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>
const double EPS = 1e-10;
const long long int MOD = 1000000007ll;
const long long int mod1 = 1000000009ll;
const long long int mod2 = 1100000009ll;
const double PI = 3.14159265359;
int INF = 2147483645;
long long int INFINF = 9223372036854775807;
int debug = 0;
using namespace std;
long long int bit_count(long long int _x) {
  long long int _ret = 0;
  while (_x) {
    if (_x % 2 == 1) _ret++;
    _x /= 2;
  }
  return _ret;
}
long long int bit(long long int _mask, long long int _i) {
  return (_mask & (1 << _i)) == 0 ? 0 : 1;
}
long long int powermod(long long int _a, long long int _b, long long int _m) {
  long long int _r = 1;
  while (_b) {
    if (_b % 2 == 1) _r = (_r * _a) % _m;
    _b /= 2;
    _a = (_a * _a) % _m;
  }
  return _r;
}
long long int add(long long int a, long long int b) {
  long long int x = a + b;
  while (x >= MOD) x -= MOD;
  return x;
}
long long int sub(long long int a, long long int b) {
  long long int x = a - b;
  while (x < 0) x += MOD;
  return x;
}
long long int mul(long long int a, long long int b) {
  long long int x = a * b;
  x %= MOD;
  return x;
}
struct PT {
  long double x, y;
  PT() {}
  PT(long double x, long double y) : x(x), y(y) {}
  PT(const PT &p) : x(p.x), y(p.y) {}
  PT operator+(const PT &p) const { return PT(x + p.x, y + p.y); }
  PT operator-(const PT &p) const { return PT(x - p.x, y - p.y); }
  PT operator*(long double c) const { return PT(x * c, y * c); }
  PT operator/(long double c) const { return PT(x / c, y / c); }
};
long double dot(PT p, PT q) { return p.x * q.x + p.y * q.y; }
long double dist2(PT p, PT q) { return dot(p - q, p - q); }
long double cross(PT p, PT q) { return p.x * q.y - p.y * q.x; }
PT RotateCCW90(PT p) { return PT(-p.y, p.x); }
PT RotateCW90(PT p) { return PT(p.y, -p.x); }
PT RotateCCW(PT p, long double t) {
  return PT(p.x * cos(t) - p.y * sin(t), p.x * sin(t) + p.y * cos(t));
}
PT ProjectPointLine(PT a, PT b, PT c) {
  return a + (b - a) * dot(c - a, b - a) / dot(b - a, b - a);
}
PT ProjectPointSegment(PT a, PT b, PT c) {
  long double r = dot(b - a, b - a);
  if (fabs(r) < EPS) return a;
  r = dot(c - a, b - a) / r;
  if (r < 0) return a;
  if (r > 1) return b;
  return a + (b - a) * r;
}
long double DistancePointSegment(PT a, PT b, PT c) {
  return sqrt(dist2(c, ProjectPointSegment(a, b, c)));
}
long long int n, px, py;
long long int pointx[100010], pointy[100010];
int main() {
  srand(time(NULL));
  scanf("%lld", &n);
  ;
  scanf("%lld", &px);
  ;
  scanf("%lld", &py);
  ;
  long double ans = 0.0;
  long double maxDist = -1e18, minDist = 1e18;
  cout << fixed << setprecision(15);
  for (int i = 0; i < n; i++) {
    long long int x, y;
    scanf("%lld", &x);
    ;
    scanf("%lld", &y);
    ;
    pointx[i] = x;
    pointy[i] = y;
    long double ddd = dist2(PT((long double)px, (long double)py),
                            PT((long double)x, (long double)y));
    ddd = sqrt((long double)ddd);
    if (ddd > maxDist) maxDist = ddd;
    if (ddd < minDist) minDist = ddd;
  }
  for (int i = 0; i < n; i++) {
    long long int x1 = pointx[i];
    long long int y1 = pointy[i];
    long long int x2 = pointx[(i + 1) % n];
    long long int y2 = pointy[(i + 1) % n];
    long double ddd =
        DistancePointSegment(PT((long double)x1, (long double)y1),
                             PT((long double)x2, (long double)y2),
                             PT((long double)px, (long double)py));
    if (ddd > maxDist) maxDist = ddd;
    if (ddd < minDist) minDist = ddd;
  }
  ans = PI * (maxDist * maxDist - minDist * minDist);
  cout << ans;
  return 0;
}