#include <bits/stdc++.h>
using namespace std;
inline void OPEN(const string &s) {
  freopen((s + ".in").c_str(), "r", stdin);
  freopen((s + ".out").c_str(), "w", stdout);
}
double _acos(double x) {
  double ret = acos(x);
  if (ret == ret) return ret;
  if (x < 0) return acos(-1.0);
  return acos(1.0);
}
const double PI = _acos(-1);
const double EPS = 1e-9;
const double INF = 1e300;
struct point {
  double x, y;
  point() { x = y = 0; }
  point(double x, double y) : x(x), y(y) {}
};
struct segment {
  point p1, p2;
  segment() { p1 = p2 = point(0, 0); }
  segment(point p1, point p2) : p1(p1), p2(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, const double &s) {
  return point(p.x * s, p.y * s);
}
point operator/(const point &p, const double &s) { return p * (1. / s); }
bool operator<(const point &p1, const point &p2) {
  if (p1.x != p2.x) return p1.x < p2.x;
  return p1.y < p2.y;
}
bool operator==(const point &p1, const point &p2) {
  return fabs(p1.x - p2.x) < EPS && fabs(p1.y - p2.y) < EPS;
}
double cross(const point &p1, const point &p2) {
  return p1.x * p2.y - p1.y * p2.x;
}
double dot(const point &p1, const point &p2) {
  return p1.x * p2.x + p1.y * p2.y;
}
double dist(const point &p) { return sqrt(((p.x) * (p.x)) + ((p.y) * (p.y))); }
double dist(const point &p1, const point &p2) {
  return sqrt(((p1.x - p2.x) * (p1.x - p2.x)) +
              ((p1.y - p2.y) * (p1.y - p2.y)));
}
double length(const segment &s) {
  return sqrt(((s.p1.x - s.p2.x) * (s.p1.x - s.p2.x)) +
              ((s.p1.y - s.p2.y) * (s.p1.y - s.p2.y)));
}
double getAngle(const point &p1, const point &p2) {
  return fabs(
      _acos(dot(p1, p2) / dist(p1, point(0, 0)) / dist(p2, point(0, 0))));
}
double getAngle(const point &p1, const point &center, const point &p2) {
  return getAngle(p1 - center, p2 - center);
}
double distToSegment(const point &p, const segment &s) {
  if (getAngle(s.p2, s.p1, p) > PI / 2 + EPS ||
      getAngle(s.p1, s.p2, p) > PI / 2 + EPS)
    return min(dist(p, s.p1), dist(p, s.p2));
  return fabs(cross(s.p1 - p, s.p2 - p)) / dist(s.p1, s.p2);
}
double distToLine(const point &p, const segment &s) {
  return fabs(cross(s.p1 - p, s.p2 - p)) / dist(s.p1, s.p2);
}
point rotate(const point &p, const double &alpha) {
  return point(p.x * cos(alpha) - p.y * sin(alpha),
               p.x * sin(alpha) + p.y * cos(alpha));
}
point rotate(const point &p, const point &center, const double &alpha) {
  return center + rotate(p - center, alpha);
}
point rescale(const point &p, const double s) {
  return point(p.x * s, p.y * s);
}
point dilate(const point &p, const double Factor) { return rescale(p, Factor); }
point dilate(const point &p, const point &center, double factor) {
  return dilate(p - center, factor) + center;
}
bool isRightTurn(const point &p1, const point &p2, const point &p3) {
  return cross(p2 - p1, p3 - p2) <= 0;
}
bool isOnSameSide(const point &p1, const point &p2, const segment &s) {
  double z1 = cross(s.p2 - s.p1, p1 - s.p1);
  double z2 = cross(s.p2 - s.p1, p2 - s.p1);
  return (z1 + EPS < 0 && z2 + EPS < 0) || (0 < z1 - EPS && 0 < z2 - EPS) ||
         fabs(z1) < EPS || fabs(z2) < EPS;
}
bool isOnLine(const point &p, const segment &l) {
  return fabs((l.p1.y - p.y) * (l.p2.x - p.x) -
              (l.p2.y - p.y) * (l.p1.x - p.x)) < EPS;
}
bool isOnSegment(const point &p, const segment &s) {
  return fabs(dist(p, s.p1) + dist(p, s.p2) - dist(s.p1, s.p2)) < EPS;
}
bool isIntersecting(const segment &s1, const segment &s2) {
  return !(isOnSameSide(s1.p1, s1.p2, s2) || isOnSameSide(s2.p1, s2.p2, s1)) ||
         isOnSegment(s1.p1, s2) || isOnSegment(s1.p2, s2) ||
         isOnSegment(s2.p1, s1) || isOnSegment(s2.p2, s1);
}
bool isParallel(const segment &s1, const segment &s2) {
  return fabs((s1.p1.y - s1.p2.y) * (s2.p1.x - s2.p2.x) -
              (s2.p1.y - s2.p2.y) * (s1.p1.x - s1.p2.x)) < EPS;
}
point intersection(const segment &s1, const segment &s2) {
  double x1 = s1.p1.x - s1.p2.x;
  double x2 = s2.p1.x - s2.p2.x;
  double y1 = s1.p1.y - s1.p2.y;
  double y2 = s2.p1.y - s2.p2.y;
  double cross1 = cross(s1.p1, s1.p2);
  double cross2 = cross(s2.p1, s2.p2);
  return point((cross1 * x2 - cross2 * x1) / (x1 * y2 - x2 * y1),
               (cross1 * y2 - cross2 * y1) / (x1 * y2 - x2 * y1));
}
point projection(const point &p, const segment &s) {
  return rescale(s.p2 - s.p1,
                 dot(p - s.p1, s.p2 - s.p1) / ((length(s)) * (length(s)))) +
         s.p1;
}
point reflection(const point &p, const point &center) {
  return center * 2. - p;
}
point reflection(const point &p, const segment &s) {
  return reflection(p, projection(p, s));
}
segment lineBisector(const point &p1, const point &p2) {
  point center = (p1 + p2) / 2.;
  return segment(rotate(p1, center, PI / 2.), rotate(p2, center, PI / 2.));
}
segment lineBisector(const segment &s) { return lineBisector(s.p1, s.p2); }
struct circle {
  point center;
  double r;
  circle() {
    center = point(0, 0);
    r = 0;
  }
  circle(point p, double r) : center(p), r(r) {}
};
double area(const circle &c) { return PI * c.r * c.r; }
double perimeter(const circle &c) { return 2. * PI * c.r; }
bool isOnCircle(const point &p, const circle &c) {
  return dist(p, c.center) == c.r;
}
bool isInsideCircle(const point &p, const circle &c) {
  return dist(p, c.center) + EPS < c.r;
}
bool isOutsideCircle(const point &p, const circle &c) {
  return dist(p, c.center) > c.r + EPS;
}
bool isTangent(const segment &l, const circle &c) {
  return distToLine(c.center, l) == c.r;
}
vector<point> intersectionLineCircle(const segment &l, const circle &c) {
  vector<point> res;
  double dx = l.p2.x - l.p1.x;
  double dy = l.p2.y - l.p1.y;
  double dr = length(l);
  double d = cross(l.p1 - c.center, l.p2 - c.center);
  if (((c.r) * (c.r)) * ((dr) * (dr)) - ((d) * (d)) + EPS < 0) return res;
  double det = sqrt(fabs(((c.r) * (c.r)) * ((dr) * (dr)) - ((d) * (d))));
  double sdx = dy < 0 ? -dx : dx;
  double sdy = fabs(dy);
  res.push_back(c.center + point((d * dy + sdx * det) / ((dr) * (dr)),
                                 (-d * dx + sdy * det) / ((dr) * (dr))));
  if (det > EPS)
    res.push_back(c.center + point((d * dy - sdx * det) / ((dr) * (dr)),
                                   (-d * dx - sdy * det) / ((dr) * (dr))));
  return res;
}
vector<point> intersectionSegmentCircle(const segment &s, const circle &c) {
  vector<point> res, _res = intersectionLineCircle(s, c);
  for (vector<point>::iterator it = _res.begin(); it != _res.end(); ++it) {
    if (isOnSegment(*it, s)) res.push_back(*it);
  }
  return res;
}
vector<point> intersectionCircleCircle(const circle &c1, const circle &c2) {
  vector<point> res;
  return res;
}
point centroid(vector<point> t) {
  if (t.size() != 3) assert(false);
  return (t[0] + t[1] + t[2]) / 3.;
}
point orthocenter(vector<point> t) {
  if (t.size() != 3) assert(false);
  return intersection(segment(t[0], projection(t[0], segment(t[1], t[2]))),
                      segment(t[1], projection(t[1], segment(t[0], t[2]))));
}
point circumcenter(vector<point> t) {
  if (t.size() != 3) assert(false);
  return intersection(lineBisector(t[0], t[1]), lineBisector(t[1], t[2]));
}
double polygonArea(vector<point> p) {
  double area = p.front().y * p.back().x - p.front().x * p.back().y;
  for (int i = 0; i + 1 < (int)p.size(); ++i) {
    area += p[i].x * p[i + 1].y;
    area -= p[i].y * p[i + 1].x;
  }
  return fabs(area) / 2.;
}
bool isClockwise(vector<point> p) {
  double area = p.front().y * p.back().x - p.front().x * p.back().y;
  for (int i = 0; i + 1 < (int)p.size(); ++i) {
    area += p[i].x * p[i + 1].y;
    area -= p[i].y * p[i + 1].x;
  }
  return area < 0;
}
bool isPointInsidePolygon(point p, vector<point> poly) {
  segment ray(p, p + point(1, 0));
  int n = (int)poly.size();
  int nIntersection = 0;
  for (int i = 0; i < n; ++i) {
    segment side(poly[i], poly[(i + 1) % n]);
    if (isOnSegment(p, side)) return false;
    if (isParallel(ray, side)) continue;
    point x = intersection(ray, side);
    if (isOnSegment(x, side) && dot(x - p, ray.p2 - p) > 0) {
      if (x == side.p1) {
        if (isRightTurn(p, x, side.p2)) nIntersection++;
      } else if (x == side.p2) {
        if (isRightTurn(p, x, side.p1)) nIntersection++;
      } else
        nIntersection++;
    }
  }
  return nIntersection % 2 == 1;
}
vector<point> convexHull(vector<point> p) {
  int m = 0, n = p.size();
  vector<point> hull(2 * n);
  sort(p.begin(), p.end());
  for (int i = 0; i < n; ++i) {
    while (m >= 2 && isRightTurn(hull[m - 2], hull[m - 1], p[i])) --m;
    hull[m++] = p[i];
  }
  for (int i = n - 1, t = m + 1; i >= 0; --i) {
    while (m >= t && isRightTurn(hull[m - 2], hull[m - 1], p[i])) --m;
    hull[m++] = p[i];
  }
  hull.resize(m);
  return hull;
}
int n, m = 0;
double minr, maxr;
point p, t[100100];
int main() {
  scanf("%d%lf%lf", &n, &p.x, &p.y);
  maxr = 0;
  for (int i = 0; i < (n); ++i) {
    scanf("%lf%lf", &t[i].x, &t[i].y);
    maxr = max((maxr), (dist(t[i], p)));
    ;
  }
  minr = maxr;
  for (int i = 0; i < (n); ++i) {
    minr = min((minr), (distToSegment(p, segment(t[i], t[(i + 1) % n]))));
    ;
  }
  printf("%.17lf\n", PI * (maxr * maxr - minr * minr));
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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>
using namespace std;
inline void OPEN(const string &s) {
  freopen((s + ".in").c_str(), "r", stdin);
  freopen((s + ".out").c_str(), "w", stdout);
}
double _acos(double x) {
  double ret = acos(x);
  if (ret == ret) return ret;
  if (x < 0) return acos(-1.0);
  return acos(1.0);
}
const double PI = _acos(-1);
const double EPS = 1e-9;
const double INF = 1e300;
struct point {
  double x, y;
  point() { x = y = 0; }
  point(double x, double y) : x(x), y(y) {}
};
struct segment {
  point p1, p2;
  segment() { p1 = p2 = point(0, 0); }
  segment(point p1, point p2) : p1(p1), p2(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, const double &s) {
  return point(p.x * s, p.y * s);
}
point operator/(const point &p, const double &s) { return p * (1. / s); }
bool operator<(const point &p1, const point &p2) {
  if (p1.x != p2.x) return p1.x < p2.x;
  return p1.y < p2.y;
}
bool operator==(const point &p1, const point &p2) {
  return fabs(p1.x - p2.x) < EPS && fabs(p1.y - p2.y) < EPS;
}
double cross(const point &p1, const point &p2) {
  return p1.x * p2.y - p1.y * p2.x;
}
double dot(const point &p1, const point &p2) {
  return p1.x * p2.x + p1.y * p2.y;
}
double dist(const point &p) { return sqrt(((p.x) * (p.x)) + ((p.y) * (p.y))); }
double dist(const point &p1, const point &p2) {
  return sqrt(((p1.x - p2.x) * (p1.x - p2.x)) +
              ((p1.y - p2.y) * (p1.y - p2.y)));
}
double length(const segment &s) {
  return sqrt(((s.p1.x - s.p2.x) * (s.p1.x - s.p2.x)) +
              ((s.p1.y - s.p2.y) * (s.p1.y - s.p2.y)));
}
double getAngle(const point &p1, const point &p2) {
  return fabs(
      _acos(dot(p1, p2) / dist(p1, point(0, 0)) / dist(p2, point(0, 0))));
}
double getAngle(const point &p1, const point &center, const point &p2) {
  return getAngle(p1 - center, p2 - center);
}
double distToSegment(const point &p, const segment &s) {
  if (getAngle(s.p2, s.p1, p) > PI / 2 + EPS ||
      getAngle(s.p1, s.p2, p) > PI / 2 + EPS)
    return min(dist(p, s.p1), dist(p, s.p2));
  return fabs(cross(s.p1 - p, s.p2 - p)) / dist(s.p1, s.p2);
}
double distToLine(const point &p, const segment &s) {
  return fabs(cross(s.p1 - p, s.p2 - p)) / dist(s.p1, s.p2);
}
point rotate(const point &p, const double &alpha) {
  return point(p.x * cos(alpha) - p.y * sin(alpha),
               p.x * sin(alpha) + p.y * cos(alpha));
}
point rotate(const point &p, const point &center, const double &alpha) {
  return center + rotate(p - center, alpha);
}
point rescale(const point &p, const double s) {
  return point(p.x * s, p.y * s);
}
point dilate(const point &p, const double Factor) { return rescale(p, Factor); }
point dilate(const point &p, const point &center, double factor) {
  return dilate(p - center, factor) + center;
}
bool isRightTurn(const point &p1, const point &p2, const point &p3) {
  return cross(p2 - p1, p3 - p2) <= 0;
}
bool isOnSameSide(const point &p1, const point &p2, const segment &s) {
  double z1 = cross(s.p2 - s.p1, p1 - s.p1);
  double z2 = cross(s.p2 - s.p1, p2 - s.p1);
  return (z1 + EPS < 0 && z2 + EPS < 0) || (0 < z1 - EPS && 0 < z2 - EPS) ||
         fabs(z1) < EPS || fabs(z2) < EPS;
}
bool isOnLine(const point &p, const segment &l) {
  return fabs((l.p1.y - p.y) * (l.p2.x - p.x) -
              (l.p2.y - p.y) * (l.p1.x - p.x)) < EPS;
}
bool isOnSegment(const point &p, const segment &s) {
  return fabs(dist(p, s.p1) + dist(p, s.p2) - dist(s.p1, s.p2)) < EPS;
}
bool isIntersecting(const segment &s1, const segment &s2) {
  return !(isOnSameSide(s1.p1, s1.p2, s2) || isOnSameSide(s2.p1, s2.p2, s1)) ||
         isOnSegment(s1.p1, s2) || isOnSegment(s1.p2, s2) ||
         isOnSegment(s2.p1, s1) || isOnSegment(s2.p2, s1);
}
bool isParallel(const segment &s1, const segment &s2) {
  return fabs((s1.p1.y - s1.p2.y) * (s2.p1.x - s2.p2.x) -
              (s2.p1.y - s2.p2.y) * (s1.p1.x - s1.p2.x)) < EPS;
}
point intersection(const segment &s1, const segment &s2) {
  double x1 = s1.p1.x - s1.p2.x;
  double x2 = s2.p1.x - s2.p2.x;
  double y1 = s1.p1.y - s1.p2.y;
  double y2 = s2.p1.y - s2.p2.y;
  double cross1 = cross(s1.p1, s1.p2);
  double cross2 = cross(s2.p1, s2.p2);
  return point((cross1 * x2 - cross2 * x1) / (x1 * y2 - x2 * y1),
               (cross1 * y2 - cross2 * y1) / (x1 * y2 - x2 * y1));
}
point projection(const point &p, const segment &s) {
  return rescale(s.p2 - s.p1,
                 dot(p - s.p1, s.p2 - s.p1) / ((length(s)) * (length(s)))) +
         s.p1;
}
point reflection(const point &p, const point &center) {
  return center * 2. - p;
}
point reflection(const point &p, const segment &s) {
  return reflection(p, projection(p, s));
}
segment lineBisector(const point &p1, const point &p2) {
  point center = (p1 + p2) / 2.;
  return segment(rotate(p1, center, PI / 2.), rotate(p2, center, PI / 2.));
}
segment lineBisector(const segment &s) { return lineBisector(s.p1, s.p2); }
struct circle {
  point center;
  double r;
  circle() {
    center = point(0, 0);
    r = 0;
  }
  circle(point p, double r) : center(p), r(r) {}
};
double area(const circle &c) { return PI * c.r * c.r; }
double perimeter(const circle &c) { return 2. * PI * c.r; }
bool isOnCircle(const point &p, const circle &c) {
  return dist(p, c.center) == c.r;
}
bool isInsideCircle(const point &p, const circle &c) {
  return dist(p, c.center) + EPS < c.r;
}
bool isOutsideCircle(const point &p, const circle &c) {
  return dist(p, c.center) > c.r + EPS;
}
bool isTangent(const segment &l, const circle &c) {
  return distToLine(c.center, l) == c.r;
}
vector<point> intersectionLineCircle(const segment &l, const circle &c) {
  vector<point> res;
  double dx = l.p2.x - l.p1.x;
  double dy = l.p2.y - l.p1.y;
  double dr = length(l);
  double d = cross(l.p1 - c.center, l.p2 - c.center);
  if (((c.r) * (c.r)) * ((dr) * (dr)) - ((d) * (d)) + EPS < 0) return res;
  double det = sqrt(fabs(((c.r) * (c.r)) * ((dr) * (dr)) - ((d) * (d))));
  double sdx = dy < 0 ? -dx : dx;
  double sdy = fabs(dy);
  res.push_back(c.center + point((d * dy + sdx * det) / ((dr) * (dr)),
                                 (-d * dx + sdy * det) / ((dr) * (dr))));
  if (det > EPS)
    res.push_back(c.center + point((d * dy - sdx * det) / ((dr) * (dr)),
                                   (-d * dx - sdy * det) / ((dr) * (dr))));
  return res;
}
vector<point> intersectionSegmentCircle(const segment &s, const circle &c) {
  vector<point> res, _res = intersectionLineCircle(s, c);
  for (vector<point>::iterator it = _res.begin(); it != _res.end(); ++it) {
    if (isOnSegment(*it, s)) res.push_back(*it);
  }
  return res;
}
vector<point> intersectionCircleCircle(const circle &c1, const circle &c2) {
  vector<point> res;
  return res;
}
point centroid(vector<point> t) {
  if (t.size() != 3) assert(false);
  return (t[0] + t[1] + t[2]) / 3.;
}
point orthocenter(vector<point> t) {
  if (t.size() != 3) assert(false);
  return intersection(segment(t[0], projection(t[0], segment(t[1], t[2]))),
                      segment(t[1], projection(t[1], segment(t[0], t[2]))));
}
point circumcenter(vector<point> t) {
  if (t.size() != 3) assert(false);
  return intersection(lineBisector(t[0], t[1]), lineBisector(t[1], t[2]));
}
double polygonArea(vector<point> p) {
  double area = p.front().y * p.back().x - p.front().x * p.back().y;
  for (int i = 0; i + 1 < (int)p.size(); ++i) {
    area += p[i].x * p[i + 1].y;
    area -= p[i].y * p[i + 1].x;
  }
  return fabs(area) / 2.;
}
bool isClockwise(vector<point> p) {
  double area = p.front().y * p.back().x - p.front().x * p.back().y;
  for (int i = 0; i + 1 < (int)p.size(); ++i) {
    area += p[i].x * p[i + 1].y;
    area -= p[i].y * p[i + 1].x;
  }
  return area < 0;
}
bool isPointInsidePolygon(point p, vector<point> poly) {
  segment ray(p, p + point(1, 0));
  int n = (int)poly.size();
  int nIntersection = 0;
  for (int i = 0; i < n; ++i) {
    segment side(poly[i], poly[(i + 1) % n]);
    if (isOnSegment(p, side)) return false;
    if (isParallel(ray, side)) continue;
    point x = intersection(ray, side);
    if (isOnSegment(x, side) && dot(x - p, ray.p2 - p) > 0) {
      if (x == side.p1) {
        if (isRightTurn(p, x, side.p2)) nIntersection++;
      } else if (x == side.p2) {
        if (isRightTurn(p, x, side.p1)) nIntersection++;
      } else
        nIntersection++;
    }
  }
  return nIntersection % 2 == 1;
}
vector<point> convexHull(vector<point> p) {
  int m = 0, n = p.size();
  vector<point> hull(2 * n);
  sort(p.begin(), p.end());
  for (int i = 0; i < n; ++i) {
    while (m >= 2 && isRightTurn(hull[m - 2], hull[m - 1], p[i])) --m;
    hull[m++] = p[i];
  }
  for (int i = n - 1, t = m + 1; i >= 0; --i) {
    while (m >= t && isRightTurn(hull[m - 2], hull[m - 1], p[i])) --m;
    hull[m++] = p[i];
  }
  hull.resize(m);
  return hull;
}
int n, m = 0;
double minr, maxr;
point p, t[100100];
int main() {
  scanf("%d%lf%lf", &n, &p.x, &p.y);
  maxr = 0;
  for (int i = 0; i < (n); ++i) {
    scanf("%lf%lf", &t[i].x, &t[i].y);
    maxr = max((maxr), (dist(t[i], p)));
    ;
  }
  minr = maxr;
  for (int i = 0; i < (n); ++i) {
    minr = min((minr), (distToSegment(p, segment(t[i], t[(i + 1) % n]))));
    ;
  }
  printf("%.17lf\n", PI * (maxr * maxr - minr * minr));
  return 0;
}

```