#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);
    if (U[i] < 0) U[i] += 2 * pi;
    lf ang = asinl(r / sqrtl(a[i].len2()));
    L[i] = U[i] - ang;
    R[i] = U[i] + ang;
    if (L[i] < 0) {
      L[i] += 2 * pi;
      R[i] += 2 * pi;
    }
  }
  lf ansl = 1000, ansr = -1000;
  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;
    lf l, r;
    if (diff <= pi) {
      l = L[f];
      r = R[g];
    } else {
      l = L[g];
      r = R[f];
    }
    log("f=%d g=%d l=%.5Lf r=%.5Lf\n", f, g, l, r);
    if (r < l) {
      r += 2 * pi;
    }
    ansl = min(ansl, l);
    ansr = max(ansr, r);
  }
  log(">> ansl=%.10Lf ansr=%.10Lf\n", ansl, ansr);
  if (ansr - ansl >= 2 * pi) {
    log("all covered!!\n");
    printf("%.9lf\n", double(t));
    return 0;
  }
  lf len = ansr - ansl;
  lf cir = floor(t / (2 * pi));
  lf ans = len * 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;
  log(">> s=%.10Lf e=%.10Lf\n", s, e);
  log(">> %.10Lf\n", cover(ansl, ansr, s, e));
  log(">> %.10Lf\n", cover(ansl, ansr, s + 2 * pi, e + 2 * pi));
  ans += cover(ansl, ansr, s, e);
  ans += cover(ansl, ansr, s + 2 * pi, e + 2 * pi);
  cout << fixed << setprecision(12) << ans << endl;
  return 0;
}

answer.code:20:1: error: extended character   is not valid in an identifier
   20 |   ll x, y;
      | ^
answer.code:21:1: error: extended character   is not valid in an identifier
   21 |   pt(ll _x = 0, ll _y = 0) { x = _x, y = _y; }
      | ^
answer.code:22:1: error: extended character   is not valid in an identifier
   22 |   pt operator-(const pt &you) { return pt(x - you.x, y - you.y); }
      | ^
answer.code:23:1: error: extended character   is not valid in an identifier
   23 |   pt rotate() { return pt(-y, x); }
      | ^
answer.code:24:1: error: extended character   is not valid in an identifier
   24 |   ll dot(pt you) { return (ll)x * you.x + (ll)y * you.y; }
      | ^
answer.code:25:1: error: extended character   is not valid in an identifier
   25 |   ll len2() { return (ll)x * x + (ll)y * y; }
      | ^
answer.code:26:1: error: extended character   is not valid in an identifier
   26 |   double angle() { return atan2(y, x); }
      | ^
answer.code:27:1: error: extended character   is not valid in an identifier
   27 |   pt operator-() { return pt(-x, -y); }
      | ^
answer.code:31:1: error: extended character   is not valid in an identifier
   31 |   pt r = p - st, v = ed - st;
      | ^
answer.code:32:1: error: extended character   is not valid in an identifier
   32 |   return sqrtl(r.len2() - lf(r.dot(v)) * (r.dot(v)) / v.len2());
      | ^
answer.code:38:1: error: extended character   is not valid in an identifier
   38 |   if (l1 > l2) {
      | ^
answer.code:39:1: error: extended character   is not valid in an identifier
   39 |     return cover(l2, r2, l1, r1);
      | ^
answer.code:39:3: error: extended character   is not valid in an identifier
   39 |     return cover(l2, r2, l1, r1);
      |   ^
answer.code:40:1: error: extended character   is not valid in an identifier
   40 |   }
      | ^
answer.code:41:1: error: extended character   is not valid in an identifier
   41 |   return max(lf(0), min(r1, r2) - l2);
      | ^
answer.code:46:1: error: extended character   is not valid in an identifier
   46 |   freopen("M.in", "r", stdin);
      | ^
answer.code:48:1: error: extended character   is not valid in an identifier
   48 |   cin.tie(0)->sync_with_stdio(0);
      | ^
answer.code:49:1: error: extended character   is not valid in an identifier
   49 |   int n, x0, y0, r, _t;
      | ^
answer.code:50:1: error: extended character   is not valid in an identifier
   50 |   cin >> n >> x0 >> y0 >> r >> _t;
      | ^
answer.code:51:1: error: extended character   is not valid in an identifier
   51 |   lf t = _t;
      | ^
answer.code:52:1: error: extended character   is not valid in an identifier
   52 |   pt O(0, 0);
      | ^
answer.code:53:1: error: extended character   is not valid in an identifier
   53 |   for (int i = 1; i <= n; ++i) {
      | ^
answer.code:54:1: error: extended character   is not valid in an identifier
   54 |     cin >> a[i].x >> a[i].y;
      | ^
answer.code:54:3: error: extended character   is not valid in an identifier
   54 |     cin >> a[i].x >> a[i].y;
      |   ^
answer.code:55:1: error: extended character   is not valid in an identifier
   55 |     if (a[i].len2() <= (ll)r * r) {
      | ^
answer.code:55:3: error: extended character   is not valid in an identifier
   55 |     if (a[i].len2() <= (ll)r * r) {
      |   ^
answer.code:56:1: error: extended character   is not valid in an identifier
   56 |       log("touched!!\n");
      | ^
answer.code:56:3: error: extended character   is not valid in an identifier
   56 |       log("touched!!\n");
      |   ^
answer.code:56:5: error: extended character   is not valid in an identifier
   56 |       log("touched!!\n");
      |     ^
answer.code:57:1: error: extended character   is not valid in an identifier
   57 |       printf("%.9lf\n", double(t));
      | ^
answer.code:57:3: error: extended character   is not valid in an identifier
   57 |       printf("%.9lf\n", double(t));
      |   ^
answer.code:57:5: error: extended character   is not valid in an identifier
   57 |       printf("%.9lf\n", double(t));
      |     ^
answer.code:58:1: error: extended character   is not valid in an identifier
   58 |       return 0;
      | ^
answer.code:58:3: error: extended character   is not valid in an identifier
   58 |       return 0;
      |   ^
answer.code:58:5: error: extended character   is not valid in an identifier
   58 |       return 0;
      |     ^
answer.code:59:1: error: extended character   is not valid in an identifier
   59 |     }
      | ^
answer.code:59:3: error: extended character   is not valid in an identifier
   59 |     }
      |   ^
answer.code:60:1: error: extended character   is not valid in an identifier
   60 |   }
      | ^
answer.code:61:1: error: extended character   is not valid in an identifier
   61 |   // sort(a + 1, a + n + 1);
      | ^
answer.code:62:1: error: extended character   is not valid in an identifier
   62 |   for (int i = 1; i <= n; ++i) {
      | ^
answer.code:63:1: ...