Problem:
Runaway Domino
``Domino effect'' is a famous play using dominoes.
A player sets up a chain of dominoes stood.
After a chain is formed, the player topples one end of the dominoes.
The first domino topples the second domino, the second topples the third and so on.
You are playing domino effect.
Before you finish to set up a chain of domino,
a domino block started to topple, unfortunately.
You have to stop the toppling as soon as possible.
The domino chain forms a polygonal line on a two-dimensional coordinate system without self intersections.
The toppling starts from a certain point on the domino chain
and continues toward the both end of the chain.
If the toppling starts on an end of the chain, the toppling continue toward the other end.
The toppling of a direction stops when you touch the toppling point or the toppling reaches an end of the domino chain.
You can assume that:
You are a point without volume on the two-dimensional coordinate system.
The toppling stops soon after touching the toppling point.
You can step over the domino chain without toppling it.
You will given the form of the domino chain, the starting point of the toppling,
your coordinates when the toppling started, the toppling velocity and the your velocity.
You are task is to write a program that calculates your optimal move to stop the toppling at the earliest timing and
calculates the minimum time to stop the toppling.
Input
The first line contains one integer
N
,
which denotes the number of vertices in the polygonal line of the domino chain
(2 \leq N \leq 1000)
.
Then
N
lines follow, each consists of two integers
x_{i}
and
y_{i}
,
which denote the coordinates of the
i
-th vertex
(-10,000 \leq x, y \leq 10000)
.
The next line consists of three integers
x_{t}
,
y_{t}
and
v_{t}
,
which denote the coordinates of the starting point and the velocity of the toppling.
The last line consists of three integers
x_{p}
,
y_{p}
and
v_{p}
,
which denotes the coordinates of you when the toppling started and the velocity
(1 \leq v_{t} \lt v_{p} \leq 10)
.
You may assume that the starting point of the toppling lies on the polygonal line.
Output
Print the minimum time to stop the toppling.
The output must have a relative or absolute error less than
10^{-6}
.
Sample Input 1
2
0 0
15 0
5 0 1
10 10 2
Output for the Sample Input 1
5.0
Sample Input 2
3
-10 0
0 0
0 10
-1 0 1
3 0 2
Output for the Sample Input 2
4.072027
Sample Input 3
2
0 0
10 0
5 0 1
9 0 3
Output for the Sample Input 3
2.0

Submitted solutions:

code_snippet: #include<stdio.h>
#include <iostream>
#include <math.h>
#include <numeric>
#include <vector>
#include <map>
#include <functional>
#include <stdio.h>
#include <array>
#include <algorithm>
#include <string>
#include <string.h>
#include <assert.h>
#include <stdio.h>
#include <queue>
#include<iomanip>
#include<bitset>
#include<stack>
#include<set>
#include<limits>
#include <complex>
using namespace std;



#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()




/* 幾何の基本 */

#include <complex>

typedef long double ld;
typedef complex<ld> Point;

const ld eps = 1e-9, pi = acos(-1.0);

namespace std {
	bool operator<(const Point &lhs, const Point &rhs) {
		if (lhs.real() < rhs.real() - eps) return true;
		if (lhs.real() > rhs.real() + eps) return false;
		return lhs.imag() < rhs.imag();
	}
}

// 点の入力
Point input_point() {
	ld x, y;
	cin >> x >> y;
	return Point(x, y);
}

// 誤差つき等号判定
bool eq(ld a, ld b) {
	return (abs(a - b) < eps);
}

// 内積
ld dot(Point a, Point b) {
	return real(conj(a) * b);
}

// 外積
ld cross(Point a, Point b) {
	return imag(conj(a) * b);
}

// 直線の定義
class Line {
public:
	Point a, b;
	Line() : a(Point(0, 0)), b(Point(0, 0)) {}
	Line(Point a, Point b) : a(a), b(b) {}
};

// 円の定義
class Circle {
public:
	Point p;
	ld r;
	Circle() : p(Point(0, 0)), r(0) {}
	Circle(Point p, ld r) : p(p), r(r) {}
};

// CCW
int ccw(Point a, Point b, Point c) {
	b -= a; c -= a;
	if (cross(b, c) > eps) return 1;   // a,b,cが反時計周りの順に並ぶ
	if (cross(b, c) < -eps) return -1; // a,b,cが時計周りの順に並ぶ
	if (dot(b, c) < 0) return 2;       // c,a,bの順に直線に並ぶ
	if (norm(b) < norm(c)) return -2;  // a,b,cの順に直線に並ぶ
	return 0;                          // a,c,bの順に直線に並ぶ
}


/* 交差判定 */

// 直線と直線の交差判定
bool isis_ll(Line l, Line m) {
	return !eq(cross(l.b - l.a, m.b - m.a), 0);
}

// 直線と線分の交差判定
bool isis_ls(Line l, Line s) {
	return isis_ll(l, s) &&
		(cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

// 線分と線分の交差判定
bool isis_ss(Line s, Line t) {
	return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
		ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

// 点の直線上判定
bool isis_lp(Line l, Point p) {
	return (abs(cross(l.b - p, l.a - p)) < eps);
}

// 点の線分上判定
bool isis_sp(Line s, Point p) {
	return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

// 垂線の足
Point proj(Line l, Point p) {
	ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
	return l.a + t * (l.a - l.b);
}

// 直線と直線の交点
Point is_ll(Line s, Line t) {
	Point sv = s.b - s.a, tv = t.b - t.a;
	assert(cross(sv, tv) != 0);
	return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

// 直線と点の距離
ld dist_lp(Line l, Point p) {
	return abs(p - proj(l, p));
}

// 直線と直線の距離
ld dist_ll(Line l, Line m) {
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

// 直線と線分の距離
ld dist_ls(Line l, Line s) {
	return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// 線分と点の距離
ld dist_sp(Line s, Point p) {
	Point r = proj(s, p);
	return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// 線分と線分の距離
ld dist_ss(Line s, Line t) {
	if (isis_ss(s, t)) return 0;
	return min({ dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b) });
}


/* 円 */

// 円と円の交点
vector<Point> is_cc(Circle c1, Circle c2) {
	vector<Point> res;
	ld d = abs(c1.p - c2.p);
	ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
	ld dfr = c1.r * c1.r - rc * rc;
	if (abs(dfr) < eps) dfr = 0.0;
	else if (dfr < 0.0) return res; // no intersection
	ld rs = sqrt(dfr);
	Point diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * Point(rc, rs));
	if (dfr != 0.0) res.push_back(c1.p + diff * Point(rc, -rs));
	return res;
}

// 円と直線の交点
vector<Point> is_lc(Circle c, Line l) {
	vector<Point> res;
	ld d = dist_lp(l, c.p);
	if (d < c.r + eps) {
		ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
		Point nor = (l.a - l.b) / abs(l.a - l.b);
		res.push_back(proj(l, c.p) + len * nor);
		res.push_back(proj(l, c.p) - len * nor);
	}
	return res;
}

// 円と線分の距離
vector<Point> is_sc(Circle c, Line l) {
	vector<Point> v = is_lc(c, l), res;
	for (Point p : v)
		if (isis_sp(l, p)) res.push_back(p);
	return res;
}

// 円と点の接線
vector<Line> tangent_cp(Circle c, Point p) {
	vector<Line> ret;
	Point v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (isnan(l)) { return ret; }
	Point v1 = v * Point(l / d, c.r / d);
	Point v2 = v * Point(l / d, -c.r / d);
	ret.push_back(Line(p, p + v1));
	if (l < eps) return ret;
	ret.push_back(Line(p, p + v2));
	return ret;
}

// 円と円の接線
vector<Line> tangent_cc(Circle c1, Circle c2) {
	vector<Line> ret;
	if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
		Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
		ret = tangent_cp(c1, center);
	}
	if (abs(c1.r - c2.r) > eps) {
		Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
		vector<Line> nret = tangent_cp(c1, out);
		ret.insert(ret.end(), ALL(nret));
	}
	else {
		Point v = c2.p - c1.p;
		v /= abs(v);
		Point q1 = c1.p + v * Point(0, 1) * c1.r;
		Point q2 = c1.p + v * Point(0, -1) * c1.r;
		ret.push_back(Line(q1, q1 + v));
		ret.push_back(Line(q2, q2 + v));
	}
	return ret;
}


/* 多角形 */

typedef vector<Point> Polygon;

// 面積
ld area(const Polygon &p) {
	ld res = 0;
	int n = p.size();
	REP(j, n) res += cross(p[j], p[(j + 1) % n]);
	return res / 2;
}

// 多角形の回転方向
bool is_counter_clockwise(const Polygon &poly) {
	ld angle = 0;
	int n = poly.size();
	REP(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
		angle += arg((c - b) / (b - a));
	}
	return angle > eps;
}

// 円の内外判定
// -1 => out
//  0 => on
//  1 => in
int is_in_polygon(const Polygon &poly, Point p) {
	ld angle = 0;
	int n = poly.size();
	REP(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n];
		if (isis_sp(Line(a, b), p)) return 1;
		angle += arg((b - p) / (a - p));
	}
	return eq(angle, 0) ? 0 : 2;
}

// 凸包
Polygon convex_hull(vector<Point> ps) {
	int n = ps.size();
	int k = 0;
	sort(ps.begin(), ps.end());
	Polygon ch(2 * n);
	for (int i = 0; i < n; ch[k++] = ps[i++])
		while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
		while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	ch.resize(k - 1);
	return ch;
}

// 凸カット
Polygon convex_cut(const Polygon &ps, Line l) {
	int n = ps.size();
	Polygon Q;
	REP(i, n) {
		Point A = ps[i], B = ps[(i + 1) % n];
		Line m = Line(A, B);
		if (ccw(l.a, l.b, A) != -1) Q.push_back(A);
		if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m))
			Q.push_back(is_ll(l, m));
	}
	return Q;
}


/* アレンジメント */
void add_point(vector<Point> &ps, Point p) {
	for (Point q : ps) if (abs(q - p) < eps) return;
	ps.push_back(p);
}

typedef int Weight;

struct Edge { int from, to; Weight weight; };

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

void add_edge(Graph &g, int from, int to, Weight weight) {
	g[from].push_back(Edge{ from, to, weight });
}

Graph segment_arrangement(const vector<Line> &s, const vector<Point> &p) {
	int n = p.size(), m = s.size();
	Graph g(n);
	REP(i, m) {
		vector<pair<ld, int>> vec;
		REP(j, n) if (isis_sp(s[i], p[j]))
			vec.emplace_back(abs(s[i].a - p[j]), j);
		sort(ALL(vec));
		REP(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			add_edge(g, from, to, abs(p[from] - p[to]));
		}
	}
	return g;
}

Graph circle_arrangement(const vector<Circle> &c, const vector<Point> &p) {
	int n = p.size(), m = c.size();
	Graph g(n);
	REP(i, m) {
		vector<pair<ld, int>> vec;
		REP(j, n) if (abs(abs(c[i].p - p[j]) - c[i].r) < eps)
			vec.emplace_back(arg(c[i].p - p[j]), j);
		sort(ALL(vec));
		REP(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			ld angle = vec[j + 1].first - vec[j].first;
			add_edge(g, from, to, angle * c[i].r);
		}
		if (vec.size() >= 2) {
			int from = vec.back().second, to = vec.front().first;
			ld angle = vec.front().first - vec.back().first;
			add_edge(g, from, to, angle * c[i].r);
		}
	}
	return g;
}


/* 双対グラフ */

// 線分集合は既にアレンジメントされていなければならない．
// 内側の円は時計回りで，外側の円は反時計回りで得られる．
// 変数 polygon は，vector<int> で表される多角形の集合であり，
// vector<int> で表される 多角形のi番目は，その頂点の頂点集合pにおける番号である．
vector<vector<int>> polygon;
vector<int> seg2p[1024][1024];

Graph dual_graph(const vector<Line> &s, const vector<Point> &p) {
	int N = p.size();
	polygon.clear();
	REP(i, 1024) REP(j, 1024) seg2p[i][j].clear();
	vector<vector<tuple<ld, int, bool>>> tup(N);
	REP(i, s.size()) {
		int a = -1, b = -1;
		REP(j, N) if (abs(s[i].a - p[j]) < eps) a = j;
		REP(j, N) if (abs(s[i].b - p[j]) < eps) b = j;
		assert(a >= 0 && b >= 0);
		tup[a].emplace_back(arg(s[i].b - s[i].a), b, false);
		tup[b].emplace_back(arg(s[i].a - s[i].b), a, false);
	}
	REP(i, N) sort(ALL(tup[i]));
	REP(i, N) {
		REP(j, tup[i].size()) {
			ld angle; int pos = j, from = i, to; bool flag;
			tie(angle, to, flag) = tup[i][j];
			if (flag) continue;
			vector<int> ps;
			while (!flag) {
				ps.push_back(from);
				get<2>(tup[from][pos]) = true;
				seg2p[from][to].push_back(polygon.size());
				seg2p[to][from].push_back(polygon.size());
				angle += pi + eps;
				if (angle > pi) angle -= 2 * pi;
				auto it = lower_bound(ALL(tup[to]), make_tuple(angle, 0, false));
				if (it == tup[to].end()) it = tup[to].begin();
				from = to; tie(angle, to, flag) = *it;
				pos = it - tup[from].begin();
			}
			polygon.push_back(ps);
		}
	}
	Graph g(polygon.size());
	REP(i, N) REP(j, i) {
		if (seg2p[i][j].size() == 2) {
			int from = seg2p[i][j][0], to = seg2p[i][j][1];
			g[from].push_back(Edge{ from, to });
			g[to].push_back(Edge{ to, from });
		}
	}
	return g;
}


/* ビジュアライザ */
const ld zoom = 25;
const ld centerX = 6;
const ld centerY = 5;

void change_color(int r, int g, int b) {
	fprintf(stderr, "c.strokeStyle = 'rgb(%d, %d, %d)';\n", r, g, b);
}

int cordx(Point p) { return 400 + zoom * (p.real() - centerX); }
int cordy(Point p) { return 400 - zoom * (p.imag() - centerY); }

#define cord(p) cordx(p),cordy(p)

void draw_point(Point p) {
	fprintf(stderr, "circle(%d, %d, %d)\n", cord(p), 2);
}

void draw_segment(Line l) {
	fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(l.a), cord(l.b));
}

void draw_line(Line l) {
	Point v = l.b - l.a;
	Line m(l.a - v * Point(1e4, 0), l.b + v * Point(1e4, 0));
	fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(m.a), cord(m.b));
}

void draw_polygon(const Polygon &p) {
	int n = p.size();
	REP(i, n) draw_segment(Line(p[i], p[(i + 1) % n]));
}

void draw_circle(Circle c) {
	fprintf(stderr, "circle(%d, %d, %d)\n", cord(c.p), (int)(zoom * c.r));
}





int main() {
	int N; cin >> N;
	vector<Point>ps;
	for (int i = 0; i < N; ++i) {
		int x, y; cin >> x >> y;
		ps.emplace_back(x, y);
	}
	vector<Line>ls;
	for (int i = 0; i < N - 1; ++i) {
		ls.emplace_back(ps[i], ps[i + 1]);
	}
	int dx, dy, dvel; cin >> dx >> dy >> dvel;
	Point dp(dx, dy);
	int snum;
	for (int i = 0; i < N - 1; ++i) {
		if (isis_sp(ls[i], dp)) {
			snum = i;
			break;
		}
	}

	vector<long double>times(N);
	{
		long double nowtime = 0;
		Point np(dp);
		for (int i = snum + 1; i < N; ++i) {
			nowtime += abs(np - ps[i]) / dvel;
			times[i] = nowtime;
			np = ps[i];
		}
	}
	{
		long double nowtime = 0;
		Point np(dp);
		for (int i = snum; i >= 0; --i) {
			nowtime += abs(np - ps[i]) / dvel;
			times[i] = nowtime;
			np = ps[i];
		}
	}
	long double ans = max(times[0], times.back());
	int sx, sy, svel; cin >> sx >> sy >> svel;
	Point sp(sx, sy);
	{
		long double nowtime = 0;
		Point fromp(dp);
		long double fromtime = 0;
		Point np(sp);
		bool flag = false;
		for (int i = snum + 1; i < N; ++i) {
			if ((abs(np-ps[i]) / svel) < times[i]) {
				long double amin = 0;
				long double amax = 1.0;
				while (amin + 1e-10 < amax) {
					long double amid = (amin + amax) / 2;
					long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
					long double dominotime = times[i] * amid + fromtime*(1 - amid);
					if (playertime > dominotime) {
						amin = amid;
					}
					else {
						amax = amid;
					}
				}
				nowtime= times[i] * amin + fromtime*(1 - amin);
				np = ps[i] * amin + fromp*(1 - amin);
				flag = true;
				break;
			}
			else {
				fromtime = times[i];
				fromp = ps[i];
			}
		}
		if (flag) {
			ans = min(ans, max(nowtime, times[0]));
			fromp = dp;
			fromtime = 0;
			for (int i = snum; i >= 0; --i) {
				if ((abs(np - ps[i]) / svel)+nowtime < times[i]) {
					long double amin = 0;
					long double amax = 1.0;
					while (amin + 1e-10 < amax) {
						long double amid = (amin + amax) / 2;
						long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
						long double dominotime = times[i] * amid + fromtime*(1 - amid);
						if (playertime + nowtime > dominotime) {
							amin = amid;
						}
						else {
							amax = amid;
						}
					}
					nowtime = times[i] * amin + fromtime*(1 - amin);
					ans = min(ans, nowtime);
					np = ps[i] * amin + fromp*(1 - amin);
					flag = true;
					break;
				}
				else {
					fromtime = times[i];
					fromp = ps[i];
				}
			}
		}

	}


	{
		long double nowtime = 0;
		Point fromp(dp);
		long double fromtime = 0;
		Point np(sp);
		bool flag = false;
		for (int i = snum; i >= 0; --i) {
			if ((abs(np - ps[i]) / svel) < times[i]) {
				long double amin = 0;
				long double amax = 1.0;
				while (amin + 1e-15 < amax) {
					long double amid = (amin + amax) / 2;
					long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
					long double dominotime = times[i] * amid + fromtime*(1 - amid);
					if (playertime > dominotime) {
						amin = amid;
					}
					else {
						amax = amid;
					}
				}
				nowtime = times[i] * amin + fromtime*(1 - amin);
				np = ps[i] * amin + fromp*(1 - amin);
				flag = true;
				break;
			}
			else {
				fromtime = times[i];
				fromp = ps[i];
			}
		}
		if (flag) {
			ans = min(ans, max(nowtime,times.back()));
			fromp = dp;
			fromtime = 0;
			for (int i = snum + 1; i < N; ++i) {
				if ((abs(np - ps[i]) / svel) + nowtime < times[i]) {
					long double amin = 0;
					long double amax = 1.0;
					while (amin + 1e-15 < amax) {
						long double amid = (amin + amax) / 2;
						long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
						long double dominotime = times[i] * amid + fromtime*(1 - amid);
						if (playertime + nowtime > dominotime) {
							amin = amid;
						}
						else {
							amax = amid;
						}
					}
					nowtime = times[i] * amin + fromtime*(1 - amin) ;
					ans = min(ans, nowtime);
					np = ps[i] * amin + fromp*(1 - amin);
					flag = true;
					break;
				}
				else {
					fromtime = times[i];
					fromp = ps[i];
				}
			}
		}

	}
	cout << fixed<<setprecision(32)<<ans << endl;
	return 0;
}
accuracy: 1
time_ms: 10
memory_kb: 28096
final_rank: 2

code_snippet: #include<stdio.h>
#include <iostream>
#include <math.h>
#include <numeric>
#include <vector>
#include <map>
#include <functional>
#include <stdio.h>
#include <array>
#include <algorithm>
#include <string>
#include <string.h>
#include <assert.h>
#include <stdio.h>
#include <queue>
#include<iomanip>
#include<bitset>
#include<stack>
#include<set>
#include<limits>
#include <complex>
using namespace std;



#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()




/* 幾何の基本 */

#include <complex>

typedef long double ld;
typedef complex<ld> Point;

const ld eps = 1e-9, pi = acos(-1.0);

namespace std {
	bool operator<(const Point &lhs, const Point &rhs) {
		if (lhs.real() < rhs.real() - eps) return true;
		if (lhs.real() > rhs.real() + eps) return false;
		return lhs.imag() < rhs.imag();
	}
}

// 点の入力
Point input_point() {
	ld x, y;
	cin >> x >> y;
	return Point(x, y);
}

// 誤差つき等号判定
bool eq(ld a, ld b) {
	return (abs(a - b) < eps);
}

// 内積
ld dot(Point a, Point b) {
	return real(conj(a) * b);
}

// 外積
ld cross(Point a, Point b) {
	return imag(conj(a) * b);
}

// 直線の定義
class Line {
public:
	Point a, b;
	Line() : a(Point(0, 0)), b(Point(0, 0)) {}
	Line(Point a, Point b) : a(a), b(b) {}
};

// 円の定義
class Circle {
public:
	Point p;
	ld r;
	Circle() : p(Point(0, 0)), r(0) {}
	Circle(Point p, ld r) : p(p), r(r) {}
};

// CCW
int ccw(Point a, Point b, Point c) {
	b -= a; c -= a;
	if (cross(b, c) > eps) return 1;   // a,b,cが反時計周りの順に並ぶ
	if (cross(b, c) < -eps) return -1; // a,b,cが時計周りの順に並ぶ
	if (dot(b, c) < 0) return 2;       // c,a,bの順に直線に並ぶ
	if (norm(b) < norm(c)) return -2;  // a,b,cの順に直線に並ぶ
	return 0;                          // a,c,bの順に直線に並ぶ
}


/* 交差判定 */

// 直線と直線の交差判定
bool isis_ll(Line l, Line m) {
	return !eq(cross(l.b - l.a, m.b - m.a), 0);
}

// 直線と線分の交差判定
bool isis_ls(Line l, Line s) {
	return isis_ll(l, s) &&
		(cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

// 線分と線分の交差判定
bool isis_ss(Line s, Line t) {
	return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
		ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

// 点の直線上判定
bool isis_lp(Line l, Point p) {
	return (abs(cross(l.b - p, l.a - p)) < eps);
}

// 点の線分上判定
bool isis_sp(Line s, Point p) {
	return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

// 垂線の足
Point proj(Line l, Point p) {
	ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
	return l.a + t * (l.a - l.b);
}

// 直線と直線の交点
Point is_ll(Line s, Line t) {
	Point sv = s.b - s.a, tv = t.b - t.a;
	assert(cross(sv, tv) != 0);
	return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

// 直線と点の距離
ld dist_lp(Line l, Point p) {
	return abs(p - proj(l, p));
}

// 直線と直線の距離
ld dist_ll(Line l, Line m) {
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

// 直線と線分の距離
ld dist_ls(Line l, Line s) {
	return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// 線分と点の距離
ld dist_sp(Line s, Point p) {
	Point r = proj(s, p);
	return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// 線分と線分の距離
ld dist_ss(Line s, Line t) {
	if (isis_ss(s, t)) return 0;
	return min({ dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b) });
}


/* 円 */

// 円と円の交点
vector<Point> is_cc(Circle c1, Circle c2) {
	vector<Point> res;
	ld d = abs(c1.p - c2.p);
	ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
	ld dfr = c1.r * c1.r - rc * rc;
	if (abs(dfr) < eps) dfr = 0.0;
	else if (dfr < 0.0) return res; // no intersection
	ld rs = sqrt(dfr);
	Point diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * Point(rc, rs));
	if (dfr != 0.0) res.push_back(c1.p + diff * Point(rc, -rs));
	return res;
}

// 円と直線の交点
vector<Point> is_lc(Circle c, Line l) {
	vector<Point> res;
	ld d = dist_lp(l, c.p);
	if (d < c.r + eps) {
		ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
		Point nor = (l.a - l.b) / abs(l.a - l.b);
		res.push_back(proj(l, c.p) + len * nor);
		res.push_back(proj(l, c.p) - len * nor);
	}
	return res;
}

// 円と線分の距離
vector<Point> is_sc(Circle c, Line l) {
	vector<Point> v = is_lc(c, l), res;
	for (Point p : v)
		if (isis_sp(l, p)) res.push_back(p);
	return res;
}

// 円と点の接線
vector<Line> tangent_cp(Circle c, Point p) {
	vector<Line> ret;
	Point v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (isnan(l)) { return ret; }
	Point v1 = v * Point(l / d, c.r / d);
	Point v2 = v * Point(l / d, -c.r / d);
	ret.push_back(Line(p, p + v1));
	if (l < eps) return ret;
	ret.push_back(Line(p, p + v2));
	return ret;
}

// 円と円の接線
vector<Line> tangent_cc(Circle c1, Circle c2) {
	vector<Line> ret;
	if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
		Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
		ret = tangent_cp(c1, center);
	}
	if (abs(c1.r - c2.r) > eps) {
		Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
		vector<Line> nret = tangent_cp(c1, out);
		ret.insert(ret.end(), ALL(nret));
	}
	else {
		Point v = c2.p - c1.p;
		v /= abs(v);
		Point q1 = c1.p + v * Point(0, 1) * c1.r;
		Point q2 = c1.p + v * Point(0, -1) * c1.r;
		ret.push_back(Line(q1, q1 + v));
		ret.push_back(Line(q2, q2 + v));
	}
	return ret;
}


/* 多角形 */

typedef vector<Point> Polygon;

// 面積
ld area(const Polygon &p) {
	ld res = 0;
	int n = p.size();
	REP(j, n) res += cross(p[j], p[(j + 1) % n]);
	return res / 2;
}

// 多角形の回転方向
bool is_counter_clockwise(const Polygon &poly) {
	ld angle = 0;
	int n = poly.size();
	REP(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
		angle += arg((c - b) / (b - a));
	}
	return angle > eps;
}

// 円の内外判定
// -1 => out
//  0 => on
//  1 => in
int is_in_polygon(const Polygon &poly, Point p) {
	ld angle = 0;
	int n = poly.size();
	REP(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n];
		if (isis_sp(Line(a, b), p)) return 1;
		angle += arg((b - p) / (a - p));
	}
	return eq(angle, 0) ? 0 : 2;
}

// 凸包
Polygon convex_hull(vector<Point> ps) {
	int n = ps.size();
	int k = 0;
	sort(ps.begin(), ps.end());
	Polygon ch(2 * n);
	for (int i = 0; i < n; ch[k++] = ps[i++])
		while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
		while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	ch.resize(k - 1);
	return ch;
}

// 凸カット
Polygon convex_cut(const Polygon &ps, Line l) {
	int n = ps.size();
	Polygon Q;
	REP(i, n) {
		Point A = ps[i], B = ps[(i + 1) % n];
		Line m = Line(A, B);
		if (ccw(l.a, l.b, A) != -1) Q.push_back(A);
		if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m))
			Q.push_back(is_ll(l, m));
	}
	return Q;
}


/* アレンジメント */
void add_point(vector<Point> &ps, Point p) {
	for (Point q : ps) if (abs(q - p) < eps) return;
	ps.push_back(p);
}

typedef int Weight;

struct Edge { int from, to; Weight weight; };

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

void add_edge(Graph &g, int from, int to, Weight weight) {
	g[from].push_back(Edge{ from, to, weight });
}

Graph segment_arrangement(const vector<Line> &s, const vector<Point> &p) {
	int n = p.size(), m = s.size();
	Graph g(n);
	REP(i, m) {
		vector<pair<ld, int>> vec;
		REP(j, n) if (isis_sp(s[i], p[j]))
			vec.emplace_back(abs(s[i].a - p[j]), j);
		sort(ALL(vec));
		REP(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			add_edge(g, from, to, abs(p[from] - p[to]));
		}
	}
	return g;
}

Graph circle_arrangement(const vector<Circle> &c, const vector<Point> &p) {
	int n = p.size(), m = c.size();
	Graph g(n);
	REP(i, m) {
		vector<pair<ld, int>> vec;
		REP(j, n) if (abs(abs(c[i].p - p[j]) - c[i].r) < eps)
			vec.emplace_back(arg(c[i].p - p[j]), j);
		sort(ALL(vec));
		REP(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			ld angle = vec[j + 1].first - vec[j].first;
			add_edge(g, from, to, angle * c[i].r);
		}
		if (vec.size() >= 2) {
			int from = vec.back().second, to = vec.front().first;
			ld angle = vec.front().first - vec.back().first;
			add_edge(g, from, to, angle * c[i].r);
		}
	}
	return g;
}


/* 双対グラフ */

// 線分集合は既にアレンジメントされていなければならない．
// 内側の円は時計回りで，外側の円は反時計回りで得られる．
// 変数 polygon は，vector<int> で表される多角形の集合であり，
// vector<int> で表される 多角形のi番目は，その頂点の頂点集合pにおける番号である．
vector<vector<int>> polygon;
vector<int> seg2p[1024][1024];

Graph dual_graph(const vector<Line> &s, const vector<Point> &p) {
	int N = p.size();
	polygon.clear();
	REP(i, 1024) REP(j, 1024) seg2p[i][j].clear();
	vector<vector<tuple<ld, int, bool>>> tup(N);
	REP(i, s.size()) {
		int a = -1, b = -1;
		REP(j, N) if (abs(s[i].a - p[j]) < eps) a = j;
		REP(j, N) if (abs(s[i].b - p[j]) < eps) b = j;
		assert(a >= 0 && b >= 0);
		tup[a].emplace_back(arg(s[i].b - s[i].a), b, false);
		tup[b].emplace_back(arg(s[i].a - s[i].b), a, false);
	}
	REP(i, N) sort(ALL(tup[i]));
	REP(i, N) {
		REP(j, tup[i].size()) {
			ld angle; int pos = j, from = i, to; bool flag;
			tie(angle, to, flag) = tup[i][j];
			if (flag) continue;
			vector<int> ps;
			while (!flag) {
				ps.push_back(from);
				get<2>(tup[from][pos]) = true;
				seg2p[from][to].push_back(polygon.size());
				seg2p[to][from].push_back(polygon.size());
				angle += pi + eps;
				if (angle > pi) angle -= 2 * pi;
				auto it = lower_bound(ALL(tup[to]), make_tuple(angle, 0, false));
				if (it == tup[to].end()) it = tup[to].begin();
				from = to; tie(angle, to, flag) = *it;
				pos = it - tup[from].begin();
			}
			polygon.push_back(ps);
		}
	}
	Graph g(polygon.size());
	REP(i, N) REP(j, i) {
		if (seg2p[i][j].size() == 2) {
			int from = seg2p[i][j][0], to = seg2p[i][j][1];
			g[from].push_back(Edge{ from, to });
			g[to].push_back(Edge{ to, from });
		}
	}
	return g;
}


/* ビジュアライザ */
const ld zoom = 25;
const ld centerX = 6;
const ld centerY = 5;

void change_color(int r, int g, int b) {
	fprintf(stderr, "c.strokeStyle = 'rgb(%d, %d, %d)';\n", r, g, b);
}

int cordx(Point p) { return 400 + zoom * (p.real() - centerX); }
int cordy(Point p) { return 400 - zoom * (p.imag() - centerY); }

#define cord(p) cordx(p),cordy(p)

void draw_point(Point p) {
	fprintf(stderr, "circle(%d, %d, %d)\n", cord(p), 2);
}

void draw_segment(Line l) {
	fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(l.a), cord(l.b));
}

void draw_line(Line l) {
	Point v = l.b - l.a;
	Line m(l.a - v * Point(1e4, 0), l.b + v * Point(1e4, 0));
	fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(m.a), cord(m.b));
}

void draw_polygon(const Polygon &p) {
	int n = p.size();
	REP(i, n) draw_segment(Line(p[i], p[(i + 1) % n]));
}

void draw_circle(Circle c) {
	fprintf(stderr, "circle(%d, %d, %d)\n", cord(c.p), (int)(zoom * c.r));
}





int main() {
	int N; cin >> N;
	vector<Point>ps;
	for (int i = 0; i < N; ++i) {
		int x, y; cin >> x >> y;
		ps.emplace_back(x, y);
	}
	vector<Line>ls;
	for (int i = 0; i < N - 1; ++i) {
		ls.emplace_back(ps[i], ps[i + 1]);
	}
	int dx, dy, dvel; cin >> dx >> dy >> dvel;
	Point dp(dx, dy);
	int snum;
	for (int i = 0; i < N - 1; ++i) {
		if (isis_sp(ls[i], dp)) {
			snum = i;
		}
	}

	vector<long double>times(N);
	{
		long double nowtime = 0;
		Point np(dp);
		for (int i = snum + 1; i < N; ++i) {
			nowtime += abs(np - ps[i]) / dvel;
			times[i] = nowtime;
			np = ps[i];
		}
	}
	{
		long double nowtime = 0;
		Point np(dp);
		for (int i = snum; i >= 0; --i) {
			nowtime += abs(np - ps[i]) / dvel;
			times[i] = nowtime;
			np = ps[i];
		}
	}
	long double ans = max(times[0], times.back());
	int sx, sy, svel; cin >> sx >> sy >> svel;
	Point sp(sx, sy);
	{
		long double nowtime = 0;
		Point fromp(dp);
		long double fromtime = 0;
		Point np(sp);
		bool flag = false;
		for (int i = snum + 1; i < N; ++i) {
			if ((abs(np-ps[i]) / svel) < times[i]) {
				long double amin = 0;
				long double amax = 1.0;
				while (amin + 1e-10 < amax) {
					long double amid = (amin + amax) / 2;
					long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
					long double dominotime = times[i] * amid + fromtime*(1 - amid);
					if (playertime > dominotime) {
						amin = amid;
					}
					else {
						amax = amid;
					}
				}
				nowtime= times[i] * amin + fromtime*(1 - amin);
				np = ps[i] * amin + fromp*(1 - amin);
				flag = true;
				break;
			}
			else {
				fromtime = times[i];
				fromp = ps[i];
			}
		}
		if (flag) {
			ans = min(ans, max(nowtime, times[0]));
			fromp = dp;
			fromtime = 0;
			for (int i = snum; i >= 0; --i) {
				if ((abs(np - ps[i]) / svel)+nowtime < times[i]) {
					long double amin = 0;
					long double amax = 1.0;
					while (amin + 1e-10 < amax) {
						long double amid = (amin + amax) / 2;
						long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
						long double dominotime = times[i] * amid + fromtime*(1 - amid);
						if (playertime + nowtime > dominotime) {
							amin = amid;
						}
						else {
							amax = amid;
						}
					}
					nowtime = times[i] * amin + fromtime*(1 - amin);
					ans = min(ans, nowtime);
					np = ps[i] * amin + fromp*(1 - amin);
					flag = true;
					break;
				}
				else {
					fromtime = times[i];
					fromp = ps[i];
				}
			}
		}

	}


	{
		long double nowtime = 0;
		Point fromp(dp);
		long double fromtime = 0;
		Point np(sp);
		bool flag = false;
		for (int i = snum; i >= 0; --i) {
			if ((abs(np - ps[i]) / svel) < times[i]) {
				long double amin = 0;
				long double amax = 1.0;
				while (amin + 1e-15 < amax) {
					long double amid = (amin + amax) / 2;
					long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
					long double dominotime = times[i] * amid + fromtime*(1 - amid);
					if (playertime > dominotime) {
						amin = amid;
					}
					else {
						amax = amid;
					}
				}
				nowtime = times[i] * amin + fromtime*(1 - amin);
				np = ps[i] * amin + fromp*(1 - amin);
				flag = true;
				break;
			}
			else {
				fromtime = times[i];
				fromp = ps[i];
			}
		}
		if (flag) {
			ans = min(ans, max(nowtime,times.back()));
			fromp = dp;
			fromtime = 0;
			for (int i = snum + 1; i < N; ++i) {
				if ((abs(np - ps[i]) / svel) + nowtime < times[i]) {
					long double amin = 0;
					long double amax = 1.0;
					while (amin + 1e-15 < amax) {
						long double amid = (amin + amax) / 2;
						long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
						long double dominotime = times[i] * amid + fromtime*(1 - amid);
						if (playertime + nowtime > dominotime) {
							amin = amid;
						}
						else {
							amax = amid;
						}
					}
					nowtime = times[i] * amin + fromtime*(1 - amin) ;
					ans = min(ans, nowtime);
					np = ps[i] * amin + fromp*(1 - amin);
					flag = true;
					break;
				}
				else {
					fromtime = times[i];
					fromp = ps[i];
				}
			}
		}

	}
	cout << fixed<<setprecision(32)<<ans << endl;
	return 0;
}
accuracy: 0.6395348837209303
time_ms: 10
memory_kb: 28016
final_rank: 6

code_snippet: #include<stdio.h>
#include <iostream>
#include <math.h>
#include <numeric>
#include <vector>
#include <map>
#include <functional>
#include <stdio.h>
#include <array>
#include <algorithm>
#include <string>
#include <string.h>
#include <assert.h>
#include <stdio.h>
#include <queue>
#include<iomanip>
#include<bitset>
#include<stack>
#include<set>
#include<limits>
#include <complex>
using namespace std;



#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()




/* 幾何の基本 */

#include <complex>

typedef long double ld;
typedef complex<ld> Point;

const ld eps = 1e-9, pi = acos(-1.0);

namespace std {
	bool operator<(const Point &lhs, const Point &rhs) {
		if (lhs.real() < rhs.real() - eps) return true;
		if (lhs.real() > rhs.real() + eps) return false;
		return lhs.imag() < rhs.imag();
	}
}

// 点の入力
Point input_point() {
	ld x, y;
	cin >> x >> y;
	return Point(x, y);
}

// 誤差つき等号判定
bool eq(ld a, ld b) {
	return (abs(a - b) < eps);
}

// 内積
ld dot(Point a, Point b) {
	return real(conj(a) * b);
}

// 外積
ld cross(Point a, Point b) {
	return imag(conj(a) * b);
}

// 直線の定義
class Line {
public:
	Point a, b;
	Line() : a(Point(0, 0)), b(Point(0, 0)) {}
	Line(Point a, Point b) : a(a), b(b) {}
};

// 円の定義
class Circle {
public:
	Point p;
	ld r;
	Circle() : p(Point(0, 0)), r(0) {}
	Circle(Point p, ld r) : p(p), r(r) {}
};

// CCW
int ccw(Point a, Point b, Point c) {
	b -= a; c -= a;
	if (cross(b, c) > eps) return 1;   // a,b,cが反時計周りの順に並ぶ
	if (cross(b, c) < -eps) return -1; // a,b,cが時計周りの順に並ぶ
	if (dot(b, c) < 0) return 2;       // c,a,bの順に直線に並ぶ
	if (norm(b) < norm(c)) return -2;  // a,b,cの順に直線に並ぶ
	return 0;                          // a,c,bの順に直線に並ぶ
}


/* 交差判定 */

// 直線と直線の交差判定
bool isis_ll(Line l, Line m) {
	return !eq(cross(l.b - l.a, m.b - m.a), 0);
}

// 直線と線分の交差判定
bool isis_ls(Line l, Line s) {
	return isis_ll(l, s) &&
		(cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

// 線分と線分の交差判定
bool isis_ss(Line s, Line t) {
	return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
		ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

// 点の直線上判定
bool isis_lp(Line l, Point p) {
	return (abs(cross(l.b - p, l.a - p)) < eps);
}

// 点の線分上判定
bool isis_sp(Line s, Point p) {
	return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

// 垂線の足
Point proj(Line l, Point p) {
	ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
	return l.a + t * (l.a - l.b);
}

// 直線と直線の交点
Point is_ll(Line s, Line t) {
	Point sv = s.b - s.a, tv = t.b - t.a;
	assert(cross(sv, tv) != 0);
	return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

// 直線と点の距離
ld dist_lp(Line l, Point p) {
	return abs(p - proj(l, p));
}

// 直線と直線の距離
ld dist_ll(Line l, Line m) {
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

// 直線と線分の距離
ld dist_ls(Line l, Line s) {
	return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// 線分と点の距離
ld dist_sp(Line s, Point p) {
	Point r = proj(s, p);
	return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// 線分と線分の距離
ld dist_ss(Line s, Line t) {
	if (isis_ss(s, t)) return 0;
	return min({ dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b) });
}


/* 円 */

// 円と円の交点
vector<Point> is_cc(Circle c1, Circle c2) {
	vector<Point> res;
	ld d = abs(c1.p - c2.p);
	ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
	ld dfr = c1.r * c1.r - rc * rc;
	if (abs(dfr) < eps) dfr = 0.0;
	else if (dfr < 0.0) return res; // no intersection
	ld rs = sqrt(dfr);
	Point diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * Point(rc, rs));
	if (dfr != 0.0) res.push_back(c1.p + diff * Point(rc, -rs));
	return res;
}

// 円と直線の交点
vector<Point> is_lc(Circle c, Line l) {
	vector<Point> res;
	ld d = dist_lp(l, c.p);
	if (d < c.r + eps) {
		ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
		Point nor = (l.a - l.b) / abs(l.a - l.b);
		res.push_back(proj(l, c.p) + len * nor);
		res.push_back(proj(l, c.p) - len * nor);
	}
	return res;
}

// 円と線分の距離
vector<Point> is_sc(Circle c, Line l) {
	vector<Point> v = is_lc(c, l), res;
	for (Point p : v)
		if (isis_sp(l, p)) res.push_back(p);
	return res;
}

// 円と点の接線
vector<Line> tangent_cp(Circle c, Point p) {
	vector<Line> ret;
	Point v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (isnan(l)) { return ret; }
	Point v1 = v * Point(l / d, c.r / d);
	Point v2 = v * Point(l / d, -c.r / d);
	ret.push_back(Line(p, p + v1));
	if (l < eps) return ret;
	ret.push_back(Line(p, p + v2));
	return ret;
}

// 円と円の接線
vector<Line> tangent_cc(Circle c1, Circle c2) {
	vector<Line> ret;
	if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
		Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
		ret = tangent_cp(c1, center);
	}
	if (abs(c1.r - c2.r) > eps) {
		Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
		vector<Line> nret = tangent_cp(c1, out);
		ret.insert(ret.end(), ALL(nret));
	}
	else {
		Point v = c2.p - c1.p;
		v /= abs(v);
		Point q1 = c1.p + v * Point(0, 1) * c1.r;
		Point q2 = c1.p + v * Point(0, -1) * c1.r;
		ret.push_back(Line(q1, q1 + v));
		ret.push_back(Line(q2, q2 + v));
	}
	return ret;
}


/* 多角形 */

typedef vector<Point> Polygon;

// 面積
ld area(const Polygon &p) {
	ld res = 0;
	int n = p.size();
	REP(j, n) res += cross(p[j], p[(j + 1) % n]);
	return res / 2;
}

// 多角形の回転方向
bool is_counter_clockwise(const Polygon &poly) {
	ld angle = 0;
	int n = poly.size();
	REP(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
		angle += arg((c - b) / (b - a));
	}
	return angle > eps;
}

// 円の内外判定
// -1 => out
//  0 => on
//  1 => in
int is_in_polygon(const Polygon &poly, Point p) {
	ld angle = 0;
	int n = poly.size();
	REP(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n];
		if (isis_sp(Line(a, b), p)) return 1;
		angle += arg((b - p) / (a - p));
	}
	return eq(angle, 0) ? 0 : 2;
}

// 凸包
Polygon convex_hull(vector<Point> ps) {
	int n = ps.size();
	int k = 0;
	sort(ps.begin(), ps.end());
	Polygon ch(2 * n);
	for (int i = 0; i < n; ch[k++] = ps[i++])
		while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
		while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	ch.resize(k - 1);
	return ch;
}

// 凸カット
Polygon convex_cut(const Polygon &ps, Line l) {
	int n = ps.size();
	Polygon Q;
	REP(i, n) {
		Point A = ps[i], B = ps[(i + 1) % n];
		Line m = Line(A, B);
		if (ccw(l.a, l.b, A) != -1) Q.push_back(A);
		if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m))
			Q.push_back(is_ll(l, m));
	}
	return Q;
}


/* アレンジメント */
void add_point(vector<Point> &ps, Point p) {
	for (Point q : ps) if (abs(q - p) < eps) return;
	ps.push_back(p);
}

typedef int Weight;

struct Edge { int from, to; Weight weight; };

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

void add_edge(Graph &g, int from, int to, Weight weight) {
	g[from].push_back(Edge{ from, to, weight });
}

Graph segment_arrangement(const vector<Line> &s, const vector<Point> &p) {
	int n = p.size(), m = s.size();
	Graph g(n);
	REP(i, m) {
		vector<pair<ld, int>> vec;
		REP(j, n) if (isis_sp(s[i], p[j]))
			vec.emplace_back(abs(s[i].a - p[j]), j);
		sort(ALL(vec));
		REP(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			add_edge(g, from, to, abs(p[from] - p[to]));
		}
	}
	return g;
}

Graph circle_arrangement(const vector<Circle> &c, const vector<Point> &p) {
	int n = p.size(), m = c.size();
	Graph g(n);
	REP(i, m) {
		vector<pair<ld, int>> vec;
		REP(j, n) if (abs(abs(c[i].p - p[j]) - c[i].r) < eps)
			vec.emplace_back(arg(c[i].p - p[j]), j);
		sort(ALL(vec));
		REP(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			ld angle = vec[j + 1].first - vec[j].first;
			add_edge(g, from, to, angle * c[i].r);
		}
		if (vec.size() >= 2) {
			int from = vec.back().second, to = vec.front().first;
			ld angle = vec.front().first - vec.back().first;
			add_edge(g, from, to, angle * c[i].r);
		}
	}
	return g;
}


/* 双対グラフ */

// 線分集合は既にアレンジメントされていなければならない．
// 内側の円は時計回りで，外側の円は反時計回りで得られる．
// 変数 polygon は，vector<int> で表される多角形の集合であり，
// vector<int> で表される 多角形のi番目は，その頂点の頂点集合pにおける番号である．
vector<vector<int>> polygon;
vector<int> seg2p[1024][1024];

Graph dual_graph(const vector<Line> &s, const vector<Point> &p) {
	int N = p.size();
	polygon.clear();
	REP(i, 1024) REP(j, 1024) seg2p[i][j].clear();
	vector<vector<tuple<ld, int, bool>>> tup(N);
	REP(i, s.size()) {
		int a = -1, b = -1;
		REP(j, N) if (abs(s[i].a - p[j]) < eps) a = j;
		REP(j, N) if (abs(s[i].b - p[j]) < eps) b = j;
		assert(a >= 0 && b >= 0);
		tup[a].emplace_back(arg(s[i].b - s[i].a), b, false);
		tup[b].emplace_back(arg(s[i].a - s[i].b), a, false);
	}
	REP(i, N) sort(ALL(tup[i]));
	REP(i, N) {
		REP(j, tup[i].size()) {
			ld angle; int pos = j, from = i, to; bool flag;
			tie(angle, to, flag) = tup[i][j];
			if (flag) continue;
			vector<int> ps;
			while (!flag) {
				ps.push_back(from);
				get<2>(tup[from][pos]) = true;
				seg2p[from][to].push_back(polygon.size());
				seg2p[to][from].push_back(polygon.size());
				angle += pi + eps;
				if (angle > pi) angle -= 2 * pi;
				auto it = lower_bound(ALL(tup[to]), make_tuple(angle, 0, false));
				if (it == tup[to].end()) it = tup[to].begin();
				from = to; tie(angle, to, flag) = *it;
				pos = it - tup[from].begin();
			}
			polygon.push_back(ps);
		}
	}
	Graph g(polygon.size());
	REP(i, N) REP(j, i) {
		if (seg2p[i][j].size() == 2) {
			int from = seg2p[i][j][0], to = seg2p[i][j][1];
			g[from].push_back(Edge{ from, to });
			g[to].push_back(Edge{ to, from });
		}
	}
	return g;
}


/* ビジュアライザ */
const ld zoom = 25;
const ld centerX = 6;
const ld centerY = 5;

void change_color(int r, int g, int b) {
	fprintf(stderr, "c.strokeStyle = 'rgb(%d, %d, %d)';\n", r, g, b);
}

int cordx(Point p) { return 400 + zoom * (p.real() - centerX); }
int cordy(Point p) { return 400 - zoom * (p.imag() - centerY); }

#define cord(p) cordx(p),cordy(p)

void draw_point(Point p) {
	fprintf(stderr, "circle(%d, %d, %d)\n", cord(p), 2);
}

void draw_segment(Line l) {
	fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(l.a), cord(l.b));
}

void draw_line(Line l) {
	Point v = l.b - l.a;
	Line m(l.a - v * Point(1e4, 0), l.b + v * Point(1e4, 0));
	fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(m.a), cord(m.b));
}

void draw_polygon(const Polygon &p) {
	int n = p.size();
	REP(i, n) draw_segment(Line(p[i], p[(i + 1) % n]));
}

void draw_circle(Circle c) {
	fprintf(stderr, "circle(%d, %d, %d)\n", cord(c.p), (int)(zoom * c.r));
}





int main() {
	int N; cin >> N;
	vector<Point>ps;
	for (int i = 0; i < N; ++i) {
		int x, y; cin >> x >> y;
		ps.emplace_back(x, y);
	}
	vector<Line>ls;
	for (int i = 0; i < N - 1; ++i) {
		ls.emplace_back(ps[i], ps[i + 1]);
	}
	int dx, dy, dvel; cin >> dx >> dy >> dvel;
	Point dp(dx, dy);
	int snum;
	for (int i = 0; i < N - 1; ++i) {
		if (isis_sp(ls[i], dp)) {
			snum = i;
		}
	}

	vector<long double>times(N);
	{
		long double nowtime = 0;
		Point np(dp);
		for (int i = snum + 1; i < N; ++i) {
			nowtime += abs(np - ps[i]) / dvel;
			times[i] = nowtime;
			np = ps[i];
		}
	}
	{
		long double nowtime = 0;
		Point np(dp);
		for (int i = snum; i >= 0; --i) {
			nowtime += abs(np - ps[i]) / dvel;
			times[i] = nowtime;
			np = ps[i];
		}
	}
	long double ans = max(times[0], times.back());
	int sx, sy, svel; cin >> sx >> sy >> svel;
	Point sp(sx, sy);
	{
		long double nowtime = 0;
		Point fromp(dp);
		long double fromtime = 0;
		Point np(sp);
		bool flag = false;
		for (int i = snum + 1; i < N; ++i) {
			if ((abs(np-ps[i]) / svel) < times[i]) {
				long double amin = 0;
				long double amax = 1.0;
				while (amin + 1e-10 < amax) {
					long double amid = (amin + amax) / 2;
					long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
					long double dominotime = times[i] * amid + fromtime*(1 - amid);
					if (playertime > dominotime) {
						amin = amid;
					}
					else {
						amax = amid;
					}
				}
				nowtime= times[i] * amin + fromtime*(1 - amin);
				np = ps[i] * amin + fromp*(1 - amin);
				flag = true;
				break;
			}
			else {
				fromtime = times[i];
				fromp = ps[i];
			}
		}
		if (flag) {
			ans = min(ans, max(nowtime, times[0]));
			fromp = dp;
			fromtime = 0;
			for (int i = snum; i >= 0; --i) {
				if ((abs(np - ps[i]) / svel)+nowtime < times[i]) {
					long double amin = 0;
					long double amax = 1.0;
					while (amin + 1e-10 < amax) {
						long double amid = (amin + amax) / 2;
						long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
						long double dominotime = times[i] * amid + fromtime*(1 - amid);
						if (playertime + nowtime > dominotime) {
							amin = amid;
						}
						else {
							amax = amid;
						}
					}
					nowtime = times[i] * amin + fromtime*(1 - amin);
					ans = min(ans, nowtime);
					np = ps[i] * amin + fromp*(1 - amin);
					flag = true;
					break;
				}
				else {
					fromtime = times[i];
					fromp = ps[i];
				}
			}
		}

	}


	{
		long double nowtime = 0;
		Point fromp(dp);
		long double fromtime = 0;
		Point np(sp);
		bool flag = false;
		for (int i = snum; i >= 0; --i) {
			if ((abs(np - ps[i]) / svel) < times[i]) {
				long double amin = 0;
				long double amax = 1.0;
				while (amin + 1e-10 < amax) {
					long double amid = (amin + amax) / 2;
					long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
					long double dominotime = times[i] * amid + fromtime*(1 - amid);
					if (playertime > dominotime) {
						amin = amid;
					}
					else {
						amax = amid;
					}
				}
				nowtime = times[i] * amin + fromtime*(1 - amin);
				np = ps[i] * amin + fromp*(1 - amin);
				flag = true;
				break;
			}
			else {
				fromtime = times[i];
				fromp = ps[i];
			}
		}
		if (flag) {
			ans = min(ans, max(nowtime,times.back()));
			fromp = dp;
			fromtime = 0;
			for (int i = snum + 1; i < N; ++i) {
				if ((abs(np - ps[i]) / svel) + nowtime < times[i]) {
					long double amin = 0;
					long double amax = 1.0;
					while (amin + 1e-10 < amax) {
						long double amid = (amin + amax) / 2;
						long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
						long double dominotime = times[i] * amid + fromtime*(1 - amid);
						if (playertime + nowtime > dominotime) {
							amin = amid;
						}
						else {
							amax = amid;
						}
					}
					nowtime = times[i] * amin + fromtime*(1 - amin) ;
					ans = min(ans, nowtime);
					np = ps[i] * amin + fromp*(1 - amin);
					flag = true;
					break;
				}
				else {
					fromtime = times[i];
					fromp = ps[i];
				}
			}
		}

	}
	cout << fixed<<setprecision(32)<<ans << endl;
	return 0;
}
accuracy: 0.6395348837209303
time_ms: 10
memory_kb: 27984
final_rank: 5

code_snippet: #include<stdio.h>
#include <iostream>
#include <math.h>
#include <numeric>
#include <vector>
#include <map>
#include <functional>
#include <stdio.h>
#include <array>
#include <algorithm>
#include <string>
#include <string.h>
#include <assert.h>
#include <stdio.h>
#include <queue>
#include<iomanip>
#include<bitset>
#include<stack>
#include<set>
#include<limits>
#include <complex>
using namespace std;



#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()




/* 幾何の基本 */

#include <complex>

typedef long double ld;
typedef complex<ld> Point;

const ld eps = 1e-9, pi = acos(-1.0);

namespace std {
	bool operator<(const Point &lhs, const Point &rhs) {
		if (lhs.real() < rhs.real() - eps) return true;
		if (lhs.real() > rhs.real() + eps) return false;
		return lhs.imag() < rhs.imag();
	}
}

// 点の入力
Point input_point() {
	ld x, y;
	cin >> x >> y;
	return Point(x, y);
}

// 誤差つき等号判定
bool eq(ld a, ld b) {
	return (abs(a - b) < eps);
}

// 内積
ld dot(Point a, Point b) {
	return real(conj(a) * b);
}

// 外積
ld cross(Point a, Point b) {
	return imag(conj(a) * b);
}

// 直線の定義
class Line {
public:
	Point a, b;
	Line() : a(Point(0, 0)), b(Point(0, 0)) {}
	Line(Point a, Point b) : a(a), b(b) {}
};

// 円の定義
class Circle {
public:
	Point p;
	ld r;
	Circle() : p(Point(0, 0)), r(0) {}
	Circle(Point p, ld r) : p(p), r(r) {}
};

// CCW
int ccw(Point a, Point b, Point c) {
	b -= a; c -= a;
	if (cross(b, c) > eps) return 1;   // a,b,cが反時計周りの順に並ぶ
	if (cross(b, c) < -eps) return -1; // a,b,cが時計周りの順に並ぶ
	if (dot(b, c) < 0) return 2;       // c,a,bの順に直線に並ぶ
	if (norm(b) < norm(c)) return -2;  // a,b,cの順に直線に並ぶ
	return 0;                          // a,c,bの順に直線に並ぶ
}


/* 交差判定 */

// 直線と直線の交差判定
bool isis_ll(Line l, Line m) {
	return !eq(cross(l.b - l.a, m.b - m.a), 0);
}

// 直線と線分の交差判定
bool isis_ls(Line l, Line s) {
	return isis_ll(l, s) &&
		(cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

// 線分と線分の交差判定
bool isis_ss(Line s, Line t) {
	return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
		ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

// 点の直線上判定
bool isis_lp(Line l, Point p) {
	return (abs(cross(l.b - p, l.a - p)) < eps);
}

// 点の線分上判定
bool isis_sp(Line s, Point p) {
	return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

// 垂線の足
Point proj(Line l, Point p) {
	ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
	return l.a + t * (l.a - l.b);
}

// 直線と直線の交点
Point is_ll(Line s, Line t) {
	Point sv = s.b - s.a, tv = t.b - t.a;
	assert(cross(sv, tv) != 0);
	return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

// 直線と点の距離
ld dist_lp(Line l, Point p) {
	return abs(p - proj(l, p));
}

// 直線と直線の距離
ld dist_ll(Line l, Line m) {
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

// 直線と線分の距離
ld dist_ls(Line l, Line s) {
	return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// 線分と点の距離
ld dist_sp(Line s, Point p) {
	Point r = proj(s, p);
	return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// 線分と線分の距離
ld dist_ss(Line s, Line t) {
	if (isis_ss(s, t)) return 0;
	return min({ dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b) });
}


/* 円 */

// 円と円の交点
vector<Point> is_cc(Circle c1, Circle c2) {
	vector<Point> res;
	ld d = abs(c1.p - c2.p);
	ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
	ld dfr = c1.r * c1.r - rc * rc;
	if (abs(dfr) < eps) dfr = 0.0;
	else if (dfr < 0.0) return res; // no intersection
	ld rs = sqrt(dfr);
	Point diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * Point(rc, rs));
	if (dfr != 0.0) res.push_back(c1.p + diff * Point(rc, -rs));
	return res;
}

// 円と直線の交点
vector<Point> is_lc(Circle c, Line l) {
	vector<Point> res;
	ld d = dist_lp(l, c.p);
	if (d < c.r + eps) {
		ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
		Point nor = (l.a - l.b) / abs(l.a - l.b);
		res.push_back(proj(l, c.p) + len * nor);
		res.push_back(proj(l, c.p) - len * nor);
	}
	return res;
}

// 円と線分の距離
vector<Point> is_sc(Circle c, Line l) {
	vector<Point> v = is_lc(c, l), res;
	for (Point p : v)
		if (isis_sp(l, p)) res.push_back(p);
	return res;
}

// 円と点の接線
vector<Line> tangent_cp(Circle c, Point p) {
	vector<Line> ret;
	Point v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (isnan(l)) { return ret; }
	Point v1 = v * Point(l / d, c.r / d);
	Point v2 = v * Point(l / d, -c.r / d);
	ret.push_back(Line(p, p + v1));
	if (l < eps) return ret;
	ret.push_back(Line(p, p + v2));
	return ret;
}

// 円と円の接線
vector<Line> tangent_cc(Circle c1, Circle c2) {
	vector<Line> ret;
	if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
		Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
		ret = tangent_cp(c1, center);
	}
	if (abs(c1.r - c2.r) > eps) {
		Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
		vector<Line> nret = tangent_cp(c1, out);
		ret.insert(ret.end(), ALL(nret));
	}
	else {
		Point v = c2.p - c1.p;
		v /= abs(v);
		Point q1 = c1.p + v * Point(0, 1) * c1.r;
		Point q2 = c1.p + v * Point(0, -1) * c1.r;
		ret.push_back(Line(q1, q1 + v));
		ret.push_back(Line(q2, q2 + v));
	}
	return ret;
}


/* 多角形 */

typedef vector<Point> Polygon;

// 面積
ld area(const Polygon &p) {
	ld res = 0;
	int n = p.size();
	REP(j, n) res += cross(p[j], p[(j + 1) % n]);
	return res / 2;
}

// 多角形の回転方向
bool is_counter_clockwise(const Polygon &poly) {
	ld angle = 0;
	int n = poly.size();
	REP(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
		angle += arg((c - b) / (b - a));
	}
	return angle > eps;
}

// 円の内外判定
// -1 => out
//  0 => on
//  1 => in
int is_in_polygon(const Polygon &poly, Point p) {
	ld angle = 0;
	int n = poly.size();
	REP(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n];
		if (isis_sp(Line(a, b), p)) return 1;
		angle += arg((b - p) / (a - p));
	}
	return eq(angle, 0) ? 0 : 2;
}

// 凸包
Polygon convex_hull(vector<Point> ps) {
	int n = ps.size();
	int k = 0;
	sort(ps.begin(), ps.end());
	Polygon ch(2 * n);
	for (int i = 0; i < n; ch[k++] = ps[i++])
		while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
		while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	ch.resize(k - 1);
	return ch;
}

// 凸カット
Polygon convex_cut(const Polygon &ps, Line l) {
	int n = ps.size();
	Polygon Q;
	REP(i, n) {
		Point A = ps[i], B = ps[(i + 1) % n];
		Line m = Line(A, B);
		if (ccw(l.a, l.b, A) != -1) Q.push_back(A);
		if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m))
			Q.push_back(is_ll(l, m));
	}
	return Q;
}


/* アレンジメント */
void add_point(vector<Point> &ps, Point p) {
	for (Point q : ps) if (abs(q - p) < eps) return;
	ps.push_back(p);
}

typedef int Weight;

struct Edge { int from, to; Weight weight; };

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

void add_edge(Graph &g, int from, int to, Weight weight) {
	g[from].push_back(Edge{ from, to, weight });
}

Graph segment_arrangement(const vector<Line> &s, const vector<Point> &p) {
	int n = p.size(), m = s.size();
	Graph g(n);
	REP(i, m) {
		vector<pair<ld, int>> vec;
		REP(j, n) if (isis_sp(s[i], p[j]))
			vec.emplace_back(abs(s[i].a - p[j]), j);
		sort(ALL(vec));
		REP(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			add_edge(g, from, to, abs(p[from] - p[to]));
		}
	}
	return g;
}

Graph circle_arrangement(const vector<Circle> &c, const vector<Point> &p) {
	int n = p.size(), m = c.size();
	Graph g(n);
	REP(i, m) {
		vector<pair<ld, int>> vec;
		REP(j, n) if (abs(abs(c[i].p - p[j]) - c[i].r) < eps)
			vec.emplace_back(arg(c[i].p - p[j]), j);
		sort(ALL(vec));
		REP(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			ld angle = vec[j + 1].first - vec[j].first;
			add_edge(g, from, to, angle * c[i].r);
		}
		if (vec.size() >= 2) {
			int from = vec.back().second, to = vec.front().first;
			ld angle = vec.front().first - vec.back().first;
			add_edge(g, from, to, angle * c[i].r);
		}
	}
	return g;
}


/* 双対グラフ */

// 線分集合は既にアレンジメントされていなければならない．
// 内側の円は時計回りで，外側の円は反時計回りで得られる．
// 変数 polygon は，vector<int> で表される多角形の集合であり，
// vector<int> で表される 多角形のi番目は，その頂点の頂点集合pにおける番号である．
vector<vector<int>> polygon;
vector<int> seg2p[1024][1024];

Graph dual_graph(const vector<Line> &s, const vector<Point> &p) {
	int N = p.size();
	polygon.clear();
	REP(i, 1024) REP(j, 1024) seg2p[i][j].clear();
	vector<vector<tuple<ld, int, bool>>> tup(N);
	REP(i, s.size()) {
		int a = -1, b = -1;
		REP(j, N) if (abs(s[i].a - p[j]) < eps) a = j;
		REP(j, N) if (abs(s[i].b - p[j]) < eps) b = j;
		assert(a >= 0 && b >= 0);
		tup[a].emplace_back(arg(s[i].b - s[i].a), b, false);
		tup[b].emplace_back(arg(s[i].a - s[i].b), a, false);
	}
	REP(i, N) sort(ALL(tup[i]));
	REP(i, N) {
		REP(j, tup[i].size()) {
			ld angle; int pos = j, from = i, to; bool flag;
			tie(angle, to, flag) = tup[i][j];
			if (flag) continue;
			vector<int> ps;
			while (!flag) {
				ps.push_back(from);
				get<2>(tup[from][pos]) = true;
				seg2p[from][to].push_back(polygon.size());
				seg2p[to][from].push_back(polygon.size());
				angle += pi + eps;
				if (angle > pi) angle -= 2 * pi;
				auto it = lower_bound(ALL(tup[to]), make_tuple(angle, 0, false));
				if (it == tup[to].end()) it = tup[to].begin();
				from = to; tie(angle, to, flag) = *it;
				pos = it - tup[from].begin();
			}
			polygon.push_back(ps);
		}
	}
	Graph g(polygon.size());
	REP(i, N) REP(j, i) {
		if (seg2p[i][j].size() == 2) {
			int from = seg2p[i][j][0], to = seg2p[i][j][1];
			g[from].push_back(Edge{ from, to });
			g[to].push_back(Edge{ to, from });
		}
	}
	return g;
}


/* ビジュアライザ */
const ld zoom = 25;
const ld centerX = 6;
const ld centerY = 5;

void change_color(int r, int g, int b) {
	fprintf(stderr, "c.strokeStyle = 'rgb(%d, %d, %d)';\n", r, g, b);
}

int cordx(Point p) { return 400 + zoom * (p.real() - centerX); }
int cordy(Point p) { return 400 - zoom * (p.imag() - centerY); }

#define cord(p) cordx(p),cordy(p)

void draw_point(Point p) {
	fprintf(stderr, "circle(%d, %d, %d)\n", cord(p), 2);
}

void draw_segment(Line l) {
	fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(l.a), cord(l.b));
}

void draw_line(Line l) {
	Point v = l.b - l.a;
	Line m(l.a - v * Point(1e4, 0), l.b + v * Point(1e4, 0));
	fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(m.a), cord(m.b));
}

void draw_polygon(const Polygon &p) {
	int n = p.size();
	REP(i, n) draw_segment(Line(p[i], p[(i + 1) % n]));
}

void draw_circle(Circle c) {
	fprintf(stderr, "circle(%d, %d, %d)\n", cord(c.p), (int)(zoom * c.r));
}





int main() {
	int N; cin >> N;
	vector<Point>ps;
	for (int i = 0; i < N; ++i) {
		int x, y; cin >> x >> y;
		ps.emplace_back(x, y);
	}
	vector<Line>ls;
	for (int i = 0; i < N - 1; ++i) {
		ls.emplace_back(ps[i], ps[i + 1]);
	}
	int dx, dy, dvel; cin >> dx >> dy >> dvel;
	Point dp(dx, dy);
	int snum;
	for (int i = 0; i < N - 1; ++i) {
		if (isis_sp(ls[i], dp)) {
			snum = i;
		}
	}

	vector<double>times(N);
	{
		double nowtime = 0;
		Point np(dp);
		for (int i = snum + 1; i < N; ++i) {
			nowtime += abs(np - ps[i]) / dvel;
			times[i] = nowtime;
			np = ps[i];
		}
	}
	{
		double nowtime = 0;
		Point np(dp);
		for (int i = snum; i >= 0; --i) {
			nowtime += abs(np - ps[i]) / dvel;
			times[i] = nowtime;
			np = ps[i];
		}
	}
	double ans = max(times[0], times.back());
	int sx, sy, svel; cin >> sx >> sy >> svel;
	Point sp(sx, sy);
	{
		double nowtime = 0;
		Point fromp(dp);
		long double fromtime = 0;
		Point np(sp);
		bool flag = false;
		for (int i = snum + 1; i < N; ++i) {
			if ((abs(np-ps[i]) / svel) < times[i]) {
				long double amin = 0;
				long double amax = 1.0;
				while (amin + 1e-10 < amax) {
					long double amid = (amin + amax) / 2;
					long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
					long double dominotime = times[i] * amid + fromtime*(1 - amid);
					if (playertime > dominotime) {
						amin = amid;
					}
					else {
						amax = amid;
					}
				}
				nowtime= times[i] * amin + fromtime*(1 - amin);
				np = ps[i] * amin + fromp*(1 - amin);
				flag = true;
				break;
			}
			else {
				fromtime = times[i];
				fromp = ps[i];
			}
		}
		if (flag) {
			ans = min(ans, max(nowtime, times[0]));
			fromp = dp;
			fromtime = 0;
			for (int i = snum; i >= 0; --i) {
				if ((abs(np - ps[i]) / svel)+nowtime < times[i]) {
					long double amin = 0;
					long double amax = 1.0;
					while (amin + 1e-10 < amax) {
						long double amid = (amin + amax) / 2;
						long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
						long double dominotime = times[i] * amid + fromtime*(1 - amid);
						if (playertime + nowtime > dominotime) {
							amin = amid;
						}
						else {
							amax = amid;
						}
					}
					nowtime = times[i] * amin + fromtime*(1 - amin);
					ans = min(ans, nowtime);
					np = ps[i] * amin + fromp*(1 - amin);
					flag = true;
					break;
				}
				else {
					fromtime = times[i];
					fromp = ps[i];
				}
			}
		}

	}


	{
		double nowtime = 0;
		Point fromp(dp);
		long double fromtime = 0;
		Point np(sp);
		bool flag = false;
		for (int i = snum; i >= 0; --i) {
			if ((abs(np - ps[i]) / svel) < times[i]) {
				long double amin = 0;
				long double amax = 1.0;
				while (amin + 1e-10 < amax) {
					long double amid = (amin + amax) / 2;
					long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
					long double dominotime = times[i] * amid + fromtime*(1 - amid);
					if (playertime > dominotime) {
						amin = amid;
					}
					else {
						amax = amid;
					}
				}
				nowtime = times[i] * amin + fromtime*(1 - amin);
				np = ps[i] * amin + fromp*(1 - amin);
				flag = true;
				break;
			}
			else {
				fromtime = times[i];
				fromp = ps[i];
			}
		}
		if (flag) {
			ans = min(ans, max(nowtime,times.back()));
			fromp = dp;
			fromtime = 0;
			for (int i = snum + 1; i < N; ++i) {
				if ((abs(np - ps[i]) / svel) + nowtime < times[i]) {
					long double amin = 0;
					long double amax = 1.0;
					while (amin + 1e-10 < amax) {
						long double amid = (amin + amax) / 2;
						long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
						long double dominotime = times[i] * amid + fromtime*(1 - amid);
						if (playertime + nowtime > dominotime) {
							amin = amid;
						}
						else {
							amax = amid;
						}
					}
					nowtime = times[i] * amin + fromtime*(1 - amin) ;
					ans = min(ans, nowtime);
					np = ps[i] * amin + fromp*(1 - amin);
					flag = true;
					break;
				}
				else {
					fromtime = times[i];
					fromp = ps[i];
				}
			}
		}

	}
	cout << fixed<<setprecision(32)<<ans << endl;
	return 0;
}
accuracy: 0.6395348837209303
time_ms: 10
memory_kb: 28040
final_rank: 7

code_snippet: #include<stdio.h>
#include <iostream>
#include <math.h>
#include <numeric>
#include <vector>
#include <map>
#include <functional>
#include <stdio.h>
#include <array>
#include <algorithm>
#include <string>
#include <string.h>
#include <assert.h>
#include <stdio.h>
#include <queue>
#include<iomanip>
#include<bitset>
#include<stack>
#include<set>
#include<limits>
#include <complex>
using namespace std;



#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()




/* 幾何の基本 */

#include <complex>

typedef long double ld;
typedef complex<ld> Point;

const ld eps = 1e-9, pi = acos(-1.0);

namespace std {
	bool operator<(const Point &lhs, const Point &rhs) {
		if (lhs.real() < rhs.real() - eps) return true;
		if (lhs.real() > rhs.real() + eps) return false;
		return lhs.imag() < rhs.imag();
	}
}

// 点の入力
Point input_point() {
	ld x, y;
	cin >> x >> y;
	return Point(x, y);
}

// 誤差つき等号判定
bool eq(ld a, ld b) {
	return (abs(a - b) < eps);
}

// 内積
ld dot(Point a, Point b) {
	return real(conj(a) * b);
}

// 外積
ld cross(Point a, Point b) {
	return imag(conj(a) * b);
}

// 直線の定義
class Line {
public:
	Point a, b;
	Line() : a(Point(0, 0)), b(Point(0, 0)) {}
	Line(Point a, Point b) : a(a), b(b) {}
};

// 円の定義
class Circle {
public:
	Point p;
	ld r;
	Circle() : p(Point(0, 0)), r(0) {}
	Circle(Point p, ld r) : p(p), r(r) {}
};

// CCW
int ccw(Point a, Point b, Point c) {
	b -= a; c -= a;
	if (cross(b, c) > eps) return 1;   // a,b,cが反時計周りの順に並ぶ
	if (cross(b, c) < -eps) return -1; // a,b,cが時計周りの順に並ぶ
	if (dot(b, c) < 0) return 2;       // c,a,bの順に直線に並ぶ
	if (norm(b) < norm(c)) return -2;  // a,b,cの順に直線に並ぶ
	return 0;                          // a,c,bの順に直線に並ぶ
}


/* 交差判定 */

// 直線と直線の交差判定
bool isis_ll(Line l, Line m) {
	return !eq(cross(l.b - l.a, m.b - m.a), 0);
}

// 直線と線分の交差判定
bool isis_ls(Line l, Line s) {
	return isis_ll(l, s) &&
		(cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

// 線分と線分の交差判定
bool isis_ss(Line s, Line t) {
	return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
		ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

// 点の直線上判定
bool isis_lp(Line l, Point p) {
	return (abs(cross(l.b - p, l.a - p)) < eps);
}

// 点の線分上判定
bool isis_sp(Line s, Point p) {
	return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

// 垂線の足
Point proj(Line l, Point p) {
	ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
	return l.a + t * (l.a - l.b);
}

// 直線と直線の交点
Point is_ll(Line s, Line t) {
	Point sv = s.b - s.a, tv = t.b - t.a;
	assert(cross(sv, tv) != 0);
	return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

// 直線と点の距離
ld dist_lp(Line l, Point p) {
	return abs(p - proj(l, p));
}

// 直線と直線の距離
ld dist_ll(Line l, Line m) {
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

// 直線と線分の距離
ld dist_ls(Line l, Line s) {
	return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// 線分と点の距離
ld dist_sp(Line s, Point p) {
	Point r = proj(s, p);
	return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// 線分と線分の距離
ld dist_ss(Line s, Line t) {
	if (isis_ss(s, t)) return 0;
	return min({ dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b) });
}


/* 円 */

// 円と円の交点
vector<Point> is_cc(Circle c1, Circle c2) {
	vector<Point> res;
	ld d = abs(c1.p - c2.p);
	ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
	ld dfr = c1.r * c1.r - rc * rc;
	if (abs(dfr) < eps) dfr = 0.0;
	else if (dfr < 0.0) return res; // no intersection
	ld rs = sqrt(dfr);
	Point diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * Point(rc, rs));
	if (dfr != 0.0) res.push_back(c1.p + diff * Point(rc, -rs));
	return res;
}

// 円と直線の交点
vector<Point> is_lc(Circle c, Line l) {
	vector<Point> res;
	ld d = dist_lp(l, c.p);
	if (d < c.r + eps) {
		ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
		Point nor = (l.a - l.b) / abs(l.a - l.b);
		res.push_back(proj(l, c.p) + len * nor);
		res.push_back(proj(l, c.p) - len * nor);
	}
	return res;
}

// 円と線分の距離
vector<Point> is_sc(Circle c, Line l) {
	vector<Point> v = is_lc(c, l), res;
	for (Point p : v)
		if (isis_sp(l, p)) res.push_back(p);
	return res;
}

// 円と点の接線
vector<Line> tangent_cp(Circle c, Point p) {
	vector<Line> ret;
	Point v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (isnan(l)) { return ret; }
	Point v1 = v * Point(l / d, c.r / d);
	Point v2 = v * Point(l / d, -c.r / d);
	ret.push_back(Line(p, p + v1));
	if (l < eps) return ret;
	ret.push_back(Line(p, p + v2));
	return ret;
}

// 円と円の接線
vector<Line> tangent_cc(Circle c1, Circle c2) {
	vector<Line> ret;
	if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
		Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
		ret = tangent_cp(c1, center);
	}
	if (abs(c1.r - c2.r) > eps) {
		Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
		vector<Line> nret = tangent_cp(c1, out);
		ret.insert(ret.end(), ALL(nret));
	}
	else {
		Point v = c2.p - c1.p;
		v /= abs(v);
		Point q1 = c1.p + v * Point(0, 1) * c1.r;
		Point q2 = c1.p + v * Point(0, -1) * c1.r;
		ret.push_back(Line(q1, q1 + v));
		ret.push_back(Line(q2, q2 + v));
	}
	return ret;
}


/* 多角形 */

typedef vector<Point> Polygon;

// 面積
ld area(const Polygon &p) {
	ld res = 0;
	int n = p.size();
	REP(j, n) res += cross(p[j], p[(j + 1) % n]);
	return res / 2;
}

// 多角形の回転方向
bool is_counter_clockwise(const Polygon &poly) {
	ld angle = 0;
	int n = poly.size();
	REP(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
		angle += arg((c - b) / (b - a));
	}
	return angle > eps;
}

// 円の内外判定
// -1 => out
//  0 => on
//  1 => in
int is_in_polygon(const Polygon &poly, Point p) {
	ld angle = 0;
	int n = poly.size();
	REP(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n];
		if (isis_sp(Line(a, b), p)) return 1;
		angle += arg((b - p) / (a - p));
	}
	return eq(angle, 0) ? 0 : 2;
}

// 凸包
Polygon convex_hull(vector<Point> ps) {
	int n = ps.size();
	int k = 0;
	sort(ps.begin(), ps.end());
	Polygon ch(2 * n);
	for (int i = 0; i < n; ch[k++] = ps[i++])
		while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
		while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	ch.resize(k - 1);
	return ch;
}

// 凸カット
Polygon convex_cut(const Polygon &ps, Line l) {
	int n = ps.size();
	Polygon Q;
	REP(i, n) {
		Point A = ps[i], B = ps[(i + 1) % n];
		Line m = Line(A, B);
		if (ccw(l.a, l.b, A) != -1) Q.push_back(A);
		if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m))
			Q.push_back(is_ll(l, m));
	}
	return Q;
}


/* アレンジメント */
void add_point(vector<Point> &ps, Point p) {
	for (Point q : ps) if (abs(q - p) < eps) return;
	ps.push_back(p);
}

typedef int Weight;

struct Edge { int from, to; Weight weight; };

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

void add_edge(Graph &g, int from, int to, Weight weight) {
	g[from].push_back(Edge{ from, to, weight });
}

Graph segment_arrangement(const vector<Line> &s, const vector<Point> &p) {
	int n = p.size(), m = s.size();
	Graph g(n);
	REP(i, m) {
		vector<pair<ld, int>> vec;
		REP(j, n) if (isis_sp(s[i], p[j]))
			vec.emplace_back(abs(s[i].a - p[j]), j);
		sort(ALL(vec));
		REP(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			add_edge(g, from, to, abs(p[from] - p[to]));
		}
	}
	return g;
}

Graph circle_arrangement(const vector<Circle> &c, const vector<Point> &p) {
	int n = p.size(), m = c.size();
	Graph g(n);
	REP(i, m) {
		vector<pair<ld, int>> vec;
		REP(j, n) if (abs(abs(c[i].p - p[j]) - c[i].r) < eps)
			vec.emplace_back(arg(c[i].p - p[j]), j);
		sort(ALL(vec));
		REP(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			ld angle = vec[j + 1].first - vec[j].first;
			add_edge(g, from, to, angle * c[i].r);
		}
		if (vec.size() >= 2) {
			int from = vec.back().second, to = vec.front().first;
			ld angle = vec.front().first - vec.back().first;
			add_edge(g, from, to, angle * c[i].r);
		}
	}
	return g;
}


/* 双対グラフ */

// 線分集合は既にアレンジメントされていなければならない．
// 内側の円は時計回りで，外側の円は反時計回りで得られる．
// 変数 polygon は，vector<int> で表される多角形の集合であり，
// vector<int> で表される 多角形のi番目は，その頂点の頂点集合pにおける番号である．
vector<vector<int>> polygon;
vector<int> seg2p[1024][1024];

Graph dual_graph(const vector<Line> &s, const vector<Point> &p) {
	int N = p.size();
	polygon.clear();
	REP(i, 1024) REP(j, 1024) seg2p[i][j].clear();
	vector<vector<tuple<ld, int, bool>>> tup(N);
	REP(i, s.size()) {
		int a = -1, b = -1;
		REP(j, N) if (abs(s[i].a - p[j]) < eps) a = j;
		REP(j, N) if (abs(s[i].b - p[j]) < eps) b = j;
		assert(a >= 0 && b >= 0);
		tup[a].emplace_back(arg(s[i].b - s[i].a), b, false);
		tup[b].emplace_back(arg(s[i].a - s[i].b), a, false);
	}
	REP(i, N) sort(ALL(tup[i]));
	REP(i, N) {
		REP(j, tup[i].size()) {
			ld angle; int pos = j, from = i, to; bool flag;
			tie(angle, to, flag) = tup[i][j];
			if (flag) continue;
			vector<int> ps;
			while (!flag) {
				ps.push_back(from);
				get<2>(tup[from][pos]) = true;
				seg2p[from][to].push_back(polygon.size());
				seg2p[to][from].push_back(polygon.size());
				angle += pi + eps;
				if (angle > pi) angle -= 2 * pi;
				auto it = lower_bound(ALL(tup[to]), make_tuple(angle, 0, false));
				if (it == tup[to].end()) it = tup[to].begin();
				from = to; tie(angle, to, flag) = *it;
				pos = it - tup[from].begin();
			}
			polygon.push_back(ps);
		}
	}
	Graph g(polygon.size());
	REP(i, N) REP(j, i) {
		if (seg2p[i][j].size() == 2) {
			int from = seg2p[i][j][0], to = seg2p[i][j][1];
			g[from].push_back(Edge{ from, to });
			g[to].push_back(Edge{ to, from });
		}
	}
	return g;
}


/* ビジュアライザ */
const ld zoom = 25;
const ld centerX = 6;
const ld centerY = 5;

void change_color(int r, int g, int b) {
	fprintf(stderr, "c.strokeStyle = 'rgb(%d, %d, %d)';\n", r, g, b);
}

int cordx(Point p) { return 400 + zoom * (p.real() - centerX); }
int cordy(Point p) { return 400 - zoom * (p.imag() - centerY); }

#define cord(p) cordx(p),cordy(p)

void draw_point(Point p) {
	fprintf(stderr, "circle(%d, %d, %d)\n", cord(p), 2);
}

void draw_segment(Line l) {
	fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(l.a), cord(l.b));
}

void draw_line(Line l) {
	Point v = l.b - l.a;
	Line m(l.a - v * Point(1e4, 0), l.b + v * Point(1e4, 0));
	fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(m.a), cord(m.b));
}

void draw_polygon(const Polygon &p) {
	int n = p.size();
	REP(i, n) draw_segment(Line(p[i], p[(i + 1) % n]));
}

void draw_circle(Circle c) {
	fprintf(stderr, "circle(%d, %d, %d)\n", cord(c.p), (int)(zoom * c.r));
}





int main() {
	int N; cin >> N;
	vector<Point>ps;
	for (int i = 0; i < N; ++i) {
		int x, y; cin >> x >> y;
		ps.emplace_back(x, y);
	}
	vector<Line>ls;
	for (int i = 0; i < N - 1; ++i) {
		ls.emplace_back(ps[i], ps[i + 1]);
	}
	int dx, dy, dvel; cin >> dx >> dy >> dvel;
	Point dp(dx, dy);
	int snum;
	for (int i = 0; i < N - 1; ++i) {
		if (isis_sp(ls[i], dp)) {
			snum = i;
		}
	}

	vector<double>times(N);
	{
		double nowtime = 0;
		Point np(dp);
		for (int i = snum + 1; i < N; ++i) {
			nowtime += abs(np - ps[i]) / dvel;
			times[i] = nowtime;
			np = ps[i];
		}
	}
	{
		double nowtime = 0;
		Point np(dp);
		for (int i = snum; i >= 0; --i) {
			nowtime += abs(np - ps[i]) / dvel;
			times[i] = nowtime;
			np = ps[i];
		}
	}
	double ans = max(times[0], times.back());
	int sx, sy, svel; cin >> sx >> sy >> svel;
	Point sp(sx, sy);
	{
		double nowtime = 0;
		Point fromp(dp);
		long double fromtime = 0;
		Point np(sp);
		bool flag = false;
		for (int i = snum + 1; i < N; ++i) {
			if ((abs(np-ps[i]) / svel) < times[i]) {
				long double amin = 0;
				long double amax = 1.0;
				while (amin + 1e-10 < amax) {
					long double amid = (amin + amax) / 2;
					long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
					long double dominotime = times[i] * amid + fromtime*(1 - amid);
					if (playertime > dominotime) {
						amin = amid;
					}
					else {
						amax = amid;
					}
				}
				nowtime= times[i] * amin + fromtime*(1 - amin);
				np = ps[i] * amin + fromp*(1 - amin);
				flag = true;
				break;
			}
			else {
				fromtime = times[i];
				fromp = ps[i];
			}
		}
		if (flag) {
			ans = min(ans, times[0]);
			fromp = dp;
			fromtime = 0;
			for (int i = snum; i >= 0; --i) {
				if ((abs(np - ps[i]) / svel)+nowtime < times[i]) {
					long double amin = 0;
					long double amax = 1.0;
					while (amin + 1e-10 < amax) {
						long double amid = (amin + amax) / 2;
						long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
						long double dominotime = times[i] * amid + fromtime*(1 - amid);
						if (playertime + nowtime > dominotime) {
							amin = amid;
						}
						else {
							amax = amid;
						}
					}
					nowtime = times[i] * amin + fromtime*(1 - amin);
					ans = min(ans, nowtime);
					np = ps[i] * amin + fromp*(1 - amin);
					flag = true;
					break;
				}
				else {
					fromtime = times[i];
					fromp = ps[i];
				}
			}
		}

	}


	{
		double nowtime = 0;
		Point fromp(dp);
		long double fromtime = 0;
		Point np(sp);
		bool flag = false;
		for (int i = snum; i >= 0; --i) {
			if ((abs(np - ps[i]) / svel) < times[i]) {
				long double amin = 0;
				long double amax = 1.0;
				while (amin + 1e-10 < amax) {
					long double amid = (amin + amax) / 2;
					long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
					long double dominotime = times[i] * amid + fromtime*(1 - amid);
					if (playertime > dominotime) {
						amin = amid;
					}
					else {
						amax = amid;
					}
				}
				nowtime = times[i] * amin + fromtime*(1 - amin);
				np = ps[i] * amin + fromp*(1 - amin);
				flag = true;
				break;
			}
			else {
				fromtime = times[i];
				fromp = ps[i];
			}
		}
		if (flag) {
			ans = min(ans, times.back());
			fromp = dp;
			fromtime = 0;
			for (int i = snum + 1; i < N; ++i) {
				if ((abs(np - ps[i]) / svel) + nowtime < times[i]) {
					long double amin = 0;
					long double amax = 1.0;
					while (amin + 1e-10 < amax) {
						long double amid = (amin + amax) / 2;
						long double playertime = abs(np - (ps[i] * amid + fromp*(1 - amid))) / svel;
						long double dominotime = times[i] * amid + fromtime*(1 - amid);
						if (playertime + nowtime > dominotime) {
							amin = amid;
						}
						else {
							amax = amid;
						}
					}
					nowtime = times[i] * amin + fromtime*(1 - amin) ;
					ans = min(ans, nowtime);
					np = ps[i] * amin + fromp*(1 - amin);
					flag = true;
					break;
				}
				else {
					fromtime = times[i];
					fromp = ps[i];
				}
			}
		}

	}
	cout << fixed<<setprecision(32)<<ans << endl;
	return 0;
}
accuracy: 0.06976744186046512
time_ms: 10
memory_kb: 27928
final_rank: 8

code_snippet: #include<bits/stdc++.h>

#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define EPS (1e-7)
#define equals(a,b) (fabs((a)-(b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1 
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

class Point{
public:
  double x,y;

  Point(double x = 0,double y = 0): x(x),y(y){}

  Point operator + (Point p){return Point(x+p.x,y+p.y);}
  Point operator - (Point p){return Point(x-p.x,y-p.y);}
  Point operator * (double a){return Point(a*x,a*y);}
  Point operator / (double a){return Point(x/a,y/a);}
  Point operator * (Point a){ return Point(x * a.x - y * a.y, x * a.y + y * a.x); }

  bool operator < (const Point& p) const{ return !equals(x,p.x)?x<p.x:(!equals(y,p.y)&&y<p.y); }

  bool operator == (const Point& p)const{ return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS; }

};

typedef Point Vector;


double dot(Point a,Point b){ return a.x*b.x + a.y*b.y; }
double cross(Point a,Point b){ return a.x*b.y - a.y*b.x; }
double norm(Point a){ return a.x*a.x+a.y*a.y; }
double abs(Point a){ return sqrt(norm(a)); }

int ccw(Point p0,Point p1,Point p2){
  Point a = p1-p0;
  Point b = p2-p0;
  if(cross(a,b) > EPS)return COUNTER_CLOCKWISE;
  if(cross(a,b) < -EPS)return CLOCKWISE;
  if(dot(a,b) < -EPS)return ONLINE_BACK;
  if(norm(a) < norm(b))return ONLINE_FRONT;
  return ON_SEGMENT;
}

double cross3p(Point p,Point q,Point r) { return (r.x-q.x) * (p.y -q.y) - (r.y - q.y) * (p.x - q.x); }
  
bool collinear(Point p,Point q,Point r) { return fabs(cross3p(p,q,r)) < EPS; }
 
bool onSegment(Point p,Point q,Point r){
  return collinear(p,q,r) && equals(sqrt(pow(p.x-r.x,2)+pow(p.y-r.y,2)) + sqrt(pow(r.x-q.x,2) + pow(r.y-q.y,2) ),sqrt(pow(p.x-q.x,2)+pow(p.y-q.y,2)) ) ;
}

int n,tp;
vector<Point> ps,nps;
Point topple,sp;
double v[2];

inline bool isValid(int x) { return 0 <= x && x < nps.size(); }
inline bool LTE(double a,double b) { return  equals(a,b) || a < b; }
inline bool LT(double  a,double b) { return !equals(a,b) && a < b; }

Point getPoint(double t,int dir){
  int coef = (dir?1:-1);
  int cur = tp;
  double remain = t;
  while( isValid(cur+coef) ) {
    double len = abs( nps[cur+coef] - nps[cur] );
    Vector e = ( nps[cur+coef] - nps[cur] ) / len;
    Point p = nps[cur] + e * ( remain * v[0] );
    if( onSegment(nps[cur],nps[cur+coef],p) ) return p;
    cur += coef;
    remain -= len / v[0];
    assert( LTE(0,remain) );
  }
  return nps[cur];
}

bool check(double limit,int dir){

  Point LP = getPoint(limit,dir);

  Point temp_P = getPoint(limit,!dir);

  if( ( LP == nps[0] || LP == nps[(int)nps.size()-1] ) && ( temp_P == nps[0] || temp_P == nps[(int)nps.size()-1] ) ) return true;

  double len_temp = abs( LP - sp );
  double time_temp = len_temp / v[1];
  if( !LTE(time_temp,limit) ) return false;

  Point p = getPoint(limit,!dir);
  if( p == nps[0] || p == nps[(int)nps.size()-1] ) {
      double len = abs( LP - sp );
      double ntime = len / v[1];
      if( LTE(ntime,limit) ) return true;
  }

  double L = 0, R = limit;
  bool success = false;
  rep(_,120){
    double M = ( L + R ) * 0.5;
    p = getPoint(limit-M,!dir);
    double len = abs( LP - p );
    double ntime = len / v[1];
    if( !LTE(ntime,M) ) { L = M; }
    else R = M, success = true;
  }
  if( !success ) return false;
  p = getPoint(limit-L,!dir);
  double len = abs( LP - p ) + abs( p - sp );
  double ntime = len / v[1];
  return LTE(ntime,limit);
}

void compute(){
  nps.clear();
  nps.push_back(ps[0]);
  bool already = false;
  REP(i,1,n) {
    if( !already && onSegment(ps[i-1],ps[i],topple) ) { 
      tp = nps.size();
      nps.push_back(topple);
      already = true;
    }
    nps.push_back(ps[i]);
  }
  double L = 0, R = 1e10;
  bool success = false;
  rep(_,120){
    double M = ( L + R ) * 0.5;
    if( check(M,0) || check(M,1) ) R = M;
    else           L = M;
  }
  printf("%.10f\n",L);
}

int main(){
  cin >> n;
  ps.resize(n);
  rep(i,n) cin >> ps[i].x >> ps[i].y;
  cin >> topple.x >> topple.y >> v[0];
  cin >> sp.x >> sp.y >> v[1];
  compute();
  return 0;
}
accuracy: 1
time_ms: 20
memory_kb: 1300
final_rank: 3

code_snippet: #include<bits/stdc++.h>

#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define EPS (1e-7)
#define equals(a,b) (fabs((a)-(b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1 
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

class Point{
public:
  double x,y;

  Point(double x = 0,double y = 0): x(x),y(y){}

  Point operator + (Point p){return Point(x+p.x,y+p.y);}
  Point operator - (Point p){return Point(x-p.x,y-p.y);}
  Point operator * (double a){return Point(a*x,a*y);}
  Point operator / (double a){return Point(x/a,y/a);}
  Point operator * (Point a){ return Point(x * a.x - y * a.y, x * a.y + y * a.x); }

  bool operator < (const Point& p) const{ return !equals(x,p.x)?x<p.x:(!equals(y,p.y)&&y<p.y); }

  bool operator == (const Point& p)const{ return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS; }

};

struct Segment{
  Point p1,p2;
  Segment(Point p1 = Point(),Point p2 = Point()):p1(p1),p2(p2){}
  bool operator <  (const Segment& s) const { return ( p2 == s.p2 ) ? p1 < s.p1 : p2 < s.p2; }
  bool operator == (const Segment& s) const { return ( s.p1 == p1 && s.p2 == p2 ) || ( s.p1 == p2 && s.p2 == p1 ); }

};

typedef Point Vector;
typedef Segment Line;
typedef vector<Point> Polygon;

ostream& operator << (ostream& os,const Point& a){ os << "(" << a.x << "," << a.y << ")"; }

ostream& operator << (ostream& os,const Segment& a){ os << "( " << a.p1 << " , " << a.p2 << " )"; }

double dot(Point a,Point b){ return a.x*b.x + a.y*b.y; }

double cross(Point a,Point b){ return a.x*b.y - a.y*b.x; }

double norm(Point a){ return a.x*a.x+a.y*a.y; }

double abs(Point a){ return sqrt(norm(a)); }

//rad は角度をラジアンで持たせること
Point rotate(Point a,double rad){ return Point(cos(rad)*a.x - sin(rad)*a.y,sin(rad)*a.x + cos(rad)*a.y); }

// 度をラジアンに変換
double toRad(double agl){ return agl*M_PI/180.0; }

// a => prev, b => cur, c=> next
// prev から cur へ行って next へ行く際の角度を求める
double getArg(Point a,Point b,Point c){
  double arg1 = atan2(b.y-a.y,b.x-a.x);
  double arg2 = atan2(c.y-b.y,c.x-b.x);
  double arg = fabs( arg1 - arg2 );
  while( arg > M_PI ) arg -= 2.0 * M_PI;
  return fabs(arg);
}

int ccw(Point p0,Point p1,Point p2){
  Point a = p1-p0;
  Point b = p2-p0;
  if(cross(a,b) > EPS)return COUNTER_CLOCKWISE;
  if(cross(a,b) < -EPS)return CLOCKWISE;
  if(dot(a,b) < -EPS)return ONLINE_BACK;
  if(norm(a) < norm(b))return ONLINE_FRONT;
  return ON_SEGMENT;
}

bool intersectLL(Line l, Line m) {
  return abs(cross(l.p2-l.p1, m.p2-m.p1)) > EPS || // non-parallel
         abs(cross(l.p2-l.p1, m.p1-l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2-l.p1, s.p1-l.p1)*       // s[0] is left of l
         cross(l.p2-l.p1, s.p2-l.p1) < EPS; // s[1] is right of l
}
bool intersectLP(Line l,Point p) {
  return abs(cross(l.p2-p, l.p1-p)) < EPS;
}
bool intersectSS(Line s, Line t) {
  return ccw(s.p1,s.p2,t.p1)*ccw(s.p1,s.p2,t.p2) <= 0 &&
         ccw(t.p1,t.p2,s.p1)*ccw(t.p1,t.p2,s.p2) <= 0;
}
bool intersectSP(Line s, Point p) {
  return abs(s.p1-p)+abs(s.p2-p)-abs(s.p2-s.p1) < EPS; // triangle inequality
}

Point projection(Line l,Point p) {
  double t = dot(p-l.p1, l.p1-l.p2) / norm(l.p1-l.p2);
  return l.p1 + (l.p1-l.p2)*t;
}
Point reflection(Line l,Point p) {
  return p + (projection(l, p) - p) * 2;
}
double distanceLP(Line l, Point p) {
  return abs(p - projection(l, p));
}
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}

double distanceLS(Line l, Line s) {
  if (intersectLS(l, s)) return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
double distanceSP(Line s, Point p) {
  Point r = projection(s, p);
  if (intersectSP(s, r)) return abs(r - p);
  return min(abs(s.p1 - p), abs(s.p2 - p));
}

double distanceSS(Line s, Line t) {
  if (intersectSS(s, t)) return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.p2)));
}

Point crosspoint(Line l,Line m){
  double A = cross(l.p2-l.p1,m.p2-m.p1);
  double B = cross(l.p2-l.p1,l.p2-m.p1);
  if(abs(A) < EPS && abs(B) < EPS){
    vector<Point> vec;
    vec.push_back(l.p1),vec.push_back(l.p2),vec.push_back(m.p1),vec.push_back(m.p2);
    sort(vec.begin(),vec.end());
    assert(vec[1] == vec[2]); //同じセグメントかもよ
    return vec[1];
    //return m.p1;
  }
  if(abs(A) < EPS)assert(false);
  return m.p1 + (m.p2-m.p1)*(B/A);
}

//cross product of pq and pr
double cross3p(Point p,Point q,Point r) { return (r.x-q.x) * (p.y -q.y) - (r.y - q.y) * (p.x - q.x); }
  
//returns true if point r is on the same line as the line pq
bool collinear(Point p,Point q,Point r) { return fabs(cross3p(p,q,r)) < EPS; }
  
//returns true if point t is on the left side of line pq
bool ccwtest(Point p,Point q,Point r){
  return cross3p(p,q,r) > 0; //can be modified to accept collinear points
}
 
bool onSegment(Point p,Point q,Point r){
  return collinear(p,q,r) && equals(sqrt(pow(p.x-r.x,2)+pow(p.y-r.y,2)) + sqrt(pow(r.x-q.x,2) + pow(r.y-q.y,2) ),sqrt(pow(p.x-q.x,2)+pow(p.y-q.y,2)) ) ;
}
  

bool isConvex(vector<Point> p) {
  int sz = (int)p.size();
  if(sz < 3)return false;//boundary case, we treat a point or a line as not convex
  bool isLeft = ccwtest(p[0],p[1],p[2]);
  for(int i=1; i<(int)p.size();i++)
    if(ccwtest(p[i],p[(i+1)%sz],p[(i+2)%sz]) != isLeft) return false;
  return true;
}


double angle(Point a,Point b,Point c) {
  double ux = b.x - a.x, uy = b.y - a.y;
  double vx = c.x - a.x, vy = c.y - a.y;
  return acos((ux*vx + uy*vy)/sqrt((ux*ux + uy*uy) * (vx*vx + vy*vy)));
}  
  
//多角形poly内（線分上も含む）に点pが存在するかどうは判定する  
bool inPolygon(Polygon poly,Point p){
  if((int)poly.size() == 0)return false;
  rep(i,poly.size()) if(onSegment(poly[i],poly[(i+1)%poly.size()],p))return true;
  double sum = 0;
  for(int i=0; i < (int)poly.size() ;i++) {
    if( equals(cross(poly[i]-p,poly[(i+1)%poly.size()]-p),0.0) ) continue; // ３点が平行だとangleがnanを返しsumがnanになり死ぬ
    if( cross3p(p,poly[i],poly[(i+1)%poly.size()]) < 0 ) sum -= angle(p,poly[i],poly[(i+1)%poly.size()]);
    else                                                 sum += angle(p,poly[i],poly[(i+1)%poly.size()]);
  }
  // あまり誤差を厳しくしすぎると良くないので以下のほうが良い 
  const double eps = 1e-5;
  return (fabs(sum - 2*M_PI) < eps || fabs(sum + 2*M_PI) < eps);
}  


int n,tp;
vector<Point> ps,nps;
Point topple,sp;
double v[2];

inline bool isValid(int x) { return 0 <= x && x < nps.size(); }
inline bool LTE(double a,double b) { return  equals(a,b) || a < b; }
inline bool LT(double  a,double b) { return !equals(a,b) && a < b; }

Point getPoint(double t,int dir){
  int coef = (dir?1:-1);
  int cur = tp;
  double remain = t;
  while( isValid(cur+coef) ) {
    double len = abs( nps[cur+coef] - nps[cur] );
    Vector e = ( nps[cur+coef] - nps[cur] ) / len;
    Point p = nps[cur] + e * ( remain * v[0] );
    if( onSegment(nps[cur],nps[cur+coef],p) ) return p;
    cur += coef;
    remain -= len / v[0];
    assert( LTE(0,remain) );
  }
  return nps[cur];
}



bool check(double limit,int dir){

  Point LP = getPoint(limit,dir);



  Point temp_P = getPoint(limit,!dir);

  if( ( LP == nps[0] || LP == nps[(int)nps.size()-1] ) && ( temp_P == nps[0] || temp_P == nps[(int)nps.size()-1] ) ) return true;

  double len_temp = abs( LP - sp );
  double time_temp = len_temp / v[1];
  if( !LTE(time_temp,limit) ) return false;

  Point p = getPoint(limit,!dir);
  if( p == nps[0] || p == nps[(int)nps.size()-1] ) {
      double len = abs( LP - sp );
      double ntime = len / v[1];
      if( LTE(ntime,limit) ) return true;
  }

  double L = 0, R = limit;
  bool success = false;
  rep(_,120){
    double M = ( L + R ) * 0.5;
    p = getPoint(limit-M,!dir);
    double len = abs( LP - p );
    double ntime = len / v[1];
    if( !LTE(ntime,M) ) { L = M; }
    else R = M, success = true;
  }
  if( !success ) return false;
  p = getPoint(limit-L,!dir);
  double len = abs( LP - p ) + abs( p - sp );
  double ntime = len / v[1];
  return LTE(ntime,limit);
}

void compute(){
  nps.clear();
  nps.push_back(ps[0]);
  bool already = false;
  REP(i,1,n) {
    if( !already && onSegment(ps[i-1],ps[i],topple) ) { 
      tp = nps.size();
      nps.push_back(topple);
      already = true;
    }
    nps.push_back(ps[i]);
  }
  assert( already );

  //cout << check(7,1) << endl;
  //return; 
  /*
    double t;
    int d;
    while( cin >> t >> d){

    cout << getPoint(t,d) << endl;
    cout << "check = " << check(t,d) << endl;
    Point p1 = getPoint(t,d), p2 = getPoint(t,!d);
    cout << p1 << " " << p2 << endl;
    cout << ( abs( p1 - p2 ) + abs( p2 - sp ) ) / v[1] << endl;
  }

    return;
  */
  double L = 0, R = 1e10;
  bool success = false;
  rep(_,120){
    double M = ( L + R ) * 0.5;
    if( check(M,0) || check(M,1) ) R = M;
    else           L = M;
  }
  printf("%.10f\n",L);
}

int main(){
  cin >> n;
  ps.resize(n);
  rep(i,n) cin >> ps[i].x >> ps[i].y;
  cin >> topple.x >> topple.y >> v[0];
  cin >> sp.x >> sp.y >> v[1];
  compute();
  return 0;
}
accuracy: 1
time_ms: 20
memory_kb: 1308
final_rank: 4

code_snippet: #include <bits/stdc++.h>
using namespace std;

#define dump(n) cout<<"# "<<#n<<'='<<(n)<<endl
#define repi(i,a,b) for(int i=int(a);i<int(b);i++)
#define peri(i,a,b) for(int i=int(b);i-->int(a);)
#define rep(i,n) repi(i,0,n)
#define per(i,n) peri(i,0,n)
#define all(c) begin(c),end(c)
#define mp make_pair
#define mt make_tuple

typedef unsigned int uint;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<string> vs;

const int INF=1e9;
const int MOD=1e9+7;
const double EPS=1e-7;

template<typename T1,typename T2>
ostream& operator<<(ostream& os,const pair<T1,T2>& p){
	return os<<'('<<p.first<<','<<p.second<<')';
}
template<typename T>
ostream& operator<<(ostream& os,const vector<T>& a){
	os<<'[';
	rep(i,a.size()) os<<(i?" ":"")<<a[i];
	return os<<']';
}

struct Point{
	double x,y;
	Point(){}
	Point(double x,double y):x(x),y(y){}
	Point& operator+=(Point p){x+=p.x,y+=p.y; return *this;}
	Point& operator-=(Point p){x-=p.x,y-=p.y; return *this;}
	Point& operator*=(double c){x*=c,y*=c; return *this;}
	Point& operator/=(double c){x/=c,y/=c; return *this;}
};
Point operator+(Point a,Point b){return a+=b;}
Point operator-(Point a,Point b){return a-=b;}
Point operator*(Point a,double c){return a*=c;}
Point operator*(double c,Point a){return a*=c;}
Point operator/(Point a,double c){return a/=c;}
bool operator==(Point a,Point b){return abs(a.x-b.x)<EPS && abs(a.y-b.y)<EPS;}
bool operator!=(Point a,Point b){return !(a==b);}

struct Line{
	Point pos,dir;
	Line(){}
	Line(Point p,Point d):pos(p),dir(d){}
	Line(double x,double y,double u,double v):pos(x,y),dir(u,v){}
};

struct Segment{
	Point pos,dir;
	Segment(){}
	Segment(Point p,Point d):pos(p),dir(d){}
	Segment(double x,double y,double u,double v):pos(x,y),dir(u,v){}
	explicit Segment(Line l):pos(l.pos),dir(l.dir){}
	explicit operator Line()const{return Line(pos,dir);}
};

ostream& operator<<(ostream& os,const Point& p){
	return os<<'('<<p.x<<','<<p.y<<')';
}
ostream& operator<<(ostream& os,const Line& l){
	return os<<'('<<l.pos<<','<<l.dir<<')';
}
ostream& operator<<(ostream& os,const Segment& s){
	return os<<'('<<s.pos<<','<<s.dir<<')';
}

int Signum(double x){
	return x<-EPS?-1:x>EPS?1:0;
}
double Abs(Point p){
	return sqrt(p.x*p.x+p.y*p.y);
}
double Abs2(Point p){
	return p.x*p.x+p.y*p.y;
}
double Arg(Point p){
	return atan2(p.y,p.x);
}
double Dot(Point a,Point b){
	return a.x*b.x+a.y*b.y;
}
double Cross(Point a,Point b){
	return a.x*b.y-a.y*b.x;
}
Point Rot(Point p,double t){
	return Point(cos(t)*p.x-sin(t)*p.y,sin(t)*p.x+cos(t)*p.y);
}

int CCW(Point a,Point b,Point c){
	b-=a,c-=a;
	if(int sign=Signum(Cross(b,c)))
		return sign; // 1:ccw,-1:cw
	if(Dot(b,c)<-EPS)
		return -2;   // c-a-b
	if(Abs(b)<Abs(c)-EPS)
		return 2;    // a-b-c
	return 0;        // a-c-b (inclusive)
}

tuple<Point,Point> after(const vector<Point>& ps,Point pt,double vt,double t)
{
	int n=ps.size(),k=-1;
	rep(i,n-1) if(CCW(ps[i],ps[i+1],pt)==0){
		k=i;
	}
	assert(k!=-1);
	
	Point p1=pt,p2=pt;
	double tmp=t;
	{
		for(int i=k;i>=0;i--){
			Point next=ps[i];
			double d=Abs(next-p1);
			if(d/vt>t){
				p1+=vt*t/d*(next-p1);
				break;
			}
			else
				p1=next,t-=d/vt;
		}
	}
	swap(t,tmp);
	{
		for(int i=k;i<n-1;i++){
			Point next=ps[i+1];
			double d=Abs(next-p2);
			if(d/vt>t){
				p2+=vt*t/d*(next-p2);
				break;
			}
			else
				p2=next,t-=d/vt;
		}
	}
	return mt(p1,p2);
}

// p[0]に向かって倒れる方(A)を止めてから，p[n-1]に向かって倒れる方(B)を止める
// Aの停止位置までは必ず（すでにp[0]に達して停止していたとしても）移動する．
// その後，Bが停止したらそこまでの経過時間を返す．
double calc(const vector<Point>& ps,Point pt,double vt,Point pp,double vp)
{
	double t1,t2;
	{
		double lo=0,hi=INF;
		rep(_,100){
			double mi=(lo+hi)/2;
			Point p; tie(p,ignore)=after(ps,pt,vt,mi);
			if(Abs(p-pp)/vp<mi)
				hi=mi;
			else
				lo=mi;
		}
		t1=lo;
	}
	
	//{
	//	Point p1,p2;
	//	tie(p1,p2)=after(ps,pt,vt,t1);
	//	dump(t1);
	//	dump(mp(p1,p2));
	//}
	
	tie(pp,pt)=after(ps,pt,vt,t1);
	{
		double lo=0,hi=INF;
		rep(_,100){
			double mi=(lo+hi)/2;
			Point p; tie(ignore,p)=after(ps,pt,vt,mi);
			if(p==ps.back() || Abs(p-pp)/vp<mi)
				hi=mi;
			else
				lo=mi;
		}
		t2=lo;
	}
	return t1+t2;
}

int main()
{
	for(int n;cin>>n && n;){
		vector<Point> ps(n);
		for(auto& p:ps) cin>>p.x>>p.y;
		Point pt,pp;
		double vt,vp;
		cin>>pt.x>>pt.y>>vt;
		cin>>pp.x>>pp.y>>vp;
		
		double res=INF;
		{ // 全部倒れるまで待つ
			double lo=0,hi=INF;
			rep(_,100){
				double mi=(lo+hi)/2;
				Point p1,p2; tie(p1,p2)=after(ps,pt,vt,mi);
				if(p1==ps[0] && p2==ps.back())
					hi=mi;
				else
					lo=mi;
			}
			res=lo;
		}
		
		res=min(res,calc(ps,pt,vt,pp,vp));
		reverse(all(ps));
		res=min(res,calc(ps,pt,vt,pp,vp));
		printf("%.10f\n",res);
	}
}
accuracy: 1
time_ms: 10
memory_kb: 1256
final_rank: 1