Problem: Qwerty the Ranger arrived to the Diatar system with a very important task. He should deliver a special carcinogen for scientific research to planet Persephone. This is urgent, so Qwerty has to get to the planet as soon as possible. A lost day may fail negotiations as nobody is going to pay for an overdue carcinogen.

You can consider Qwerty's ship, the planet Persephone and the star Diatar points on a plane. Diatar is located in the origin of coordinate axes — at point (0, 0). Persephone goes round Diatar along a circular orbit with radius R in the counter-clockwise direction at constant linear speed vp (thus, for instance, a full circle around the star takes <image> of time). At the initial moment of time Persephone is located at point (xp, yp).

At the initial moment of time Qwerty's ship is at point (x, y). Qwerty can move in any direction at speed of at most v (v > vp). The star Diatar is hot (as all stars), so Qwerty can't get too close to it. The ship's metal sheathing melts at distance r (r < R) from the star.

Find the minimum time Qwerty needs to get the carcinogen to planet Persephone.

Input

The first line contains space-separated integers xp, yp and vp ( - 104 ≤ xp, yp ≤ 104, 1 ≤ vp < 104) — Persephone's initial position and the speed at which it goes round Diatar.

The second line contains space-separated integers x, y, v and r ( - 104 ≤ x, y ≤ 104, 1 < v ≤ 104, 1 ≤ r ≤ 104) — The intial position of Qwerty's ship, its maximum speed and the minimum safe distance to star Diatar.

It is guaranteed that r2 < x2 + y2, r2 < xp2 + yp2 and vp < v.

Output

Print a single real number — the minimum possible delivery time. The answer will be considered valid if its absolute or relative error does not exceed 10 - 6.

Examples

Input

10 0 1
-10 0 2 8


Output

9.584544103

Input

50 60 10
50 60 20 40


Output

0.000000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#pragma comment(linker, "/STACK:36777216")
template <class T>
inline void RD(T &);
template <class T>
inline void OT(const T &);
inline int RD() {
  int x;
  RD(x);
  return x;
}
template <class T>
inline T &_RD(T &x) {
  RD(x);
  return x;
}
inline void RC(char &c) { scanf(" %c", &c); }
inline void RS(char *s) { scanf("%s", s); }
template <class T0, class T1>
inline void RD(T0 &x0, T1 &x1) {
  RD(x0), RD(x1);
}
template <class T0, class T1, class T2>
inline void RD(T0 &x0, T1 &x1, T2 &x2) {
  RD(x0), RD(x1), RD(x2);
}
template <class T0, class T1, class T2, class T3>
inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3) {
  RD(x0), RD(x1), RD(x2), RD(x3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6);
}
template <class T0, class T1>
inline void OT(T0 &x0, T1 &x1) {
  OT(x0), OT(x1);
}
template <class T0, class T1, class T2>
inline void OT(T0 &x0, T1 &x1, T2 &x2) {
  OT(x0), OT(x1), OT(x2);
}
template <class T0, class T1, class T2, class T3>
inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3) {
  OT(x0), OT(x1), OT(x2), OT(x3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void OT(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);
}
template <class T>
inline void RST(T &A) {
  memset(A, 0, sizeof(A));
}
template <class T0, class T1>
inline void RST(T0 &A0, T1 &A1) {
  RST(A0), RST(A1);
}
template <class T0, class T1, class T2>
inline void RST(T0 &A0, T1 &A1, T2 &A2) {
  RST(A0), RST(A1), RST(A2);
}
template <class T0, class T1, class T2, class T3>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  RST(A0), RST(A1), RST(A2), RST(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);
}
template <class T>
inline void CLR(priority_queue<T, vector<T>, less<T> > &Q) {
  while (!Q.empty()) Q.pop();
}
template <class T>
inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q) {
  while (!Q.empty()) Q.pop();
}
template <class T>
inline void CLR(T &A) {
  A.clear();
}
template <class T0, class T1>
inline void CLR(T0 &A0, T1 &A1) {
  CLR(A0), CLR(A1);
}
template <class T0, class T1, class T2>
inline void CLR(T0 &A0, T1 &A1, T2 &A2) {
  CLR(A0), CLR(A1), CLR(A2);
}
template <class T0, class T1, class T2, class T3>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);
}
template <class T>
inline void CLR(T &A, int n) {
  for (int i = 0; i < int(n); ++i) CLR(A[i]);
}
template <class T>
inline void FLC(T &A, int x) {
  memset(A, x, sizeof(A));
}
template <class T0, class T1>
inline void FLC(T0 &A0, T1 &A1, int x) {
  FLC(A0, x), FLC(A1, x);
}
template <class T0, class T1, class T2>
inline void FLC(T0 &A0, T1 &A1, T2 &A2) {
  FLC(A0), FLC(A1), FLC(A2);
}
template <class T0, class T1, class T2, class T3>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  FLC(A0), FLC(A1), FLC(A2), FLC(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  FLC(A0), FLC(A1), FLC(A2), FLC(A3), FLC(A4), FLC(A5), FLC(A6);
}
template <class T>
inline void SRT(T &A) {
  sort(A.begin(), A.end());
}
template <class T, class C>
inline void SRT(T &A, C B) {
  sort(A.begin(), A.end(), B);
}
const int MOD = 1000000007;
const int INF = 10009;
const double EPS = 1e-2;
const double OO = 1e15;
const double PI = 3.14159265358979323846264;
template <class T>
inline void checkMin(T &a, const T b) {
  if (b < a) a = b;
}
template <class T>
inline void checkMax(T &a, const T b) {
  if (b > a) a = b;
}
template <class T, class C>
inline void checkMin(T &a, const T b, C c) {
  if (c(b, a)) a = b;
}
template <class T, class C>
inline void checkMax(T &a, const T b, C c) {
  if (c(a, b)) a = b;
}
template <class T>
inline T min(T a, T b, T c) {
  return min(min(a, b), c);
}
template <class T>
inline T max(T a, T b, T c) {
  return max(max(a, b), c);
}
template <class T>
inline T min(T a, T b, T c, T d) {
  return min(min(a, b), min(c, d));
}
template <class T>
inline T max(T a, T b, T c, T d) {
  return max(min(a, b), max(c, d));
}
template <class T>
inline T sqr(T a) {
  return a * a;
}
template <class T>
inline T cub(T a) {
  return a * a * a;
}
int Ceil(int x, int y) { return (x - 1) / y + 1; }
inline bool _1(int x, int i) { return x & 1 << i; }
inline bool _1(long long x, int i) { return x & 1LL << i; }
inline long long _1(int i) { return 1LL << i; }
inline long long _U(int i) { return _1(i) - 1; };
inline int count_bits(int x) {
  x = (x & 0x55555555) + ((x & 0xaaaaaaaa) >> 1);
  x = (x & 0x33333333) + ((x & 0xcccccccc) >> 2);
  x = (x & 0x0f0f0f0f) + ((x & 0xf0f0f0f0) >> 4);
  x = (x & 0x00ff00ff) + ((x & 0xff00ff00) >> 8);
  x = (x & 0x0000ffff) + ((x & 0xffff0000) >> 16);
  return x;
}
inline int count_bits(long long x) {
  x = (x & 0x5555555555555555LL) + ((x & 0xaaaaaaaaaaaaaaaaLL) >> 1);
  x = (x & 0x3333333333333333LL) + ((x & 0xccccccccccccccccLL) >> 2);
  x = (x & 0x0f0f0f0f0f0f0f0fLL) + ((x & 0xf0f0f0f0f0f0f0f0LL) >> 4);
  x = (x & 0x00ff00ff00ff00ffLL) + ((x & 0xff00ff00ff00ff00LL) >> 8);
  x = (x & 0x0000ffff0000ffffLL) + ((x & 0xffff0000ffff0000LL) >> 16);
  x = (x & 0x00000000ffffffffLL) + ((x & 0xffffffff00000000LL) >> 32);
  return x;
}
int reverse_bits(int x) {
  x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
  x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
  x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
  x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
  x = ((x >> 16) & 0x0000ffff) | ((x << 16) & 0xffff0000);
  return x;
}
inline void INC(int &a, int b) {
  a += b;
  if (a >= MOD) a -= MOD;
}
inline int sum(int a, int b) {
  a += b;
  if (a >= MOD) a -= MOD;
  return a;
}
inline void DEC(int &a, int b) {
  a -= b;
  if (a < 0) a += MOD;
}
inline int dff(int a, int b) {
  a -= b;
  if (a < 0) a += MOD;
  return a;
}
inline void MUL(int &a, int b) { a = (long long)a * b % MOD; }
inline int pdt(int a, int b) { return (long long)a * b % MOD; }
inline int pow(int a, int b) {
  int c = 1;
  while (b) {
    if (b & 1) MUL(c, a);
    MUL(a, a), b >>= 1;
  }
  return c;
}
template <class T>
inline int pow(T a, int b) {
  T c(1);
  while (b) {
    if (b & 1) MUL(c, a);
    MUL(a, a), b >>= 1;
  }
  return c;
}
inline int _I(int b) {
  int a = MOD, x1 = 0, x2 = 1, q;
  while (true) {
    q = a / b, a %= b;
    if (!a) return (x2 + MOD) % MOD;
    DEC(x1, pdt(q, x2));
    q = b / a, b %= a;
    if (!b) return (x1 + MOD) % MOD;
    DEC(x2, pdt(q, x1));
  }
}
inline void DIV(int &a, int b) { MUL(a, _I(b)); }
inline int qtt(int a, int b) { return pdt(a, _I(b)); }
inline int sum(int a, int b, int MOD) {
  a += b;
  if (a >= MOD) a -= MOD;
  return a;
}
inline int phi(int n) {
  int res = n;
  for (int i = 2; sqr(i) <= n; ++i)
    if (!(n % i)) {
      DEC(res, qtt(res, i));
      do {
        n /= i;
      } while (!(n % i));
    }
  if (n != 1) DEC(res, qtt(res, n));
  return res;
}
struct Po;
struct Line;
struct Seg;
inline int sgn(double x) { return x < -EPS ? -1 : x > EPS; }
inline int sgn(double x, double y) { return sgn(x - y); }
struct Po {
  double x, y;
  Po(double _x = 0, double _y = 0) : x(_x), y(_y) {}
  friend istream &operator>>(istream &in, Po &p) { return in >> p.x >> p.y; }
  friend ostream &operator<<(ostream &out, Po p) {
    return out << "(" << p.x << ", " << p.y << ")";
  }
  friend bool operator==(Po, Po);
  friend bool operator!=(Po, Po);
  friend Po operator+(Po, Po);
  friend Po operator-(Po, Po);
  friend Po operator*(Po, double);
  friend Po operator/(Po, double);
  bool operator<(const Po &rhs) const {
    return sgn(x, rhs.x) < 0 || sgn(x, rhs.x) == 0 && sgn(y, rhs.y) < 0;
  }
  Po operator-() const { return Po(-x, -y); }
  Po &operator+=(Po rhs) {
    x += rhs.x, y += rhs.y;
    return *this;
  }
  Po &operator-=(Po rhs) {
    x -= rhs.x, y -= rhs.y;
    return *this;
  }
  Po &operator*=(double k) {
    x *= k, y *= k;
    return *this;
  }
  Po &operator/=(double k) {
    x /= k, y /= k;
    return *this;
  }
  double length_sqr() { return sqr(x) + sqr(y); }
  double length() { return sqrt(length_sqr()); }
  double atan() { return atan2(y, x); }
  void input() { scanf("%lf %lf", &x, &y); }
};
bool operator==(Po a, Po b) {
  return sgn(a.x - b.x) == 0 && sgn(a.y - b.y) == 0;
}
bool operator!=(Po a, Po b) {
  return sgn(a.x - b.x) != 0 || sgn(a.y - b.y) != 0;
}
Po operator+(Po a, Po b) { return Po(a.x + b.x, a.y + b.y); }
Po operator-(Po a, Po b) { return Po(a.x - b.x, a.y - b.y); }
Po operator*(Po a, double k) { return Po(a.x * k, a.y * k); }
Po operator*(double k, Po a) { return a * k; }
Po operator/(Po a, double k) { return Po(a.x / k, a.y / k); }
struct Line {
  Po a, b;
  Line(Po _a = Po(), Po _b = Po()) : a(_a), b(_b) {}
  Line(double x0, double y0, double x1, double y1)
      : a(Po(x0, y0)), b(Po(x1, y1)) {}
  Line(Seg);
  friend ostream &operator<<(ostream &out, Line p) {
    return out << p.a << "-" << p.b;
  }
};
struct Seg {
  Po a, b;
  Seg(Po _a = Po(), Po _b = Po()) : a(_a), b(_b) {}
  Seg(double x0, double y0, double x1, double y1)
      : a(Po(x0, y0)), b(Po(x1, y1)) {}
  Seg(Line l);
  friend ostream &operator<<(ostream &out, Seg p) {
    return out << p.a << "-" << p.b;
  }
  double length() { return (b - a).length(); }
};
Line::Line(Seg l) : a(l.a), b(l.b) {}
Seg::Seg(Line l) : a(l.a), b(l.b) {}
inline double dot(double x1, double y1, double x2, double y2) {
  return x1 * x2 + y1 * y2;
}
inline double dot(Po a, Po b) { return dot(a.x, a.y, b.x, b.y); }
inline double dot(Po p0, Po p1, Po p2) { return dot(p1 - p0, p2 - p0); }
inline double dot(Line l1, Line l2) { return dot(l1.b - l1.a, l2.b - l2.a); }
inline double det(double x1, double y1, double x2, double y2) {
  return x1 * y2 - x2 * y1;
}
inline double det(Po a, Po b) { return det(a.x, a.y, b.x, b.y); }
inline double det(Po p0, Po p1, Po p2) { return det(p1 - p0, p2 - p0); }
inline double det(Line l1, Line l2) { return det(l1.b - l1.a, l2.b - l2.a); }
template <class T1, class T2>
inline double dist(T1 x, T2 y) {
  return sqrt(dist_sqr(x, y));
}
inline double dist_sqr(Po a, Po b) { return sqr(a.x - b.x) + sqr(a.y - b.y); }
inline double dist_sqr(Po p, Line l) {
  Po v0 = l.b - l.a, v1 = p - l.a;
  return sqr(fabs(det(v0, v1))) / v0.length_sqr();
}
inline double dist_sqr(Po p, Seg l) {
  Po v0 = l.b - l.a, v1 = p - l.a, v2 = p - l.b;
  if (sgn(dot(v0, v1)) * sgn(dot(v0, v2)) <= 0)
    return dist_sqr(p, Line(l));
  else
    return min(v1.length_sqr(), v2.length_sqr());
}
inline double dist_sqr(Line l, Po p) { return dist_sqr(p, l); }
inline double dist_sqr(Seg l, Po p) { return dist_sqr(p, l); }
inline double dist_sqr(Line l1, Line l2) {
  if (sgn(det(l1, l2)) != 0) return 0;
  return dist_sqr(l1.a, l2);
}
inline double dist_sqr(Line l1, Seg l2) {
  Po v0 = l1.b - l1.a, v1 = l2.a - l1.a, v2 = l2.b - l1.a;
  double c1 = det(v0, v1), c2 = det(v0, v2);
  return sgn(c1) != sgn(c2) ? 0
                            : sqr(min(fabs(c1), fabs(c2))) / v0.length_sqr();
}
bool isIntersect(Seg l1, Seg l2) {
  return min(l1.a.x, l1.b.x) <= max(l2.a.x, l2.b.x) &&
         min(l2.a.x, l2.b.x) <= max(l1.a.x, l1.b.x) &&
         min(l1.a.y, l1.b.y) <= max(l2.a.y, l2.b.y) &&
         min(l2.a.y, l2.b.y) <= max(l1.a.y, l1.b.y) &&
         sgn(det(l1.a, l2.a, l2.b)) * sgn(det(l1.b, l2.a, l2.b)) <= 0 &&
         sgn(det(l2.a, l1.a, l1.b)) * sgn(det(l2.b, l1.a, l1.b)) <= 0;
}
inline double dist_sqr(Seg l1, Seg l2) {
  if (isIntersect(l1, l2))
    return 0;
  else
    return min(dist_sqr(l1.a, l2), dist_sqr(l1.b, l2), dist_sqr(l2.a, l1),
               dist_sqr(l2.b, l1));
}
inline bool isOnExtremePoint(const Po &p, const Seg &l) {
  return p == l.a || p == l.b;
}
inline bool isOnseg(const Po &p, const Seg &l) {
  return sgn(det(p, l.a, l.b)) == 0 && sgn(l.a.x, p.x) * sgn(l.b.x, p.x) <= 0 &&
         sgn(l.a.y, p.y) * sgn(l.b.y, p.y) <= 0;
}
inline Po intersect(const Line &l1, const Line &l2) {
  return l1.a + (l1.b - l1.a) * (det(l2.a, l1.a, l2.b) / det(l2, l1));
}
inline Po intersect(const Po &p, const Line &l) {
  return intersect(Line(p, p + Po(l.a.y - l.b.y, l.b.x - l.a.x)), l);
}
inline Po rotate(Po p, double alpha, Po o = Po()) {
  p.x -= o.x, p.y -= o.y;
  return Po(p.x * cos(alpha) - p.y * sin(alpha),
            p.y * cos(alpha) + p.x * sin(alpha)) +
         o;
}
inline int rand32() {
  return (bool(rand() & 1) << 30) | (rand() << 15) + rand();
}
inline int random32(int l, int r) { return rand32() % (r - l + 1) + l; }
inline int random(int l, int r) { return rand() % (r - l + 1) + l; }
int dice() { return rand() % 6; }
bool coin() { return rand() % 2; }
template <class T>
inline void RD(T &x) {
  cin >> x;
}
template <class T>
inline void OT(const T &x) {
  printf("%.10lf\n", x);
}
const int N = 100009;
Po s, p, o;
double R_, R, r, ss, vs, vp;
double alpha, beta, theta, delta;
inline void _R(double &x) {
  x = fmod(x, 2 * PI);
  if (x < 0) x += 2 * PI;
}
double d() {
  if (theta <= beta || theta >= 2 * PI - beta)
    return sqrt(sqr(R_) + sqr(R) - 2 * R_ * R * cos(theta));
  else {
    delta = PI - beta - fabs(PI - theta);
    return ss + delta * r;
  }
}
bool f(double x) {
  theta = x * vp + alpha, _R(theta);
  return d() <= vs * x;
}
int main() {
  p.input(), RD(vp), s.input(), RD(vs, r);
  R_ = s.length(), R = p.length(), vp /= R;
  ss = sqrt(sqr(R_) - sqr(r)) + sqrt(sqr(R) - sqr(r));
  alpha = p.atan() - s.atan(), _R(alpha);
  beta = acos(r / R_) + acos(r / R), _R(beta);
  double ll = 0, rr = (ss + PI * R) * vs;
  for (int i = 0; i < int(100); ++i) {
    double m = (ll + rr) / 2;
    if (f(m))
      rr = m;
    else
      ll = m;
  }
  OT(ll);
}