////////////////////////////////////////
///  tu3 pro-con template            ///
////////////////////////////////////////
#include <cassert>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <sstream>
#include <algorithm>
#include <numeric>
#include <functional>
#include <vector>
#include <queue>
#include <string>
#include <complex>
#include <stack>
#include <set>
#include <map>
#include <list>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
#include <regex>
using namespace std;

//// MACRO ////
#define countof(a) (sizeof(a)/sizeof(a[0]))

#define REP(i,n) for (int i = 0; i < (n); i++)
#define RREP(i,n) for (int i = (n)-1; i >= 0; i--)
#define FOR(i,s,n) for (int i = (s); i < (n); i++)
#define RFOR(i,s,n) for (int i = (n)-1; i >= (s); i--)
#define pos(c,i) c.being() + (i)
#define allof(c) c.begin(), c.end()
#define aallof(a) a, countof(a)
#define partof(c,i,n) c.begin() + (i), c.begin() + (i) + (n)
#define apartof(a,i,n) a + (i), a + (i) + (n)

#define EPS 1e-9
#define INF (1L << 30)
#define LINF (1LL << 60)

#define PREDICATE(t,a,exp) [&](const t & a) -> bool { return exp; }
#define COMPARISON_T(t) bool(*)(const t &, const t &)
#define COMPARISON(t,a,b,exp) [&](const t & a, const t & b) -> bool { return exp; }
#define CONVERTER(TSrc,t,TDest,exp) [&](const TSrc &t)->TDest { return exp; }

inline int sign(double x) { return (abs(x) < EPS ? 0 : x > 0 ? 1 : -1); }

//// i/o helper ////

struct _Reader { template <class T> _Reader operator ,(T &rhs) { cin >> rhs; return *this; } };
struct _Writer { bool f; _Writer() : f(false) { } template <class T> _Writer operator ,(const T &rhs) { cout << (f ? " " : "") << rhs; f = true; return *this; } };
#define READ(t,...) t __VA_ARGS__; _Reader(), __VA_ARGS__
#define WRITE(...) _Writer(), __VA_ARGS__; cout << endl

template <class T> struct vevector : public vector<vector<T>> { vevector(int n = 0, int m = 0, const T &initial = T()) : vector<vector<T>>(n, vector<T>(m, initial)) { } };
template <class T> struct vevevector : public vector<vevector<T>> { vevevector(int n = 0, int m = 0, int l = 0, const T &initial = T()) : vector<vevector<T>>(n, vevector<T>(m, l, initial)) { } };
template <class T> struct vevevevector : public vector<vevevector<T>> { vevevevector(int n = 0, int m = 0, int l = 0, int k = 0, const T &initial = T()) : vector<vevevector<T>>(n, vevevector<T>(m, l, k, initial)) { } };
template <class T> T read() { T t; cin >> t; return t; }
template <class T> vector<T> read(int n) { vector<T> v; REP(i, n) { v.push_back(read<T>()); } return v; }
template <class T> vevector<T> read(int n, int m) { vevector<T> v; REP(i, n) v.push_back(read<T>(m)); return v; }
template <class T> vevector<T> readjag() { return read<T>(read<int>()); }
template <class T> vevector<T> readjag(int n) { vevector<T> v; REP(i, n) v.push_back(readjag<T>()); return v; }

template <class T1, class T2> inline istream & operator >> (istream & in, pair<T1, T2> &p) { in >> p.first >> p.second; return in; }
template <class T1, class T2> inline ostream & operator << (ostream &out, pair<T1, T2> &p) { out << p.first << p.second; return out; }
template <class T> inline ostream & operator << (ostream &out, vector<T> &v)
{
	ostringstream ss;
	for (auto x : v) ss << x << ' ';
	auto s = ss.str();
	out << s.substr(0, s.length() - 1) << endl;
	return out;
}

//// start up ////
void solve();
int main()
{
	solve();
	return 0;
}

//// geometry ////
/// 2次元
struct P2
{
	double x, y;
	P2(double x = 0, double y = 0) : x(x), y(y) { }
	P2(complex<double> c) : x(c.real()), y(c.imag()) { }
	P2 operator +() const { return *this; }
	P2 operator +(const P2 &_) const { return P2(x + _.x, y + _.y); }
	P2 operator -() const { return P2(-x, -y); }
	P2 operator -(const P2 &_) const { return *this + -_; }
	P2 operator *(double _) const { return P2(x*_, y*_); }
	P2 operator /(double _) const { return P2(x / _, y / _); }
	double dot(const P2 &_) const { return x*_.x + y*_.y; } // 内積
	double cross(const P2 &_) const { return x*_.y - y*_.x; } // 外積
	double sqlength() const { return x*x + y*y; } // 二乗長さ
	double length() const { return sqrt(sqlength()); } // 長さ
	P2 orthogonal() const { return P2(y, -x); }
	P2 direction() const { return *this / length(); } // 方向ベクトル
	bool operator ==(const P2 &_) const { return (*this - _).sqlength() < EPS; }
	bool operator !=(const P2 &_) const { return !(*this == _); }
};
inline istream & operator>>(istream & in, P2 & p) { in >> p.x >> p.y; return in; }
inline ostream & operator<<(ostream & out, const P2 & p) { out << p.x << ' ' << p.y; return out; }
inline double abs(P2 p2) { return p2.length(); }

// 範囲内チェック
inline bool contains(int x, int min, int max) { return x >= min && x < max; }
inline bool contains(int x, int y, int W, int H) { return x >= 0 && x < W && y >= 0 && y < H; }

////////////////////
/// template end ///
////////////////////

void solve()
{
	int cases = INF;
	REP(_, cases)
	{
		READ(int, n);
		if (!n) { break; }
		auto ps = read<P2>(n);
		
		vector<P2> g;
		for (auto p : ps)
		{
			g.emplace_back(p.x, p.y);
			REP(j, n - 1)
			{
				P2 p1 = ps[j], p2 = ps[j + 1];

				if (min(p1.y, p2.y) < p.y && max(p1.y, p2.y) > p.y)
				{
					P2 d = p - p1, d2 = p2 - p1;
					g.emplace_back(d.y / d2.y * d2.x + p1.x, p.y);
				}
			}
		}
		sort(allof(g), COMPARISON(P2, a, b, a.x < b.x));
		g.erase(unique(allof(g)), g.end());

		struct S { pair<int, int> next; double cost; };
		double result = 0;

		priority_queue<S, vector<S>, COMPARISON_T(S)> q(COMPARISON(S, a, b, a.cost > b.cost));
		q.push({ { 0, g.size() - 1 }, 0 });
		set<pair<int, int>> visited;
		while (!q.empty())
		{
			S c = q.top(); q.pop();
			if (visited.count(c.next)) continue;
			visited.insert(c.next);
			if (c.next.first == c.next.second) { result = c.cost; break; }

			int p1 = c.next.first, p2 = c.next.second;
			int dp[] = { -1, 0, 1 };
			REP(i, 3) REP(j, 3)
			{
				int np1 = p1 + dp[i], np2 = p2 + dp[j];
				if (!contains(np1, np2, g.size(), g.size())) continue;
				if (visited.count({ np1, np2 })) continue;
				if (abs(g[np1].y - g[np2].y) > EPS) continue;
				double cost = (g[np1] - g[p1]).length() + (g[np2] - g[p2]).length();
				q.push({ { np1, np2 }, c.cost + cost });
			}
		}
		printf("%.16f\n", result);
	}
}

Measured memory_bytes: 2684