersection(Line l1, Line l2) {
  assert(parallel(l1, l2) == false);
  return Point((l1.b * l2.c - l2.b * l1.c) / (l1.a * l2.b - l2.a * l1.b),
               (l1.a * l2.c - l2.a * l1.c) / (l2.a * l1.b - l1.a * l2.b));
}
Point footPoint(Point pt, Line ln) {
  Line pl(ln.b, -ln.a, pt.y * ln.a - pt.x * ln.b);
  return intersection(ln, pl);
}
long double dist(Point pt, Line ln) {
  return fabsl(ln.a * pt.x + ln.b * pt.y + ln.c) / sqrtl(sq(ln.a) + sq(ln.b));
}
}  // namespace Geometry
}  // namespace Infinity
int main() {
  int n = getint();
  long double x = getint();
  long double y = getint();
  vector<pair<int, int>> a = getpairs(n);
  long double maxr = 0;
  long double minr = LLONG_MAX;
  for (unsigned i = 0; i < a.size(); i++)
    maxr = max(maxr, dist(Point(a[i].first, a[i].second), Point(x, y)));
  for (unsigned i = 0; i < a.size(); i++) {
    Point p1(a[i].first, a[i].second);
    Point p2(a[(i + 1) % a.size()].first, a[(i + 1) % a.size()].second);
    Point fp = footPoint(Point(x, y), Line(p1, p2));
    if (dist(p1, fp) + dist(fp, p2) <= dist(p1, p2) + eps)
      minr = min(minr, dist(Point(x, y), Line(p1, p2)));
    minr = min(minr, dist(p1, Point(x, y)));
    minr = min(minr, dist(p2, Point(x, y)));
  }
  writefln(pi * (maxr * maxr - minr * minr));
  return 0;
}