#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <algorithm>
#include <vector>

using namespace std;

#define SOLUTION 1
#define LOCAL 0
#define DEBUG 0
#define eps 1e-1
#define NMAX 211111
#define XMAX 10000000

namespace GEOM {
int Sign(double a, double b, double c, double x, double y) {
	double r = a*x + b*y + c;
	if (fabs(r) < eps) return 0;
	else if (r > 0) return 1;
	else return -1;
}

int Parallel(double a1, double b1, double a2, double b2) {
	return fabs(a2*b1 - a1*b2) < eps;
}

int InBetween(double a, double b, double c) {
	if (fabs(a-c) < eps || fabs(b-c) < eps || (a <= c && c <= b) || (b <= c && c <= a)) return 1;
	else return 0;
}

int Intersect(double a1, double b1, double c1,
	          double x2a, double y2a, double x2b, double y2b,
			  double *xi, double *yi) {
	double a2, b2, c2;

	a2 = y2a - y2b;
	b2 = x2b - x2a;
	c2 = x2a * y2b - x2b * y2a;

	if (Parallel(a1, b1, a2, b2)) return 0;
	else {
		*xi = (b2*c1-b1*c2) / (a2*b1-a1*b2);
		*yi = (c2*a1-c1*a2) / (a2*b1-a1*b2);
		return 1;
	}
}
}

int x[NMAX], y[NMAX], N;

void ReadInput() {
	if (LOCAL) {
		srand(12345);
		N = 100000;
	} else scanf("%d", &N);
	int dif = 0;
	for (int i = 0; i < N; i++)
		if (LOCAL) {
			x[i] = i;
			if (i == 0) y[i] = -99000;
			else y[i] = y[i - 1] + dif;
			if ((i % 100) == 0) dif++;
		} else scanf("%d %d", &x[i], &y[i]);
	if (!LOCAL) {
		int i = 0, j = N - 1, tmp;
		while (i < j) {
			tmp = x[i]; x[i] = x[j]; x[j] = tmp;
			tmp = y[i]; y[i] = y[j]; y[j] = tmp;
			i++; j--;
		}
	}
}

double xpoly[NMAX], ypoly[NMAX];
int pnext[NMAX], pprev[NMAX], np, pstart;

void ClipPoly(double a, double b, double c) {
	int q = pstart;
	int s = GEOM::Sign(a, b, c, xpoly[q], ypoly[q]);
	
	if (DEBUG) fprintf(stderr, "[ClipPoly] a=%.3lf b=%.3lf c=%.3lf q=%d s=%d\n", a, b, c, q, s);
	
	while (1) {
		int qnext = pnext[q];
		int snext = GEOM::Sign(a, b, c, xpoly[qnext], ypoly[qnext]);
		if (s < 0 && snext >= 0) break;
		q = qnext;
		s = snext;
		if (q == pstart) break;
	}
		
	if (s >= 0) return;
		
	int qnext = pnext[q];
	int snext = GEOM::Sign(a, b, c, xpoly[qnext], ypoly[qnext]);
	if (snext < 0) {
		pstart = -1;
		return;
	}
		
	if (snext == 0) pstart = qnext;
	else {
		assert(GEOM::Intersect(a, b, c, xpoly[q], ypoly[q], xpoly[qnext], ypoly[qnext], &xpoly[np], &ypoly[np]));
		pstart = np++;
		pnext[pstart] = qnext;
	}
	
	for (q = pstart; 1; q = pnext[q]) {
		qnext = pnext[q];
		snext = GEOM::Sign(a, b, c, xpoly[qnext], ypoly[qnext]);
		if (snext < 0) break;
	}
		
	s = GEOM::Sign(a, b, c, xpoly[q], ypoly[q]);
	if (s == 0) pnext[q] = pstart;
	else {
		assert(GEOM::Intersect(a, b, c, xpoly[q], ypoly[q], xpoly[qnext], ypoly[qnext], &xpoly[np], &ypoly[np]));
		pnext[q] = np++;
		pnext[pnext[q]] = pstart;
	}
}

double SolveN2() {
	np = 4;
	xpoly[0] = ypoly[0] = -XMAX;
	xpoly[1] = XMAX; ypoly[1] = -XMAX;
	xpoly[2] = XMAX; ypoly[2] = XMAX;
	xpoly[3] = -XMAX; ypoly[3] = XMAX;
	pnext[0] = 1; pnext[1] = 2; pnext[2] = 3; pnext[3] = 0;
	pstart = 0;
	
	for (int p = 0; p < N; p++) {
		double a = y[p] - y[(p + 1) % N];
		double b = x[(p + 1) % N] - x[p];
		double c = (long long) x[p] * (long long) y[(p + 1) % N] - (long long) x[(p + 1) % N] * (long long) y[p];
		ClipPoly(a, b, c);
		if (pstart < 0) break;
		
		if (DEBUG) {
			fprintf(stderr, "p=%d/%d (%d,%d)-(%d,%d): ", p, N, x[p], y[p], x[(p + 1) % N], y[(p + 1) % N]);
			int q = pstart;
			while (1) {
				fprintf(stderr, "%d(%.4lf,%.4lf) ", q, xpoly[q], ypoly[q]);
				q = pnext[q];
				if (q == pstart) break;
			}
			fprintf(stderr, "\n");
		}
	}

	if (pstart < 0) return 0.0;

	double area = 0.0;	
	int q = pstart;
	while (1) {
		int qnext = pnext[q];
		area += (xpoly[q] + xpoly[qnext]) * (ypoly[qnext] - ypoly[q]);
		q = qnext;
		if (q == pstart) break;
	}	
	return 0.5 * fabs(area);
}

void ClipPoly2(double a, double b, double c, int q) {
	assert(GEOM::Sign(a, b, c, xpoly[q], ypoly[q]) < 0);
	pstart = q;
	while (1) {
		if (GEOM::Sign(a, b, c, xpoly[q], ypoly[q]) >= 0) break;
		q = pnext[q];
		if (q == pstart) break;
	}
	if (q == pstart) {
		pstart = -1;
		return;
	}
	assert(GEOM::Sign(a, b, c, xpoly[q], ypoly[q]) >= 0);	
	if (GEOM::Sign(a, b, c, xpoly[q], ypoly[q]) > 0) {
		assert(GEOM::Intersect(a, b, c, xpoly[q], ypoly[q], xpoly[pprev[q]], ypoly[pprev[q]], &xpoly[np], &ypoly[np]));
		pnext[np] = q;
		pprev[np] = pprev[q];
		pprev[q] = np;
		pnext[pprev[np]] = np;
		q = np;
		np++;
	}
	int qa = q;
	q = pstart;
	while (GEOM::Sign(a, b, c, xpoly[q], ypoly[q]) < 0) q = pprev[q];
	if (GEOM::Sign(a, b, c, xpoly[q], ypoly[q]) > 0) {
		assert(GEOM::Intersect(a, b, c, xpoly[q], ypoly[q], xpoly[pnext[q]], ypoly[pnext[q]], &xpoly[np], &ypoly[np]));
		/*if (!GEOM::Intersect(a, b, c, xpoly[q], ypoly[q], xpoly[pnext[q]], ypoly[pnext[q]], &xpoly[np], &ypoly[np])) {
			fprintf(stderr, "sq=%d snextq=%d\n", GEOM::Sign(a, b, c, xpoly[q], ypoly[q]), GEOM::Sign(a, b, c, xpoly[pnext[q]], ypoly[pnext[q]]));
			exit(7);
		}*/
		pprev[np] = q;
		pnext[np] = pnext[q];
		pnext[q] = np;
		pprev[pnext[np]] = np;
		q = np;
		np++;
	}
	pnext[q] = qa;
	pprev[qa] = q;
	pstart = q;
}

vector<pair<double, int>> vu;

double SolveNlogN() {
	vu.resize(N);
	for (int p = 0; p < N; p++) {
		vu[p].first = atan2(y[(p + 1) % N] - y[p], x[(p + 1) % N] - x[p]);
		vu[p].second = p;
	}
	sort(vu.begin(), vu.end());

	np = 4;
	xpoly[0] = ypoly[0] = -XMAX;
	xpoly[1] = XMAX; ypoly[1] = -XMAX;
	xpoly[2] = XMAX; ypoly[2] = XMAX;
	xpoly[3] = -XMAX; ypoly[3] = XMAX;
	pnext[0] = 1; pnext[1] = 2; pnext[2] = 3; pnext[3] = 0;
	pprev[1] = 0; pprev[2] = 1; pprev[3] = 2; pprev[0] = 3;
	pstart = 0;

	for (int i = 0; i < N; i++) {
		int p = vu[i].second;
		double a = y[p] - y[(p + 1) % N];
		double b = x[(p + 1) % N] - x[p];
		double c = (long long) x[p] * (long long) y[(p + 1) % N] - (long long) x[(p + 1) % N] * (long long) y[p];

		int q = pstart;
		int s = GEOM::Sign(a, b, c, xpoly[q], ypoly[q]);
		
		if (s >= 0) {
			while (1) {
				int qnext = pnext[q], qprev = pprev[q];
				double vprev = a * xpoly[qprev] + b * ypoly[qprev];
				double vnext = a * xpoly[qnext] + b * ypoly[qnext];
				double vq = a * xpoly[q] + b * ypoly[q];
				//fprintf(stderr, "   q=%d qprev=%d qnext=%d: vq=%.9lf vprev=%.9lf vnext=%.9lf\n", q, qprev, qnext, vq, vprev, vnext);
				if (vq < vprev + eps && vq < vnext + eps) break;
				q = pnext[q];
				s = GEOM::Sign(a, b, c, xpoly[q], ypoly[q]);
				if (q == pstart) break;
			}
		}

		if (DEBUG) fprintf(stderr, "i=%d/%d (%.9lf): p=%d q=%d(%.3lf,%.3lf) s=%d\n", i, N, vu[i].first, p, q, xpoly[q], ypoly[q], s);
		
		if (s >= 0) continue;
		ClipPoly2(a, b, c, q);
		if (pstart < 0) break;

		if (DEBUG) {
			fprintf(stderr, "p=%d/%d (%d,%d)-(%d,%d): ", p, N, x[p], y[p], x[(p + 1) % N], y[(p + 1) % N]);
			int q = pstart;
			while (1) {
				fprintf(stderr, "%d(%.4lf,%.4lf) ", q, xpoly[q], ypoly[q]);
				q = pnext[q];
				if (q == pstart) break;
			}
			fprintf(stderr, "\n");
		}
	}

	if (pstart < 0) return 0.0;

	double area = 0.0;
	int q = pstart;
	while (1) {
		int qnext = pnext[q];
		area += (xpoly[q] + xpoly[qnext]) * (ypoly[qnext] - ypoly[q]);
		q = qnext;
		if (q == pstart) break;
	}
	return 0.5 * fabs(area);
}

int main() {
	//freopen("allpoly_bad.in", "r", stdin);
	//freopen("all.out", "w", stdout);
	int T;
	if (LOCAL) T = 1;
	else scanf("%d", &T);
	while (T--) {
		ReadInput();
		double area;
		if (SOLUTION == 0) area = SolveN2();
		else area = SolveNlogN();
		printf("%.20lf\n", area / 4e14);
	}
	return 0;
}