#include <iostream>
#include <iomanip>
#include <map>
#include <complex>

using namespace std;

const int N = 12;
const int K = 14;

const double EPS = 1e-12;

static complex<double> zp[N+1];
static complex<double> zq[N+1];

static int n;

static map<double,double> cache[N+1];

#define Z(i,s) (zp[i] * (1.0 - (s)) + zq[i] * (s))

int cmp(double x, double y)
{
	if(x - y > EPS) return +1;
	if(y - x > EPS) return -1;
	return 0;
}

double compute(int i, double s)
{
	if(i == 1) {
		complex<double> z = Z(1,s);
		complex<double> w = (z - zp[0]) / (zq[0] - zp[0]);

		if(real(w) < 0.0) return abs(z - zp[0]);
		if(real(w) > 1.0) return abs(z - zq[0]);

		return abs(imag(w)) * abs(zq[0] - zp[0]);
	}

	if(cache[i].find(s) != cache[i].end())
		return cache[i][s];

	double mul = (i == n) ? 0.0 : 1.0;

	double su = 0.0;
	double sv = 1.0;
	double dmin;

	for(int k = 0; k < K; k++) {
		double d[5];

		for(int j = 0; j <= 4; j++) {
			double t = (su * (4 - j) + sv * j) / 4.0;
			d[j] = mul * abs(Z(i,s) - Z(i-1,t)) + compute(i-1, t);
		}

		int m = min_element(d, d + 5) - d;
		dmin = d[m];

		int m0 = max(1, min(m, 3));

		if(cmp(d[m0-1], dmin) == 0 && cmp(d[m0+1], dmin) == 0) { break; }

		int mu = max(0, m - 1);
		int mv = min(4, m + 1);

		double su1 = (su * (4 - mu) + sv * mu) / 4.0;
		double sv1 = (su * (4 - mv) + sv * mv) / 4.0;

		su = su1;
		sv = sv1;

		if(mv - mu == 1) { k++; }
	}

	cache[i][s] = dmin;
	return dmin;
}

int main(void)
{
	while(cin >> n, n != 0) {
		for(int i = 0; i < n; i++) {
			double x, y;
			cin >> x >> y; zp[i] = complex<double>(x, y);
			cin >> x >> y; zq[i] = complex<double>(x, y);
		}

		zp[n] = zq[n] = 0.0;
		cout << setprecision(15) << compute(n, 0.0) << endl;

		for(int i = 0; i <= n; i++)
			cache[i].clear();
	}

	return 0;
}