Problem: Dima is living in a dormitory, as well as some cockroaches.

At the moment 0 Dima saw a cockroach running on a table and decided to kill it. Dima needs exactly T seconds for aiming, and after that he will precisely strike the cockroach and finish it.

To survive the cockroach has to run into a shadow, cast by round plates standing on the table, in T seconds. Shadow casted by any of the plates has the shape of a circle. Shadow circles may intersect, nest or overlap arbitrarily.

The cockroach uses the following strategy: first he equiprobably picks a direction to run towards and then runs towards it with the constant speed v. If at some moment t ≤ T it reaches any shadow circle, it immediately stops in the shadow and thus will stay alive. Otherwise the cockroach is killed by the Dima's precise strike. Consider that the Dima's precise strike is instant.

Determine the probability of that the cockroach will stay alive.

Input

In the first line of the input the four integers x0, y0, v, T (|x0|, |y0| ≤ 109, 0 ≤ v, T ≤ 109) are given — the cockroach initial position on the table in the Cartesian system at the moment 0, the cockroach's constant speed and the time in seconds Dima needs for aiming respectively.

In the next line the only number n (1 ≤ n ≤ 100 000) is given — the number of shadow circles casted by plates.

In the next n lines shadow circle description is given: the ith of them consists of three integers xi, yi, ri (|xi|, |yi| ≤ 109, 0 ≤ r ≤ 109) — the ith shadow circle on-table position in the Cartesian system and its radius respectively.

Consider that the table is big enough for the cockroach not to run to the table edges and avoid Dima's precise strike.

Output

Print the only real number p — the probability of that the cockroach will stay alive.

Your answer will be considered correct if its absolute or relative error does not exceed 10 - 4.

Examples

Input

0 0 1 1
3
1 1 1
-1 -1 1
-2 2 1


Output

0.50000000000

Input

0 0 1 0
1
1 0 1


Output

1.00000000000

Note

The picture for the first sample is given below. 

<image>

Red color stands for points which being chosen as the cockroach's running direction will cause him being killed, green color for those standing for survival directions. Please note that despite containing a circle centered in ( - 2, 2) a part of zone is colored red because the cockroach is not able to reach it in one second.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <class T>
inline T bigmod(T p, T e, T M) {
  long long ret = 1;
  for (; e > 0; e >>= 1) {
    if (e & 1) ret = (ret * p) % M;
    p = (p * p) % M;
  }
  return (T)ret;
}
template <class T>
inline T gcd(T a, T b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
template <class T>
inline T modinverse(T a, T M) {
  return bigmod(a, M - 2, M);
}
const double eps = 1e-6;
const double pi = acos(-1.0);
const double inf = 1e20;
const int maxp = 1111;
int dblcmp(double d) {
  if (fabs(d) < eps) return 0;
  return d > eps ? 1 : -1;
}
inline double sqr(double x) { return x * x; }
struct point {
  double x, y;
  point() {}
  point(double _x, double _y) {
    x = _x;
    y = _y;
  }
  void input() { scanf("%lf%lf", &x, &y); }
  void output() { printf("%.2f %.2f\n", x, y); }
  bool operator==(point a) const {
    return dblcmp(a.x - x) == 0 && dblcmp(a.y - y) == 0;
  }
  bool operator<(point a) const {
    return dblcmp(a.x - x) == 0 ? dblcmp(y - a.y) < 0 : x < a.x;
  }
  point operator-(point a) const { return point(x - a.x, y - a.y); }
  double len() { return hypot(x, y); }
  double len2() { return x * x + y * y; }
  double distance(point p) { return hypot(x - p.x, y - p.y); }
  point add(point p) { return point(x + p.x, y + p.y); }
  point sub(point p) { return point(x - p.x, y - p.y); }
  point mul(double b) { return point(x * b, y * b); }
  point div(double b) { return point(x / b, y / b); }
  double dot(point p) { return x * p.x + y * p.y; }
  double det(point p) { return x * p.y - y * p.x; }
  double rad(point a, point b) {
    point p = *this;
    return fabs(atan2(fabs(a.sub(p).det(b.sub(p))), a.sub(p).dot(b.sub(p))));
  }
  point trunc(double r) {
    double l = len();
    if (!dblcmp(l)) return *this;
    r /= l;
    return point(x * r, y * r);
  }
  point rotleft() { return point(-y, x); }
  point rotright() { return point(y, -x); }
  point rotate(point p, double angle) {
    point v = this->sub(p);
    double c = cos(angle), s = sin(angle);
    return point(p.x + v.x * c - v.y * s, p.y + v.x * s + v.y * c);
  }
};
struct line {
  point a, b;
  line() {}
  line(point _a, point _b) {
    a = _a;
    b = _b;
  }
  bool operator==(line v) { return (a == v.a) && (b == v.b); }
  line(point p, double angle) {
    a = p;
    if (dblcmp(angle - pi / 2) == 0) {
      b = a.add(point(0, 1));
    } else {
      b = a.add(point(1, tan(angle)));
    }
  }
  line(double _a, double _b, double _c) {
    if (dblcmp(_a) == 0) {
      a = point(0, -_c / _b);
      b = point(1, -_c / _b);
    } else if (dblcmp(_b) == 0) {
      a = point(-_c / _a, 0);
      b = point(-_c / _a, 1);
    } else {
      a = point(0, -_c / _b);
      b = point(1, (-_c - _a) / _b);
    }
  }
  void input() {
    a.input();
    b.input();
  }
  void adjust() {
    if (b < a) swap(a, b);
  }
  double length() { return a.distance(b); }
  double angle() {
    double k = atan2(b.y - a.y, b.x - a.x);
    if (dblcmp(k) < 0) k += pi;
    if (dblcmp(k - pi) == 0) k -= pi;
    return k;
  }
  int relation(point p) {
    int c = dblcmp(p.sub(a).det(b.sub(a)));
    if (c < 0) return 1;
    if (c > 0) return 2;
    return 3;
  }
  bool pointonseg(point p) {
    return dblcmp(p.sub(a).det(b.sub(a))) == 0 &&
           dblcmp(p.sub(a).dot(p.sub(b))) <= 0;
  }
  bool parallel(line v) { return dblcmp(b.sub(a).det(v.b.sub(v.a))) == 0; }
  int segcrossseg(line v) {
    int d1 = dblcmp(b.sub(a).det(v.a.sub(a)));
    int d2 = dblcmp(b.sub(a).det(v.b.sub(a)));
    int d3 = dblcmp(v.b.sub(v.a).det(a.sub(v.a)));
    int d4 = dblcmp(v.b.sub(v.a).det(b.sub(v.a)));
    if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 2;
    return (d1 == 0 && dblcmp(v.a.sub(a).dot(v.a.sub(b))) <= 0 ||
            d2 == 0 && dblcmp(v.b.sub(a).dot(v.b.sub(b))) <= 0 ||
            d3 == 0 && dblcmp(a.sub(v.a).dot(a.sub(v.b))) <= 0 ||
            d4 == 0 && dblcmp(b.sub(v.a).dot(b.sub(v.b))) <= 0);
  }
  int segcrossseg_inside(line v) {
    if (v.pointonseg(a) || v.pointonseg(b) || pointonseg(v.a) ||
        pointonseg(v.b))
      return 0;
    int d1 = dblcmp(b.sub(a).det(v.a.sub(a)));
    int d2 = dblcmp(b.sub(a).det(v.b.sub(a)));
    int d3 = dblcmp(v.b.sub(v.a).det(a.sub(v.a)));
    int d4 = dblcmp(v.b.sub(v.a).det(b.sub(v.a)));
    if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 1;
    return (d1 == 0 && dblcmp(v.a.sub(a).dot(v.a.sub(b))) <= 0 ||
            d2 == 0 && dblcmp(v.b.sub(a).dot(v.b.sub(b))) <= 0 ||
            d3 == 0 && dblcmp(a.sub(v.a).dot(a.sub(v.b))) <= 0 ||
            d4 == 0 && dblcmp(b.sub(v.a).dot(b.sub(v.b))) <= 0);
  }
  int linecrossseg(line v) {
    int d1 = dblcmp(b.sub(a).det(v.a.sub(a)));
    int d2 = dblcmp(b.sub(a).det(v.b.sub(a)));
    if ((d1 ^ d2) == -2) return 2;
    return (d1 == 0 || d2 == 0);
  }
  int linecrossline(line v) {
    if ((*this).parallel(v)) {
      return v.relation(a) == 3;
    }
    return 2;
  }
  point crosspoint(line v) {
    double a1 = v.b.sub(v.a).det(a.sub(v.a));
    double a2 = v.b.sub(v.a).det(b.sub(v.a));
    return point((a.x * a2 - b.x * a1) / (a2 - a1),
                 (a.y * a2 - b.y * a1) / (a2 - a1));
  }
  double dispointtoline(point p) {
    return fabs(p.sub(a).det(b.sub(a))) / length();
  }
  double dispointtoseg(point p) {
    if (dblcmp(p.sub(b).dot(a.sub(b))) < 0 ||
        dblcmp(p.sub(a).dot(b.sub(a))) < 0) {
      return min(p.distance(a), p.distance(b));
    }
    return dispointtoline(p);
  }
  point lineprog(point p) {
    return a.add(b.sub(a).mul(b.sub(a).dot(p.sub(a)) / b.sub(a).len2()));
  }
  point symmetrypoint(point p) {
    point q = lineprog(p);
    return point(2 * q.x - p.x, 2 * q.y - p.y);
  }
};
struct circle {
  point p;
  double r;
  circle() {}
  circle(point _p, double _r) : p(_p), r(_r){};
  circle(double x, double y, double _r) : p(point(x, y)), r(_r){};
  circle(point a, point b, point c) {
    p = line(a.add(b).div(2), a.add(b).div(2).add(b.sub(a).rotleft()))
            .crosspoint(
                line(c.add(b).div(2), c.add(b).div(2).add(b.sub(c).rotleft())));
    r = p.distance(a);
  }
  circle(point a, point b, point c, bool t) {
    line u, v;
    double m = atan2(b.y - a.y, b.x - a.x), n = atan2(c.y - a.y, c.x - a.x);
    u.a = a;
    u.b = u.a.add(point(cos((n + m) / 2), sin((n + m) / 2)));
    v.a = b;
    m = atan2(a.y - b.y, a.x - b.x), n = atan2(c.y - b.y, c.x - b.x);
    v.b = v.a.add(point(cos((n + m) / 2), sin((n + m) / 2)));
    p = u.crosspoint(v);
    r = line(a, b).dispointtoseg(p);
  }
  void input() {
    p.input();
    scanf("%lf", &r);
  }
  void output() { printf("%.2lf %.2lf %.2lf\n", p.x, p.y, r); }
  bool operator==(circle v) { return ((p == v.p) && dblcmp(r - v.r) == 0); }
  bool operator<(circle v) const {
    return ((p < v.p) || (p == v.p) && dblcmp(r - v.r) < 0);
  }
  double area() { return pi * sqr(r); }
  double circumference() { return 2 * pi * r; }
  int relation(point b) {
    double dst = b.distance(p);
    if (dblcmp(dst - r) < 0) return 2;
    if (dblcmp(dst - r) == 0) return 1;
    return 0;
  }
  int relationseg(line v) {
    double dst = v.dispointtoseg(p);
    if (dblcmp(dst - r) < 0) return 2;
    if (dblcmp(dst - r) == 0) return 1;
    return 0;
  }
  int relationline(line v) {
    double dst = v.dispointtoline(p);
    if (dblcmp(dst - r) < 0) return 2;
    if (dblcmp(dst - r) == 0) return 1;
    return 0;
  }
  int getcircle(point a, point b, double r, circle &c1, circle &c2) {
    circle x(a, r), y(b, r);
    int t = x.pointcrosscircle(y, c1.p, c2.p);
    if (!t) return 0;
    c1.r = c2.r = r;
    return t;
  }
  int getcircle(line u, point q, double r1, circle &c1, circle &c2) {
    double dis = u.dispointtoline(q);
    if (dblcmp(dis - r1 * 2) > 0) return 0;
    if (dblcmp(dis) == 0) {
      c1.p = q.add(u.b.sub(u.a).rotleft().trunc(r1));
      c2.p = q.add(u.b.sub(u.a).rotright().trunc(r1));
      c1.r = c2.r = r1;
      return 2;
    }
    line u1 = line(u.a.add(u.b.sub(u.a).rotleft().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotleft().trunc(r1)));
    line u2 = line(u.a.add(u.b.sub(u.a).rotright().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotright().trunc(r1)));
    circle cc = circle(q, r1);
    point p1, p2;
    if (!cc.pointcrossline(u1, p1, p2)) cc.pointcrossline(u2, p1, p2);
    c1 = circle(p1, r1);
    if (p1 == p2) {
      c2 = c1;
      return 1;
    }
    c2 = circle(p2, r1);
    return 2;
  }
  int getcircle(line u, line v, double r1, circle &c1, circle &c2, circle &c3,
                circle &c4) {
    if (u.parallel(v)) return 0;
    line u1 = line(u.a.add(u.b.sub(u.a).rotleft().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotleft().trunc(r1)));
    line u2 = line(u.a.add(u.b.sub(u.a).rotright().trunc(r1)),
                   u.b.add(u.b.sub(u.a).rotright().trunc(r1)));
    line v1 = line(v.a.add(v.b.sub(v.a).rotleft().trunc(r1)),
                   v.b.add(v.b.sub(v.a).rotleft().trunc(r1)));
    line v2 = line(v.a.add(v.b.sub(v.a).rotright().trunc(r1)),
                   v.b.add(v.b.sub(v.a).rotright().trunc(r1)));
    c1.r = c2.r = c3.r = c4.r = r1;
    c1.p = u1.crosspoint(v1);
    c2.p = u1.crosspoint(v2);
    c3.p = u2.crosspoint(v1);
    c4.p = u2.crosspoint(v2);
    return 4;
  }
  int getcircle(circle cx, circle cy, double r1, circle &c1, circle &c2) {
    circle x(cx.p, r1 + cx.r), y(cy.p, r1 + cy.r);
    int t = x.pointcrosscircle(y, c1.p, c2.p);
    if (!t) return 0;
    c1.r = c2.r = r1;
    return t;
  }
  int pointcrossline(line v, point &p1, point &p2) {
    if (!(*this).relationline(v)) return 0;
    point a = v.lineprog(p);
    double d = v.dispointtoline(p);
    d = sqrt(r * r - d * d);
    if (dblcmp(d) == 0) {
      p1 = a;
      p2 = a;
      return 1;
    }
    p1 = a.sub(v.b.sub(v.a).trunc(d));
    p2 = a.add(v.b.sub(v.a).trunc(d));
    return 2;
  }
  int relationcircle(circle v) {
    double d = p.distance(v.p);
    if (dblcmp(d - r - v.r) > 0) return 5;
    if (dblcmp(d - r - v.r) == 0) return 4;
    double l = fabs(r - v.r);
    if (dblcmp(d - r - v.r) < 0 && dblcmp(d - l) > 0) return 3;
    if (dblcmp(d - l) == 0) return 2;
    if (dblcmp(d - l) < 0) return 1;
  }
  int pointcrosscircle(circle v, point &p1, point &p2) {
    int rel = relationcircle(v);
    if (rel == 1 || rel == 5) return 0;
    double d = p.distance(v.p);
    double l = (d + (sqr(r) - sqr(v.r)) / d) / 2;
    double h = sqrt(sqr(r) - sqr(l));
    p1 = p.add(v.p.sub(p).trunc(l).add(v.p.sub(p).rotleft().trunc(h)));
    p2 = p.add(v.p.sub(p).trunc(l).add(v.p.sub(p).rotright().trunc(h)));
    if (rel == 2 || rel == 4) return 1;
    return 2;
  }
  int tangentline(point q, line &u, line &v) {
    int x = relation(q);
    if (x == 2) return 0;
    if (x == 1) {
      u = line(q, q.add(q.sub(p).rotleft()));
      v = u;
      return 1;
    }
    double d = p.distance(q);
    double l = sqr(r) / d;
    double h = sqrt(sqr(r) - sqr(l));
    u = line(q, p.add(q.sub(p).trunc(l).add(q.sub(p).rotleft().trunc(h))));
    v = line(q, p.add(q.sub(p).trunc(l).add(q.sub(p).rotright().trunc(h))));
    return 2;
  }
  double areacircle(circle v) {
    int rel = relationcircle(v);
    if (rel >= 4) return 0.0;
    if (rel <= 2) return min(area(), v.area());
    double d = p.distance(v.p);
    double hf = (r + v.r + d) / 2.0;
    double ss = 2 * sqrt(hf * (hf - r) * (hf - v.r) * (hf - d));
    double a1 = acos((r * r + d * d - v.r * v.r) / (2.0 * r * d));
    a1 = a1 * r * r;
    double a2 = acos((v.r * v.r + d * d - r * r) / (2.0 * v.r * d));
    a2 = a2 * v.r * v.r;
    return a1 + a2 - ss;
  }
  double areatriangle(point a, point b) {
    if (dblcmp(p.sub(a).det(p.sub(b)) == 0)) return 0.0;
    point q[5];
    int len = 0;
    q[len++] = a;
    line l(a, b);
    point p1, p2;
    if (pointcrossline(l, q[1], q[2]) == 2) {
      if (dblcmp(a.sub(q[1]).dot(b.sub(q[1]))) < 0) q[len++] = q[1];
      if (dblcmp(a.sub(q[2]).dot(b.sub(q[2]))) < 0) q[len++] = q[2];
    }
    q[len++] = b;
    if (len == 4 && (dblcmp(q[0].sub(q[1]).dot(q[2].sub(q[1]))) > 0))
      swap(q[1], q[2]);
    double res = 0;
    int i;
    for (i = 0; i < len - 1; i++) {
      if (relation(q[i]) == 0 || relation(q[i + 1]) == 0) {
        double arg = p.rad(q[i], q[i + 1]);
        res += r * r * arg / 2.0;
      } else
        res += fabs(q[i].sub(p).det(q[i + 1].sub(p)) / 2.0);
    }
    return res;
  }
};
double polarAngle(point p) {
  if (fabs(p.x) <= eps && fabs(p.y) <= eps) return -1.0;
  if (fabs(p.x) <= eps) return (p.y > eps ? 1.0 : 3.0) * acos(0);
  double theta = atan(1.0 * p.y / p.x);
  if (p.x > eps) return (p.y >= -eps ? theta : (4 * acos(0) + theta));
  return (2 * acos(0) + theta);
}
pair<double, double> pp[100001];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int X, Y;
  cin >> X >> Y;
  point P = point(X, Y);
  double V, T;
  cin >> V >> T;
  int n;
  cin >> n;
  int cnt = 0;
  circle C1, C2;
  point p1, p2;
  for (int i = (0); i < (n); ++i) {
    int x, y, v;
    cin >> x >> y >> v;
    long long sqDis = (long long)(x - X) * (long long)(x - X) +
                      (long long)(y - Y) * (long long)(y - Y);
    double dis = P.distance(point(x, y));
    if (sqDis <= (long long)v * (long long)v) {
      cout << "1.0" << endl;
      return 0;
    }
    double rad = sqrt(sqDis - (long long)v * (long long)v);
    rad = min(rad, V * T);
    if (rad + (double)v < dis - eps) continue;
    C1.p = P, C1.r = rad;
    C2.p = point(x, y), C2.r = v;
    C1.pointcrosscircle(C2, p1, p2);
    double ang1 = polarAngle(P - p1), ang2 = polarAngle(P - p2),
           ang3 = polarAngle(P - C2.p);
    if (ang1 > ang2) swap(ang1, ang2);
    if (ang1 < ang3 && ang3 < ang2)
      ;
    else
      swap(ang1, ang2);
    pp[cnt++] = make_pair(ang1, ang2);
  }
  if (cnt == 0) {
    cout << "0.0" << endl;
    return 0;
  }
  double sum = 0, hi = 0.0;
  sort(pp, pp + cnt);
  for (int i = (0); i < (cnt); ++i) {
    if (pp[i].first > pp[i].second + eps) {
      hi = max(hi, pp[i].second);
      pp[i].second = 2.0 * pi;
    }
  }
  sum += hi;
  for (int i = (0); i < (cnt); ++i) {
    if (pp[i].second < hi) continue;
    if (pp[i].first < hi) {
      sum += pp[i].second - hi;
    } else {
      sum += pp[i].second - pp[i].first;
    }
    hi = max(hi, pp[i].second);
  }
  cout << fixed << setprecision(10) << sum / (2.0 * pi) << endl;
}