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;
void read_file(bool outToFile = true) {}
struct point;
struct vec;
struct line;
struct circle;
struct triangle;
double to_rad(double theta);
double to_deg(double theta);
double dist(point p, point q);
point middle(point p, point q);
point translate(point p, vec u);
double norm_sq(vec u);
double dot(vec u, vec v);
double cross(vec u, vec v);
bool are_parallel(line l, line d);
bool are_same(line l, line d);
double dist_to_line(point p, point a, point b);
bool ccw(point p, point q, point r);
bool collinear(point p, point q, point r);
double angle(point a, point o, point b);
point rotate(point p, double theta, point q);
point intersection(line l, line d);
bool check_range(double v, double l1, double r1, double l2, double r2);
point segment_intersection(point p, point q, point r, point t);
bool point_on_ray(point p, point a, point b);
bool point_on_segment(point p, point a, point b);
point projection(point p, point a, point b);
double dist_to_segment(point p, point a, point b);
point reflection(point p, point a, point b);
line perpendicular(point p, point a, point b);
line bisector(point a, point o, point b);
circle find_circle(point p, point q, double r);
circle in_circle(triangle t);
circle circum_circle(triangle t);
double perimeter(vector<point> P);
double area(vector<point> P);
bool is_convex(vector<point> P);
bool is_in(point p, vector<point> P);
vector<point> cut(vector<point> P, point a, point b);
bool ch_cmp(point a, point b);
vector<point> convex_hull(vector<point> P);
void print(vector<point> P);
struct point {
  double x, y;
  point(double nx = 0, double ny = 0) { x = nx, y = ny; }
  bool operator==(point p) {
    return fabs(x - p.x) <= (1e-9) && fabs(y - p.y) <= (1e-9);
  }
  bool operator!=(point p) {
    return fabs(x - p.x) > (1e-9) || fabs(y - p.y) > (1e-9);
  }
  bool operator<(point p) {
    if (fabs(x - p.x) > (1e-9)) return x < p.x - (1e-9);
    return y < p.y - (1e-9);
  }
  friend istream &operator>>(istream &is, point &p) { return is >> p.x >> p.y; }
  friend ostream &operator<<(ostream &os, point &p) {
    return os << p.x << ' ' << p.y;
  }
};
struct vec {
  double x, y;
  vec(double nx = 0, double ny = 0) { x = nx, y = ny; }
  vec(point p, point q) { x = q.x - p.x, y = q.y - p.y; }
  vec operator+(vec u) { return vec(x + u.x, y + u.y); }
  vec operator-(vec u) { return vec(x - u.x, y - u.y); }
  vec operator*(double k) { return vec(k * x, k * y); }
  friend istream &operator>>(istream &is, vec &u) { return is >> u.x >> u.y; }
  friend ostream &operator<<(ostream &os, vec &u) {
    return os << u.x << ' ' << u.y;
  }
};
struct line {
  double a, b, c;
  line(double na = 0, double nb = 0, double nc = 0) { a = na, b = nb, c = nc; }
  line(point p, point q) {
    double dx = q.x - p.x;
    double dy = q.y - p.y;
    if (fabs(dx) <= (1e-9)) {
      a = 1, b = 0, c = -p.x;
      return;
    }
    a = -dy / dx;
    b = 1.0;
    c = dy / dx * p.x - p.y;
  }
  line(point p, double m) {
    a = -m;
    b = 1.0;
    c = -(a * p.x + p.y);
  }
  pair<point, point> to_points() {
    point p, q;
    if (fabs(b) <= (1e-9))
      p.x = -c / a, q.x = p.x, p.y = 0, q.y = 1;
    else
      p.x = 0, q.x = 1, p.y = -(a * p.x + c), q.y = -(a * q.x + c);
    return make_pair(p, q);
  }
};
struct circle {
  double x, y, r;
  circle(point c = point(0, 0), double nr = 0) { x = c.x, y = c.y, r = nr; }
  int is_in(point p) {
    double dx = p.x - x, dy = p.y - y;
    double d = dx * dx + dy * dy, R = r * r;
    return (d < R - (1e-9)) ? 0 : (fabs(d - R) <= (1e-9)) ? 1 : 2;
  }
  double perimeter(double theta = 360) {
    theta = to_rad(theta);
    return theta * r;
  }
  double area(double theta = 360) {
    theta = to_rad(theta);
    return theta * r * r / 2;
  }
};
struct triangle {
  point A, B, C;
  double a, b, c;
  triangle(double na = 0, double nb = 0, double nc = 0) {
    a = na, b = nb, c = nc;
  }
  triangle(point nA, point nB, point nC) {
    A = nA, B = nB, C = nC;
    c = dist(A, B), a = dist(B, C), b = dist(C, A);
  }
  bool is_triangle() {
    return a + b > c + (1e-9) && b + c > a + (1e-9) && c + a > b + (1e-9);
  }
  double perimeter() { return a + b + c; }
  double area() {
    double s = perimeter() / 2;
    return sqrt(s * (s - a) * (s - b) * (s - c));
  }
};
double to_rad(double theta) { return theta * acos(-1.0) / 180; }
double to_deg(double theta) { return theta * 180 / acos(-1.0); }
double dist(point p, point q) { return hypot(p.x - q.x, p.y - q.y); }
point middle(point p, point q) {
  return point((p.x + q.x) / 2, (p.y + q.y) / 2);
}
point translate(point p, vec u) { return point(p.x + u.x, p.y + u.y); }
double norm_sq(vec u) { return u.x * u.x + u.y * u.y; }
double dot(vec u, vec v) { return u.x * v.x + u.y * v.y; }
double cross(vec u, vec v) { return u.x * v.y - u.y * v.x; }
bool are_parallel(line l, line d) {
  return fabs(l.a - d.a) <= (1e-9) && fabs(l.b - l.b) <= (1e-9);
}
bool are_same(line l, line d) {
  return are_parallel(l, d) && fabs(l.c - d.c) <= (1e-9);
}
double dist_to_line(point p, point a, point b) {
  return dist(p, projection(p, a, b));
}
bool ccw(point p, point q, point r) {
  return cross(vec(p, q), vec(p, r)) > 0 + (1e-9);
}
bool collinear(point p, point q, point r) {
  return fabs(cross(vec(p, q), vec(p, r))) <= (1e-9);
}
double angle(point a, point o, point b) {
  vec oa = vec(o, a), ob = vec(o, b);
  return acos(dot(oa, ob) / sqrt(norm_sq(oa) * norm_sq(ob)));
}
point rotate(point p, double theta, point q = point(0, 0)) {
  vec oq = vec(point(0, 0), q);
  p = translate(p, oq * -1);
  theta = to_rad(theta);
  double x = p.x * cos(theta) - p.y * sin(theta);
  double y = p.x * sin(theta) + p.y * cos(theta);
  p = point(x, y);
  p = translate(p, oq);
  return p;
}
point intersection(line l, line d) {
  if (are_parallel(l, d)) return point((1000000000), (1000000000));
  point p;
  p.x = (d.b * l.c - l.b * d.c) / (d.a * l.b - l.a * d.b);
  if (fabs(l.b) > (1e-9))
    p.y = -(l.a * p.x + l.c);
  else
    p.y = -(d.a * p.x + d.c);
  return p;
}
bool check_range(double v, double l, double r) {
  if (l > r + (1e-9)) swap(l, r);
  if (fabs(r - l) <= (1e-9)) return fabs(v - l) <= (1e-9);
  return l < v - (1e-9) && v < r - (1e-9);
  return l <= v + (1e-9) && v <= r + (1e-9);
}
point segment_intersection(point p, point q, point r, point t) {
  point c = intersection(line(p, q), line(r, t));
  if (point_on_segment(c, p, q) && point_on_segment(c, r, t)) return c;
  return point((1000000000), (1000000000));
}
bool point_on_ray(point p, point a, point b) {
  vec ap = vec(a, p), ab = vec(a, b);
  return collinear(p, a, b) && dot(ap, ab) >= -(1e-9);
}
bool point_on_segment(point p, point a, point b) {
  return point_on_ray(p, a, b) && point_on_ray(p, b, a);
}
point projection(point p, point a, point b) {
  vec ap = vec(a, p), ab = vec(a, b);
  double u = dot(ap, ab) / norm_sq(ab);
  return translate(a, ab * u);
}
double dist_to_segment(point p, point a, point b) {
  vec ap = vec(a, p), ab = vec(a, b);
  double u = dot(ap, ab) / norm_sq(ab);
  if (u < 0 - (1e-9)) return dist(p, a);
  if (u > 1 + (1e-9)) return dist(p, b);
  return dist_to_line(p, a, b);
}
point reflection(point p, point a, point b) {
  point c = projection(p, a, b);
  vec pc = vec(p, c);
  return translate(p, pc * 2);
}
line perpendicular(point p, point a, point b) {
  if (!collinear(p, a, b)) return line(p, projection(p, a, b));
  line l = line(a, b);
  if (fabs(l.b) <= (1e-9)) return line(p, point(p.x + 1, p.y));
  if (fabs(l.a) <= (1e-9)) return line(p, point(p.x, p.y + 1));
  return line(p, 1 / l.a);
}
line bisector(point a, point o, point b) {
  double ratio = dist(o, a) / dist(o, b);
  ratio /= ratio + 1;
  vec ab = vec(a, b);
  point c = translate(a, ab * ratio);
  return line(o, c);
}
circle find_circle(point p, point q, double r) {
  point m = middle(p, q);
  vec mp = vec(m, p);
  double mc = r * r - norm_sq(mp);
  if (mc < 0 - (1e-9)) return circle();
  mc = sqrt(mc);
  double u = mc / dist(m, p);
  point c = translate(m, mp * u);
  c = rotate(c, 90, m);
  return circle(c, r);
}
circle in_circle(triangle t) {
  double r = 2 * t.area() / t.perimeter();
  if (fabs(r) <= (1e-9)) return circle();
  line l = bisector(t.B, t.A, t.C);
  line d = bisector(t.C, t.B, t.A);
  point c = intersection(l, d);
  return circle(c, r);
}
circle circum_circle(triangle t) {
  double r = (t.a * t.b * t.c) / (4 * t.area());
  if (fabs(r) <= (1e-9)) return circle();
  line l = perpendicular(middle(t.A, t.B), t.A, t.B);
  line d = perpendicular(middle(t.A, t.C), t.A, t.C);
  point c = intersection(l, d);
  return circle(c, r);
}
point pivot;
double perimeter(vector<point> P) {
  int n = P.size();
  double ret = 0;
  for (int i = 0; i < n - 1; i++) ret += dist(P[i], P[i + 1]);
  return ret;
}
double area(vector<point> P) {
  int n = P.size();
  double ret = 0;
  double x1, x2, y1, y2;
  for (int i = 0; i < n - 1; i++) {
    x1 = P[i].x, x2 = P[i + 1].x;
    y1 = P[i].y, y2 = P[i + 1].y;
    ret += x1 * y2 - x2 * y1;
  }
  ret /= 2, ret = fabs(ret);
  return ret;
}
bool is_convex(vector<point> P) {
  int n = P.size();
  if (n <= 3) return false;
  bool turn = ccw(P[0], P[1], P[2]);
  for (int i = 1; i < n - 1; i++)
    if (ccw(P[i], P[i + 1], P[i + 2 != n ? i + 2 : 1]) != turn) return false;
  return true;
}
bool is_in(point p, vector<point> P) {
  int n = P.size();
  double sum = 0;
  for (int i = 0; i < n - 1; i++)
    if (ccw(P[i], p, P[i + 1]))
      sum += angle(P[i], p, P[i + 1]);
    else
      sum -= angle(P[i], p, P[i + 1]);
  sum = fabs(sum);
  return fabs(sum - 2 * acos(-1.0)) <= (1e-9);
}
vector<point> cut(vector<point> P, point a, point b) {
  int n = P.size();
  vector<point> ret;
  for (int i = 0; i < n; i++) {
    double left1 = cross(vec(a, b), vec(a, P[i]));
    double left2 = (i != n - 1) ? cross(vec(a, b), vec(a, P[i + 1])) : 0;
    if (left1 >= -(1e-9)) ret.push_back(P[i]);
    if (left1 * left2 < -(1e-9))
      ret.push_back(intersection(line(a, b), line(P[i], P[i + 1])));
  }
  if (!ret.empty() && ret.front() != ret.back()) ret.push_back(ret.front());
  return ret;
}
bool ch_cmp(point a, point b) {
  if (collinear(pivot, a, b)) return dist(pivot, a) < dist(pivot, b) - (1e-9);
  double dx1 = a.x - pivot.x, dy1 = a.y - pivot.y;
  double dx2 = b.x - pivot.x, dy2 = b.y - pivot.y;
  return atan2(dy1, dx1) < atan2(dy2, dx2) - (1e-9);
}
vector<point> convex_hull(vector<point> P) {
  int n = P.size();
  if (n <= 3) {
    if (n != 0 && P[0] != P[n - 1]) P.push_back(P[0]);
    return P;
  }
  int idx = 0;
  for (int i = 1; i < n; i++)
    if (P[idx].y > P[i].y + (1e-9) ||
        (fabs(P[idx].y - P[i].y) <= (1e-9) && P[idx].x < P[i].x - (1e-9)))
      idx = i;
  swap(P[0], P[idx]);
  pivot = P[0];
  sort(P.begin() + 1, P.end(), ch_cmp);
  vector<point> ch;
  ch.push_back(P[n - 1]), ch.push_back(P[0]), ch.push_back(P[1]);
  int i = 2;
  while (i < n) {
    int j = ch.size() - 1;
    if (ccw(ch[j - 1], ch[j], P[i]))
      ch.push_back(P[i]), i++;
    else
      ch.pop_back();
  }
  return ch;
}
void print(vector<point> P) {
  int n = P.size();
  cout << '\n';
  for (int i = 0; i < n; i++) cout << P[i] << '\n';
  cout << '\n';
}
int n;
point A[100000 + 9];
point O;
double r, R;
void check(double d) {
  if (d < r - (1e-9)) r = d;
  if (d > R + (1e-9)) R = d;
}
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  read_file();
  while (cin >> n) {
    cin >> O;
    for (int i = 0; i < n; i++) cin >> A[i];
    n++;
    A[n - 1] = A[0];
    r = (1000000000), R = -(1000000000);
    for (int i = 0; i < n - 1; i++) {
      double d = dist(O, A[i]);
      check(d);
      d = dist_to_segment(O, A[i], A[i + 1]);
      check(d);
    }
    double ans = acos(-1.0) * (R * R - r * r);
    cout << setprecision(25) << ans << '\n';
  }
}