#include <bits/stdc++.h>
#include <cmath>
#include <iomanip>
#define all(x) begin(x), end(x)
#define sz(x) ((int)(x).size())
#ifdef memset0
#define log(...) fprintf(stderr, __VA_ARGS__)
#else
#define endl '\n'
#define log(...) (void(0))
#endif
using namespace std;
using ll = long long;
using lf = long double;
using ull = unsigned long long;

const int N = 200011;
const lf pi = M_PI;
struct pt {
  ll x, y;
  pt(ll _x = 0, ll _y = 0) { x = _x, y = _y; }
  pt operator-(const pt &you) { return pt(x - you.x, y - you.y); }
  pt rotate() { return pt(-y, x); }
  ll dot(pt you) { return (ll)x * you.x + (ll)y * you.y; }
  ll len2() { return (ll)x * x + (ll)y * y; }
  double angle() { return atan2(y, x); }
  pt operator-() { return pt(-x, -y); }

} a[N];
lf dist(pt st, pt ed, pt p) {
  pt r = p - st, v = ed - st;
  return sqrtl(r.len2() - lf(r.dot(v)) * (r.dot(v)) / v.len2());
}

lf fx[N], U[N], L[N], R[N];

lf cover(lf l1, lf r1, lf l2, lf r2) {
  if (l1 > l2) {
    return cover(l2, r2, l1, r1);
  }
  return max(lf(0), min(r1, r2) - l2);
}

int main() {
#ifdef memset0
  freopen("M.in", "r", stdin);
#endif
  cin.tie(0)->sync_with_stdio(0);
  int n, x0, y0, r, _t;
  cin >> n >> x0 >> y0 >> r >> _t;
  lf t = _t;
  pt O(0, 0);
  for (int i = 1; i <= n; ++i) {
    cin >> a[i].x >> a[i].y;
    if (a[i].len2() <= (ll)r * r) {
      log("touched!!\n");
      printf("%.9lf\n", double(t));
      return 0;
    }
  }
  // sort(a + 1, a + n + 1);
  for (int i = 1; i <= n; ++i) {
    U[i] = atan2l(a[i].y, a[i].x);
    lf ang = asinl(r / sqrtl(a[i].len2()));
    if (ang < 0) {
      ang += 2 * pi;
    }
    L[i] = U[i] - ang;
    R[i] = U[i] + ang;
    while (L[i] < 0) {
      L[i] += 2 * pi;
      R[i] += 2 * pi;
      U[i] += 2 * pi;
    }
  }
  vector<pair<lf, lf>> tmp;
  vector<lf> val;
  for (int i = 1; i <= n; i++) {
    int f = i;
    int g = i % n + 1;
    lf diff = U[g] - U[f];
    if (diff < 0) diff += 2 * pi;
    if (diff >= 2 * pi) diff -= 2 * pi;
    lf l, r;
    if (diff <= pi) {
      l = L[f];
      r = R[g];
    } else {
      l = L[g];
      r = R[f];
    }
    if (r < l) {
      r += 2 * pi;
    }
    if (l >= 2 * pi) {
      l -= 2 * pi;
      r -= 2 * pi;
    }
    log("f=%d g=%d l=%.5Lf r=%.5Lf\n", f, g, l, r);
    auto push = [&](lf l, lf r) {
      assert(l <= r);
      tmp.emplace_back(l, r);
      val.emplace_back(l);
      val.emplace_back(r);
    };
    if (r <= 2 * pi) {
      push(l, r);
    } else {
      push(l, 2 * pi);
      push(0, r - 2 * pi);
    }
  }
  sort(all(val));
  val.erase(unique(all(val)), val.end());
  vector<int> cnt(sz(val));
  for (auto [lx, rx] : tmp) {
    int l = lower_bound(all(val), lx) - val.begin();
    int r = lower_bound(all(val), rx) - val.begin();
    for (int k = l; k < r; k++) {
      cnt[k] = 1;
    }
  }
  lf tot = 0;
  for (int i = 0; i + 1 < sz(val); i++)
    if (cnt[i]) {
      tot += val[i + 1] - val[i];
    }
  if (tot >= 2 * pi) {
    cerr << "all covered!!" << endl;
    printf("%.9lf\n", double(t));
    return 0;
  }
  lf cir = floor(t / (2 * pi));
  lf ans = tot * cir;
  lf s = atan2l(y0, x0);
  if (s < 0) {
    s += 2 * pi;
  }
  lf e = s + (t - 2 * pi * cir);
  cerr << "cir: " << fixed << setprecision(12) << cir << endl;
  for (int i = 0; i + 1 < sz(val); i++)
    if (cnt[i]) {
      ans += cover(val[i], val[i + 1], s - 2 * pi, e - 2 * pi);
      ans += cover(val[i], val[i + 1], s, e);
      ans += cover(val[i], val[i + 1], s + 2 * pi, e + 2 * pi);
    }
  cout << fixed << setprecision(12) << ans << endl;
  return 0;
}