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;
const double eps = 1e-8;
const double pi = acos(-1);
int cmp(double x) {
  if (fabs(x) < eps) return 0;
  if (x > 0) return 1;
  return -1;
}
int cmp(double x, double y) { return cmp(x - y); }
inline double sqr(double x) { return x * x; }
struct point {
  double x, y;
  point() {}
  point(double a, double b) : x(a), y(b) {}
  friend point operator+(const point &a, const point &b) {
    return point(a.x + b.x, a.y + b.y);
  }
  friend point operator-(const point &a, const point &b) {
    return point(a.x - b.x, a.y - b.y);
  }
  friend bool operator==(const point &a, const point &b) {
    return cmp(a.x - b.x) == 0 && cmp(a.y - b.y) == 0;
  }
  friend bool operator<(const point &a, const point &b) {
    if (cmp(a.x - b.x) < 0) return true;
    if (cmp(a.x - b.x) > 0) return false;
    return cmp(a.y - b.y) < 0;
  }
  friend point operator*(const point &a, const double &b) {
    return point(a.x * b, a.y * b);
  }
  friend point operator*(const double &a, const point &b) {
    return point(a * b.x, a * b.y);
  }
  friend point operator/(const point &a, const double &b) {
    return point(a.x / b, a.y / b);
  }
  friend istream &operator>>(istream &fin, point &a) {
    fin >> a.x >> a.y;
    return fin;
  }
  double norm() { return sqrt(sqr(x) + sqr(y)); }
};
double det(const point &a, const point &b) { return a.x * b.y - a.y * b.x; }
double dot(const point &a, const point &b) { return a.x * b.x + a.y * b.y; }
double dist(const point &a, const point &b) { return (a - b).norm(); }
point rorate_point(const point &p, double A) {
  double tx = p.x, ty = p.y;
  return point(tx * cos(A) - ty * sin(A), tx * sin(A) + ty * cos(A));
}
struct line {
  point a, b;
  line(point x, point y) : a(x), b(y) {}
};
double dis_point_segment(const point p, const point s, const point t) {
  if (cmp(dot(p - s, t - s)) < 0) return (p - s).norm();
  if (cmp(dot(p - t, s - t)) < 0) return (p - t).norm();
  return fabs(det(s - p, t - p) / dist(s, t));
}
void PointProjLine(const point p, const point s, const point t, point &cp) {
  double r = dot((t - s), (p - s)) / dot(t - s, t - s);
  cp = s + r * (t - s);
}
bool PointOnSegment(point p, point s, point t) {
  return cmp(det(p - s, t - s)) == 0 && cmp(dot(p - s, p - t)) <= 0;
}
bool parallel(line a, line b) { return !cmp(det(a.a - a.b, b.a - b.b)); }
bool line_make_point(line a, line b, point &res) {
  if (parallel(a, b)) return false;
  double s1 = det(a.a - b.a, b.b - b.a);
  double s2 = det(a.b - b.a, b.b - b.a);
  res = (s1 * a.b - s2 * a.a) / (s1 - s2);
  return true;
}
double multiply(point sp, point ep, point op) {
  return ((sp.x - op.x) * (ep.y - op.y) - (ep.x - op.x) * (sp.y - op.y));
}
bool intersect(line u, line v) {
  return ((max(u.a.x, u.b.x) >= min(v.a.x, v.b.x)) &&
          (max(v.a.x, v.b.x) >= min(u.a.x, u.b.x)) &&
          (max(u.a.y, u.b.y) >= min(v.a.y, v.b.y)) &&
          (max(v.a.y, v.b.y) >= min(u.a.y, u.b.y)) &&
          (multiply(v.a, u.b, u.a) * multiply(u.b, v.b, u.a) >= 0) &&
          (multiply(u.a, v.b, v.a) * multiply(v.b, u.b, v.a) >= 0));
}
const int maxn = 10001;
struct polygon {
  int n;
  point a[maxn];
  double perimeter() {
    double sum = 0;
    a[n] = a[0];
    for (int i = 0; i < n; i++) sum += (a[i + 1] - a[i]).norm();
    return sum;
  }
  double area() {
    double sum = 0;
    a[n] = a[0];
    for (int i = 0; i < n; i++) sum += det(a[i + 1], a[i]);
    return sum / 2.;
  }
  int Point_In(point t) {
    int num = 0, i, d1, d2, k;
    a[n] = a[0];
    for (int i = 0; i < n; i++) {
      if (PointOnSegment(t, a[i], a[i + 1])) return 2;
      k = cmp(det(a[i + 1] - a[i], t - a[i]));
      d1 = cmp(a[i].y - t.y);
      d2 = cmp(a[i + 1].y - t.y);
      if (k > 0 && d1 <= 0 && d2 > 0) num++;
      if (k < 0 && d2 <= 0 && d1 > 0) num++;
    }
    return num & 1;
  }
};
struct polygon_convex {
  vector<point> P;
  polygon_convex(int Size = 0) { P.resize(Size); }
};
bool comp_less(const point &a, const point &b) {
  return cmp(a.x - b.x) < 0 || cmp(a.x - b.x) == 0 && cmp(a.y - b.y) < 0;
}
polygon_convex convex_hull(vector<point> a) {
  polygon_convex res(2 * a.size() + 5);
  sort(a.begin(), a.end(), comp_less);
  a.erase(unique(a.begin(), a.end()), a.end());
  int m = 0;
  for (int i = 0; i < a.size(); ++i) {
    while (m > 1 &&
           cmp(det(res.P[m - 1] - res.P[m - 2], a[i] - res.P[m - 2])) <= 0)
      --m;
    res.P[m++] = a[i];
  }
  int k = m;
  for (int i = int(a.size()) - 2; i >= 0; --i) {
    while (m > k &&
           cmp(det(res.P[m - 1] - res.P[m - 2], a[i] - res.P[m - 2])) <= 0)
      --m;
    res.P[m++] = a[i];
  }
  res.P.resize(m);
  if (a.size() > 1) res.P.resize(m - 1);
  return res;
}
int containOlogn(const polygon_convex &a, const point &b) {
  int n = a.P.size();
  point g = (a.P[0] + a.P[n / 3] + a.P[2 * n / 3]) / 3.0;
  int l = 0, r = n;
  while (l + 1 < r) {
    int mid = (l + r) / 2;
    if (cmp(det(a.P[l] - g, a.P[mid] - g)) > 0) {
      if (cmp(det(a.P[l] - g, b - g)) >= 0 && cmp(det(a.P[mid] - g, b - g)) < 0)
        r = mid;
      else
        l = mid;
    } else {
      if (cmp(det(a.P[l] - g, b - g)) < 0 && cmp(det(a.P[mid] - g, b - g)) >= 0)
        l = mid;
      else
        r = mid;
    }
  }
  r %= n;
  int z = cmp(det(a.P[r] - b, a.P[l] - b)) - 1;
  if (z == -2) return 1;
  return z;
}
bool containOn(const polygon_convex &a, const point &b) {
  int n = a.P.size();
  int sign = 0;
  for (int i = 0; i < n; ++i) {
    int x = cmp(det(a.P[i] - b, a.P[((i + 1) % n)] - b));
    if (x) {
      if (sign) {
        if (sign != x) return false;
      } else
        sign = x;
    }
  }
  return true;
}
bool inaline(line a, line b) {
  if (!parallel(a, b)) return false;
  if (cmp(det(a.a - a.b, a.a - b.a)) == 0) return true;
  return false;
}
const double INF = 10000;
double arg(const point &p) { return atan2(p.y, p.x); }
inline double satisfy(point a, pair<point, point> p) {
  return cmp(det(a - p.first, p.second - p.first)) <= 0;
}
point crosspoint(const pair<point, point> &a, const pair<point, point> &b) {
  double k = det(b.first - b.second, a.first - b.second);
  k = k / (k - det(b.first - b.second, a.second - b.second));
  return a.first + (a.second - a.first) * k;
}
bool cmpp(const pair<point, point> &a, const pair<point, point> &b) {
  int res = cmp(arg(a.second - a.first) - arg(b.second - b.first));
  return res == 0 ? satisfy(a.first, b) : res < 0;
}
vector<point> HalfplaneIntersection(vector<pair<point, point> > v) {
  sort(v.begin(), v.end(), cmpp);
  deque<pair<point, point> > q;
  deque<point> ans;
  q.push_back(v[0]);
  for (int i = 1; i < v.size(); ++i) {
    if (cmp(arg(v[i].second - v[i].first) -
            arg(v[i - 1].second - v[i - 1].first)) == 0) {
      continue;
    }
    while (ans.size() > 0 && !satisfy(ans.back(), v[i])) {
      ans.pop_back();
      q.pop_back();
    }
    while (ans.size() > 0 && !satisfy(ans.front(), v[i])) {
      ans.pop_front();
      q.pop_front();
    }
    ans.push_back(crosspoint(q.back(), v[i]));
    q.push_back(v[i]);
  }
  while (ans.size() > 0 && !satisfy(ans.back(), q.front())) {
    ans.pop_back();
    q.pop_back();
  }
  while (ans.size() > 0 && !satisfy(ans.front(), q.back())) {
    ans.pop_front();
    q.pop_front();
  }
  ans.push_back(crosspoint(q.back(), q.front()));
  return vector<point>(ans.begin(), ans.end());
}
vector<point> convexIntersection(vector<point> v1, vector<point> v2) {
  vector<pair<point, point> > h;
  for (int i = 0; i < v1.size(); ++i)
    h.push_back(pair<point, point>(v1[i], v1[(i + 1) % v1.size()]));
  for (int i = 0; i < v2.size(); ++i)
    h.push_back(pair<point, point>(v2[i], v2[(i + 1) % v2.size()]));
  return HalfplaneIntersection(h);
}
int n;
point o, x;
int main() {
  double mmax = 0, mmin = 1e9;
  cin >> n >> o;
  vector<point> v;
  for (int i = 0; i < n; ++i) {
    cin >> x;
    mmax = max(dist(x, o), mmax);
    mmin = min(dist(x, o), mmin);
    v.push_back(x);
  }
  v.push_back(*v.begin());
  for (int i = 0; i < v.size() - 1; ++i) {
    point cp;
    PointProjLine(o, v[i], v[i + 1], cp);
    if (PointOnSegment(cp, v[i], v[i + 1]))
      mmin = min(mmin, dis_point_segment(o, v[i], v[i + 1]));
  }
  printf("%.10f\n", (sqr(mmax) - sqr(mmin)) * pi);
}