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(-1.0);
const int MAXN = 1e5 + 9;
int sgn(double x) {
  if (fabs(x) < eps) return 0;
  if (x < 0)
    return -1;
  else
    return 1;
}
struct POint {
  double x, y;
  POint() {}
  POint(double _x, double _y) {
    x = _x;
    y = _y;
  }
  POint operator-(const POint &b) const { return POint(x - b.x, y - b.y); }
  double operator^(const POint &b) const { return x * b.y - y * b.x; }
  double operator*(const POint &b) const { return x * b.x + y * b.y; }
  void transXY(double B) {
    double tx = x, ty = y;
    x = tx * cos(B) - ty * sin(B);
    y = tx * sin(B) + ty * cos(B);
  }
};
struct LIne {
  POint s, e;
  LIne() {}
  LIne(POint _s, POint _e) {
    s = _s;
    e = _e;
  }
  pair<int, POint> operator&(const LIne &b) const {
    POint res = s;
    if (sgn((s - e) ^ (b.s - b.e)) == 0) {
      if (sgn((s - b.e) ^ (b.s - b.e)) == 0)
        return make_pair(0, res);
      else
        return make_pair(1, res);
    }
    double t = ((s - b.s) ^ (b.s - b.e)) / ((s - e) ^ (b.s - b.e));
    res.x += (e.x - s.x) * t;
    res.y += (e.y - s.y) * t;
    return make_pair(2, res);
  }
};
double dist(POint a, POint b) { return sqrt((a - b) * (a - b)); }
bool inter(LIne l1, LIne l2) {
  return max(l1.s.x, l1.e.x) >= min(l2.s.x, l2.e.x) &&
         max(l2.s.x, l2.e.x) >= min(l1.s.x, l1.e.x) &&
         max(l1.s.y, l1.e.y) >= min(l2.s.y, l2.e.y) &&
         max(l2.s.y, l2.e.y) >= min(l1.s.y, l1.e.y) &&
         sgn((l2.s - l1.e) ^ (l1.s - l1.e)) *
                 sgn((l2.e - l1.e) ^ (l1.s - l1.e)) <=
             0 &&
         sgn((l1.s - l2.e) ^ (l2.s - l2.e)) *
                 sgn((l1.e - l2.e) ^ (l2.s - l2.e)) <=
             0;
}
bool Seg_inter_line(LIne l1, LIne l2) {
  return sgn((l2.s - l1.e) ^ (l1.s - l1.e)) *
             sgn((l2.e - l1.e) ^ (l1.s - l1.e)) <=
         0;
}
POint PointToLine(POint P, LIne L) {
  POint result;
  double t = ((P - L.s) * (L.e - L.s)) / ((L.e - L.s) * (L.e - L.s));
  result.x = L.s.x + (L.e.x - L.s.x) * t;
  result.y = L.s.y + (L.e.y - L.s.y) * t;
  return result;
}
POint NearestPointToLineSeg(POint P, LIne L) {
  POint result;
  double t = ((P - L.s) * (L.e - L.s)) / ((L.e - L.s) * (L.e - L.s));
  if (t >= 0 && t <= 1) {
    result.x = L.s.x + (L.e.x - L.s.x) * t;
    result.y = L.s.y + (L.e.y - L.s.y) * t;
  } else {
    if (dist(P, L.s) < dist(P, L.e))
      result = L.s;
    else
      result = L.e;
  }
  return result;
}
double CalcArea(POint p[], int n) {
  double res = 0;
  for (int i = 0; i < n; i++) res += (p[i] ^ p[(i + 1) % n]) / 2;
  return fabs(res);
}
bool OnSeg(POint P, LIne L) {
  return sgn((L.s - P) ^ (L.e - P)) == 0 &&
         sgn((P.x - L.s.x) * (P.x - L.e.x)) <= 0 &&
         sgn((P.y - L.s.y) * (P.y - L.e.y)) <= 0;
}
int inConvexPoly(POint a, POint p[], int n) {
  for (int i = 0; i < n; i++) {
    if (sgn((p[i] - a) ^ (p[(i + 1) % n] - a)) < 0)
      return -1;
    else if (OnSeg(a, LIne(p[i], p[(i + 1) % n])))
      return 0;
  }
  return 1;
}
int inPoly(POint p, POint poly[], int n) {
  int cnt;
  LIne ray, side;
  cnt = 0;
  ray.s = p;
  ray.e.y = p.y;
  ray.e.x = -100000000000.0;
  for (int i = 0; i < n; i++) {
    side.s = poly[i];
    side.e = poly[(i + 1) % n];
    if (OnSeg(p, side)) return 0;
    if (sgn(side.s.y - side.e.y) == 0) continue;
    if (OnSeg(side.s, ray)) {
      if (sgn(side.s.y - side.e.y) > 0) cnt++;
    } else if (OnSeg(side.e, ray)) {
      if (sgn(side.e.y - side.s.y) > 0) cnt++;
    } else if (inter(ray, side))
      cnt++;
  }
  if (cnt % 2 == 1)
    return 1;
  else
    return -1;
}
bool isconvex(POint poly[], int n) {
  bool s[3];
  memset(s, false, sizeof(s));
  for (int i = 0; i < n; i++) {
    s[sgn((poly[(i + 1) % n] - poly[i]) ^ (poly[(i + 2) % n] - poly[i])) + 1] =
        true;
    if (s[0] && s[2]) return false;
  }
  return true;
}
POint lis[MAXN];
int Stack[MAXN], top;
bool _cmp(POint p1, POint p2) {
  double tmp = (p1 - lis[0]) ^ (p2 - lis[0]);
  if (sgn(tmp) > 0)
    return true;
  else if (sgn(tmp) == 0 && sgn(dist(p1, lis[0]) - dist(p2, lis[0])) <= 0)
    return true;
  else
    return false;
}
void Graham(int n) {
  POint p0;
  int k = 0;
  p0 = lis[0];
  for (int i = 1; i < n; i++) {
    if ((p0.y > lis[i].y) || (p0.y == lis[i].y && p0.x > lis[i].x)) {
      p0 = lis[i];
      k = i;
    }
  }
  swap(lis[k], lis[0]);
  sort(lis + 1, lis + n, _cmp);
  if (n == 1) {
    top = 1;
    Stack[0] = 0;
    return;
  }
  if (n == 2) {
    top = 2;
    Stack[0] = 0;
    Stack[1] = 1;
    return;
  }
  Stack[0] = 0;
  Stack[1] = 1;
  top = 2;
  for (int i = 2; i < n; i++) {
    while (top > 1 && sgn((lis[Stack[top - 1]] - lis[Stack[top - 2]]) ^
                          (lis[i] - lis[Stack[top - 2]])) <= 0)
      top--;
    Stack[top++] = i;
  }
}
struct CIrcle {
  POint c;
  double r;
  CIrcle(POint c, double r) : c(c), r(r) {}
  CIrcle() {}
  CIrcle(double _x, double _y, double _r) {
    c.x = _x;
    c.y = _y;
    r = _r;
  }
};
POint operator*(double a, POint p) { return POint(a * p.x, a * p.y); }
POint operator+(POint a, POint b) { return POint(a.x + b.x, b.y + a.y); }
POint operator*(POint a, double b) { return POint(a.x * b, a.y * b); }
struct LINE {
  POint p, v;
  POint pointofline(double t) { return p + t * v; }
};
int main() {
  int a, d, e, f;
  POint o, tmp;
  cin >> a >> o.x >> o.y;
  for (d = 0; d < a; d++) {
    cin >> lis[d].x >> lis[d].y;
  }
  double res = 1e9, res1 = 0.0;
  for (d = 0; d < a; d++) {
    e = d;
    f = (d + 1) % a;
    tmp = NearestPointToLineSeg(o, LIne(lis[e], lis[f]));
    res = min(res, dist(o, lis[e]));
    res = min(res, dist(o, tmp));
    res1 = max(dist(o, lis[d]), res1);
  }
  cout << fixed << setprecision(9) << (res1 * res1 - res * res) * PI << endl;
  return 0;
}