#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx")
using namespace std;
const double eps = 1e-9;
struct Point {
  long double first, second;
  Point() : first(0), second(0) {}
  Point(double _x, double _y) : first(_x), second(_y) {}
  Point(pair<double, double> t) : first(t.first), second(t.second) {}
  inline long double squaredDistance(Point p) const {
    return (first - p.first) * (first - p.first) +
           (second - p.second) * (second - p.second);
  }
  inline double distance(Point p) const {
    return sqrt((first - p.first) * (first - p.first) +
                (second - p.second) * (second - p.second));
  }
  inline bool equals(Point other) const {
    return abs(first - other.first) < eps && abs(second - other.second) < eps;
  }
};
inline Point operator+(const Point &a, const Point &b) {
  return Point(a.first + b.first, a.second + b.second);
}
inline Point operator-(const Point &a, const Point &b) {
  return Point(a.first - b.first, a.second - b.second);
}
inline Point operator*(const Point &a, const double &b) {
  return Point(a.first * b, a.second * b);
}
inline Point operator/(const Point &a, const double &b) {
  return Point(a.first / b, a.second / b);
}
inline double vec(const Point &a, const Point &b) {
  return a.first * b.second - b.first * a.second;
}
inline double scal(const Point &a, const Point &b) {
  return a.first * b.first + a.second * b.second;
}
struct Line {
  long double a, b, c;
  Line() : a(0), b(0), c(0) {}
  Line(double _a, double _b, double _c) : a(_a), b(_b), c(_c) { normalize(); }
  Line(const Point &t1, const Point &t2) {
    a = t2.second - t1.second;
    b = t1.first - t2.first;
    c = -a * t1.first - b * t1.second;
    normalize();
  }
  inline bool degenerate() {
    return abs(a) < eps && abs(b) < eps && abs(c) < eps;
  }
  inline void normalize() {
    long double h = sqrt(a * a + b * b);
    if (a < -eps || (abs(a) < eps && b < -eps) ||
        (abs(a) < eps && abs(b) < eps && c < -eps)) {
      a = -a;
      b = -b;
      c = -c;
    }
    if (h < eps) return;
    a /= h;
    b /= h;
    c /= h;
  }
  inline Point intersect(Line other) {
    if (parallel(other)) return Point(-1e100, -1e100);
    double det = b * other.a - a * other.b;
    double first = (c * other.b - b * other.c) / det;
    double second = (a * other.c - c * other.a) / det;
    return Point(first, second);
  }
  inline bool parallel(Line other) {
    return abs(a * other.b - b * other.a) < eps;
  }
  inline long double evaluate(Point point) {
    return a * point.first + b * point.second + c;
  }
  inline bool contains(Point point) { return abs(evaluate(point)) < eps; }
  inline Line perpendicular(Point point) {
    return Line(-b, a, b * point.first - a * point.second);
  }
  inline long double distance(Point point) { return abs(evaluate(point)); }
};
struct Circle {
  Point center;
  double radius;
  Circle() : radius(0) {}
  Circle(Point _center, double _radius) : center(_center), radius(_radius) {}
  bool contains(Point point) { return center.distance(point) < radius + eps; }
  bool strictlyContains(Point point) {
    return center.distance(point) + eps < radius;
  }
  vector<Point> findTouchingPoints(Point point) {
    double distance = center.distance(point);
    if (distance + eps < radius) return vector<Point>();
    if (distance < radius + eps) return vector<Point>(1, point);
    Circle p(point, sqrt((distance - radius) * (distance + radius)));
    return intersect(p);
  }
  vector<Point> intersect(Line line) {
    double distance = line.distance(center);
    if (distance > radius + eps) return vector<Point>();
    Point intersection = line.intersect(line.perpendicular(center));
    if (abs(distance - radius) < eps) return vector<Point>(1, intersection);
    double shift = sqrt(radius * radius - distance * distance);
    vector<Point> ans;
    ans.push_back(Point(intersection.first + shift * line.b,
                        intersection.second - shift * line.a));
    ans.push_back(Point(intersection.first - shift * line.b,
                        intersection.second + shift * line.a));
    return ans;
  }
  vector<Point> intersect(Circle other) {
    double distance = center.distance(other.center);
    if (distance > radius + other.radius + eps ||
        abs(radius - other.radius) > distance + eps)
      return vector<Point>();
    double p = (radius + other.radius + distance) / 2;
    double h = 2.0 *
               sqrt(p * (p - radius) * (p - other.radius) * (p - distance)) /
               distance;
    double l1 = sqrt(radius * radius - h * h);
    double l2 = sqrt(other.radius * other.radius - h * h);
    if (radius * radius + distance * distance < other.radius * other.radius)
      l1 = -l1;
    if (radius * radius > distance * distance + other.radius * other.radius)
      l2 = -l2;
    Point middle((center.first * l2 + other.center.first * l1) / (l1 + l2),
                 (center.second * l2 + other.center.second * l1) / (l1 + l2));
    Line line(center, other.center);
    return intersect(line.perpendicular(middle));
  }
};
struct Segment {
  Point a, b;
  double distance_;
  Line line_;
  Segment() : distance_(-2), line_(0, 0, 0) {}
  Segment(Point _a, Point _b) : a(_a), b(_b), distance_(-2), line_(0, 0, 0) {}
  inline double length() {
    if (distance_ < -1) {
      distance_ = a.distance(b);
    }
    return distance_;
  }
  inline Line line() {
    if (line_.degenerate()) {
      line_ = Line(a, b);
    }
    return line_;
  }
  inline long double distance(Point point) {
    long double length = this->length();
    long double left = point.distance(a);
    if (length < eps) return left;
    long double right = point.distance(b);
    if (left * left > right * right + length * length) return right;
    if (right * right > left * left + length * length) return left;
    return line().distance(point);
  }
  inline bool contains(Point point, bool includeEnds) {
    if (a.equals(point) || b.equals(point)) return includeEnds;
    if (a.equals(b)) return 0;
    Line line = this->line();
    if (!line.contains(point)) return 0;
    Line perpendicular = line.perpendicular(a);
    double A = perpendicular.evaluate(a);
    double B = perpendicular.evaluate(b);
    double P = perpendicular.evaluate(point);
    return (A < P && P < B) || (B < P && P < A);
  }
  inline Point intersect(Segment other, bool includeEnds) {
    Line line = this->line();
    Line otherLine(other.a, other.b);
    if (line.parallel(otherLine)) return Point(-1e100, -1e100);
    Point intersection = line.intersect(otherLine);
    if (contains(intersection, includeEnds) &&
        other.contains(intersection, includeEnds))
      return intersection;
    return make_pair(-1e100, -1e100);
  }
  inline Point middle() {
    return Point((a.first + b.first) / 2, (a.second + b.second) / 2);
  }
  vector<Point> intersect(Circle circle) {
    vector<Point> result = circle.intersect(line());
    if (result.empty()) return result;
    if ((int)result.size() == 1) {
      if (contains(result[0], true)) return result;
      return vector<Point>();
    }
    if (contains(result[0], true)) {
      if (contains(result[1], true)) return result;
      return vector<Point>(1, result[0]);
    }
    if (contains(result[1], true)) return vector<Point>(1, result[1]);
    return vector<Point>();
  }
};
int a, b, c, d, n, m, k;
int main() {
  int first, second;
  scanf("%d%d%d", &n, &first, &second);
  long double mn = 8LL * 1000000000 * 1000000000;
  long double mx = -1;
  pair<int, int> last, fir;
  Point p(first, second);
  for (int _n((n + 1) - 1), i(0); i <= _n; i++) {
    if (i == n) {
      a = fir.first;
      b = fir.second;
    } else {
      scanf("%d%d", &a, &b);
    }
    if (!i) {
      fir = make_pair(a, b);
    }
    long long cur = (long long)(a - first) * (a - first) +
                    (long long)(b - second) * (b - second);
    if (cur < mn) mn = cur;
    if (cur > mx) mx = cur;
    if (i) {
      Point p1(last.first, last.second);
      Point p2(a, b);
      Segment s(p1, p2);
      auto d = s.distance(p);
      d *= d;
      if (d < mn) {
        mn = d;
      }
      if (d > mx) {
        mx = d;
      }
    }
    last = make_pair(a, b);
  }
  long double ans = 3.1415926535897932384626433832795028841971 * (mx - mn);
  cout.precision(12);
  cout << fixed << ans << endl;
}

### Prompt

Your challenge is to write a cpp solution to the following 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>

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx")
using namespace std;
const double eps = 1e-9;
struct Point {
  long double first, second;
  Point() : first(0), second(0) {}
  Point(double _x, double _y) : first(_x), second(_y) {}
  Point(pair<double, double> t) : first(t.first), second(t.second) {}
  inline long double squaredDistance(Point p) const {
    return (first - p.first) * (first - p.first) +
           (second - p.second) * (second - p.second);
  }
  inline double distance(Point p) const {
    return sqrt((first - p.first) * (first - p.first) +
                (second - p.second) * (second - p.second));
  }
  inline bool equals(Point other) const {
    return abs(first - other.first) < eps && abs(second - other.second) < eps;
  }
};
inline Point operator+(const Point &a, const Point &b) {
  return Point(a.first + b.first, a.second + b.second);
}
inline Point operator-(const Point &a, const Point &b) {
  return Point(a.first - b.first, a.second - b.second);
}
inline Point operator*(const Point &a, const double &b) {
  return Point(a.first * b, a.second * b);
}
inline Point operator/(const Point &a, const double &b) {
  return Point(a.first / b, a.second / b);
}
inline double vec(const Point &a, const Point &b) {
  return a.first * b.second - b.first * a.second;
}
inline double scal(const Point &a, const Point &b) {
  return a.first * b.first + a.second * b.second;
}
struct Line {
  long double a, b, c;
  Line() : a(0), b(0), c(0) {}
  Line(double _a, double _b, double _c) : a(_a), b(_b), c(_c) { normalize(); }
  Line(const Point &t1, const Point &t2) {
    a = t2.second - t1.second;
    b = t1.first - t2.first;
    c = -a * t1.first - b * t1.second;
    normalize();
  }
  inline bool degenerate() {
    return abs(a) < eps && abs(b) < eps && abs(c) < eps;
  }
  inline void normalize() {
    long double h = sqrt(a * a + b * b);
    if (a < -eps || (abs(a) < eps && b < -eps) ||
        (abs(a) < eps && abs(b) < eps && c < -eps)) {
      a = -a;
      b = -b;
      c = -c;
    }
    if (h < eps) return;
    a /= h;
    b /= h;
    c /= h;
  }
  inline Point intersect(Line other) {
    if (parallel(other)) return Point(-1e100, -1e100);
    double det = b * other.a - a * other.b;
    double first = (c * other.b - b * other.c) / det;
    double second = (a * other.c - c * other.a) / det;
    return Point(first, second);
  }
  inline bool parallel(Line other) {
    return abs(a * other.b - b * other.a) < eps;
  }
  inline long double evaluate(Point point) {
    return a * point.first + b * point.second + c;
  }
  inline bool contains(Point point) { return abs(evaluate(point)) < eps; }
  inline Line perpendicular(Point point) {
    return Line(-b, a, b * point.first - a * point.second);
  }
  inline long double distance(Point point) { return abs(evaluate(point)); }
};
struct Circle {
  Point center;
  double radius;
  Circle() : radius(0) {}
  Circle(Point _center, double _radius) : center(_center), radius(_radius) {}
  bool contains(Point point) { return center.distance(point) < radius + eps; }
  bool strictlyContains(Point point) {
    return center.distance(point) + eps < radius;
  }
  vector<Point> findTouchingPoints(Point point) {
    double distance = center.distance(point);
    if (distance + eps < radius) return vector<Point>();
    if (distance < radius + eps) return vector<Point>(1, point);
    Circle p(point, sqrt((distance - radius) * (distance + radius)));
    return intersect(p);
  }
  vector<Point> intersect(Line line) {
    double distance = line.distance(center);
    if (distance > radius + eps) return vector<Point>();
    Point intersection = line.intersect(line.perpendicular(center));
    if (abs(distance - radius) < eps) return vector<Point>(1, intersection);
    double shift = sqrt(radius * radius - distance * distance);
    vector<Point> ans;
    ans.push_back(Point(intersection.first + shift * line.b,
                        intersection.second - shift * line.a));
    ans.push_back(Point(intersection.first - shift * line.b,
                        intersection.second + shift * line.a));
    return ans;
  }
  vector<Point> intersect(Circle other) {
    double distance = center.distance(other.center);
    if (distance > radius + other.radius + eps ||
        abs(radius - other.radius) > distance + eps)
      return vector<Point>();
    double p = (radius + other.radius + distance) / 2;
    double h = 2.0 *
               sqrt(p * (p - radius) * (p - other.radius) * (p - distance)) /
               distance;
    double l1 = sqrt(radius * radius - h * h);
    double l2 = sqrt(other.radius * other.radius - h * h);
    if (radius * radius + distance * distance < other.radius * other.radius)
      l1 = -l1;
    if (radius * radius > distance * distance + other.radius * other.radius)
      l2 = -l2;
    Point middle((center.first * l2 + other.center.first * l1) / (l1 + l2),
                 (center.second * l2 + other.center.second * l1) / (l1 + l2));
    Line line(center, other.center);
    return intersect(line.perpendicular(middle));
  }
};
struct Segment {
  Point a, b;
  double distance_;
  Line line_;
  Segment() : distance_(-2), line_(0, 0, 0) {}
  Segment(Point _a, Point _b) : a(_a), b(_b), distance_(-2), line_(0, 0, 0) {}
  inline double length() {
    if (distance_ < -1) {
      distance_ = a.distance(b);
    }
    return distance_;
  }
  inline Line line() {
    if (line_.degenerate()) {
      line_ = Line(a, b);
    }
    return line_;
  }
  inline long double distance(Point point) {
    long double length = this->length();
    long double left = point.distance(a);
    if (length < eps) return left;
    long double right = point.distance(b);
    if (left * left > right * right + length * length) return right;
    if (right * right > left * left + length * length) return left;
    return line().distance(point);
  }
  inline bool contains(Point point, bool includeEnds) {
    if (a.equals(point) || b.equals(point)) return includeEnds;
    if (a.equals(b)) return 0;
    Line line = this->line();
    if (!line.contains(point)) return 0;
    Line perpendicular = line.perpendicular(a);
    double A = perpendicular.evaluate(a);
    double B = perpendicular.evaluate(b);
    double P = perpendicular.evaluate(point);
    return (A < P && P < B) || (B < P && P < A);
  }
  inline Point intersect(Segment other, bool includeEnds) {
    Line line = this->line();
    Line otherLine(other.a, other.b);
    if (line.parallel(otherLine)) return Point(-1e100, -1e100);
    Point intersection = line.intersect(otherLine);
    if (contains(intersection, includeEnds) &&
        other.contains(intersection, includeEnds))
      return intersection;
    return make_pair(-1e100, -1e100);
  }
  inline Point middle() {
    return Point((a.first + b.first) / 2, (a.second + b.second) / 2);
  }
  vector<Point> intersect(Circle circle) {
    vector<Point> result = circle.intersect(line());
    if (result.empty()) return result;
    if ((int)result.size() == 1) {
      if (contains(result[0], true)) return result;
      return vector<Point>();
    }
    if (contains(result[0], true)) {
      if (contains(result[1], true)) return result;
      return vector<Point>(1, result[0]);
    }
    if (contains(result[1], true)) return vector<Point>(1, result[1]);
    return vector<Point>();
  }
};
int a, b, c, d, n, m, k;
int main() {
  int first, second;
  scanf("%d%d%d", &n, &first, &second);
  long double mn = 8LL * 1000000000 * 1000000000;
  long double mx = -1;
  pair<int, int> last, fir;
  Point p(first, second);
  for (int _n((n + 1) - 1), i(0); i <= _n; i++) {
    if (i == n) {
      a = fir.first;
      b = fir.second;
    } else {
      scanf("%d%d", &a, &b);
    }
    if (!i) {
      fir = make_pair(a, b);
    }
    long long cur = (long long)(a - first) * (a - first) +
                    (long long)(b - second) * (b - second);
    if (cur < mn) mn = cur;
    if (cur > mx) mx = cur;
    if (i) {
      Point p1(last.first, last.second);
      Point p2(a, b);
      Segment s(p1, p2);
      auto d = s.distance(p);
      d *= d;
      if (d < mn) {
        mn = d;
      }
      if (d > mx) {
        mx = d;
      }
    }
    last = make_pair(a, b);
  }
  long double ans = 3.1415926535897932384626433832795028841971 * (mx - mn);
  cout.precision(12);
  cout << fixed << ans << endl;
}

```