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;
using namespace std;
struct Point {
  double x, y;
  Point(double _x, double _y) {
    x = _x;
    y = _y;
  }
  Point() {}
  double mod() { return sqrt(x * x + y * y); }
  double mod2() { return x * x + y * y; }
  double arg() { return atan2(y, x); }
  Point ort() { return Point(-y, x); }
  Point rev() { return Point(y, x); }
  Point unit() {
    double k = mod();
    return Point(x / k, y / k);
  }
  void print() { printf("%lf %lf\n", x, y); }
  void read() { scanf("%lf%lf", &x, &y); }
};
bool operator<(const Point &P1, const Point &P2) {
  return (P1.x != P2.x) ? (P1.x < P2.x) : (P1.y < P2.y);
}
bool operator==(const Point &P1, const Point &P2) {
  return fabs(P1.x - P2.x) < 1e-6 && fabs(P1.y - P2.y) < 1e-6;
}
bool operator>(const Point &P1, const Point &P2) {
  return !(P1 == P2) && !(P1 < P2);
}
bool operator!=(const Point &P1, const Point &P2) { return !(P1 == P2); }
Point operator-(const Point &p1, const Point &p2) {
  return Point(p1.x - p2.x, p1.y - p2.y);
}
Point operator+(const Point &p1, const Point &p2) {
  return Point(p1.x + p2.x, p1.y + p2.y);
}
Point operator*(const Point &p, double k) { return Point(p.x * k, p.y * k); }
Point operator/(const Point &p, double k) { return Point(p.x / k, p.y / k); }
double dot(const Point &v1, const Point &v2) {
  return v1.x * v2.x + v1.y * v2.y;
}
double cross(const Point &v1, const Point &v2) {
  return v1.x * v2.y - v1.y * v2.x;
}
double dis(const Point &P1, const Point &P2) { return (P1 - P2).mod(); }
double area(const Point &A, const Point &B, const Point &C) {
  return cross(B - A, C - A);
}
double areaHeron(double a, double b, double c) {
  double s = (a + b + c) / 2;
  return sqrt(s * (s - a) * (s - b) * (s - c));
}
double areaHeron(double a, double b, double c, double d) {
  double s = (a + b + c + d) / 2;
  return sqrt((s - a) * (s - b) * (s - c) * (s - d));
}
double circumradius(double a, double b, double c) {
  return a * b * c / (4 * areaHeron(a, b, c));
}
Point rotate(Point A, Point C, double teta) {
  Point T = Point(A.x - C.x, A.y - C.y);
  return C + Point(T.x * cos(teta) - T.y * sin(teta),
                   T.y * cos(teta) + T.x * sin(teta));
}
struct line {
  Point p1, p2;
  line(Point _p1, Point _p2) {
    p1 = _p1;
    p2 = _p2;
  }
  line() {}
  Point dir() { return p2 - p1; }
  double mod() { return (p2 - p1).mod(); }
};
bool isAntihorario(Point *poli, int n) {
  int top = 0;
  for (int i = 0; i < n; i++)
    if (poli[top].y < poli[i].y) top = i;
  return poli[(top - 1 + n) % n].x > poli[(top + 1 + n) % n].x;
}
double disPointToLine(Point P, line L) {
  Point v = P - L.p1;
  return fabs(cross(v, L.dir())) / L.mod();
}
double disLineToPoint(Point P, line L) {
  Point v = L.p2 - L.p1;
  Point v1 = P - L.p1;
  Point v2 = P - L.p2;
  if (dot(v, v1) <= 0) return v1.mod();
  if (dot(v, v2) >= 0) return v2.mod();
  return fabs(cross(v1, v)) / v.mod();
}
bool between(const Point &A, const Point &B, const Point &P) {
  return P.x + 1e-6 >= min(A.x, B.x) && P.x <= max(A.x, B.x) + 1e-6 &&
         P.y + 1e-6 >= min(A.y, B.y) && P.y <= max(A.y, B.y) + 1e-6;
}
bool onSegment(Point P, line L) {
  return fabs(cross(L.dir(), P - L.p1)) < 1e-6 &&
         dot(P - L.p1, P - L.p2) < 1e-6;
}
bool intersects(line L1, line L2) {
  if (onSegment(L1.p1, L2)) return true;
  if (onSegment(L1.p2, L2)) return true;
  if (onSegment(L2.p1, L1)) return true;
  if (onSegment(L2.p2, L1)) return true;
  double A11 = cross(L1.dir(), L2.p1 - L1.p1);
  double A12 = cross(L1.dir(), L2.p2 - L1.p1);
  double A21 = cross(L2.dir(), L1.p1 - L2.p1);
  double A22 = cross(L2.dir(), L1.p2 - L2.p1);
  if (A11 > 1e-6) swap(A11, A12);
  if (A21 > 1e-6) swap(A21, A22);
  return (A11 < 0 && A12 > 1e-6) && (A21 < 0 && A22 > 1e-6);
}
Point lineIntersection(line S1, line S2) {
  return S1.p1 + S1.dir() * (cross(S2.p1 - S1.p1, S2.dir()) /
                             cross(S1.dir(), S2.dir()));
}
Point circumcenter(const Point &A, const Point &B, const Point &C) {
  return (A + B + (A - B).ort() * dot(C - B, A - C) / cross(A - B, A - C)) / 2;
}
double distSeg(line s1, line s2) {
  double ans = (1 << 30);
  ans = min(ans, disLineToPoint(s1.p1, s2));
  ans = min(ans, disLineToPoint(s1.p2, s2));
  ans = min(ans, disLineToPoint(s2.p1, s1));
  ans = min(ans, disLineToPoint(s2.p2, s1));
  return ans;
}
double area(vector<Point> &P) {
  double ans = 0;
  int n = P.size();
  for (int i = 0; i < n; i++) ans += cross(P[i], P[(i + 1) % n]);
  return fabs(ans) / 2.0;
}
Point P[1000005], C;
pair<double, double> getInterval(int p1, int p2) {
  double d1 = (P[p1] - C).mod2();
  double d2 = (P[p2] - C).mod2();
  double maxi = max(d1, d2);
  Point dir = P[p1] - P[p2];
  Point v1 = C - dir.ort() * sqrt(maxi), v2 = C + dir.ort() * sqrt(maxi);
  line S1 = line(P[p1], P[p2]);
  line S2 = line(v1, v2);
  if (!intersects(S1, S2)) return make_pair(min(d1, d2), maxi);
  Point I = lineIntersection(S1, S2);
  double mini = (C - I).mod2();
  return make_pair(mini, maxi);
}
int main() {
  int n;
  while (cin >> n) {
    C.read();
    for (int i = 0; i < n; i++) P[i].read();
    vector<pair<double, double> > v;
    for (int i = 0; i < n; i++) {
      v.push_back(getInterval(i, (i + 1) % n));
    }
    sort(v.begin(), v.end());
    double ans = 0, last = -1;
    if (v.size() > 0) ans += v[0].second - v[0].first, last = v[0].second;
    for (int i = 1; i < v.size(); i++) {
      if (v[i].first > last) {
        ans += v[i].second - v[i].first;
      } else if (v[i].second > last)
        ans += v[i].second - last;
      last = max(last, v[i].second);
    }
    ans = ans * (atan2(0, -1));
    printf("%.10lf\n", ans);
  }
}