poj 2066

#include <iostream>
#include <cstdio>
#include <iomanip>
#include <string>
#include <cstdlib>
#include <cstring>
#include <queue>
#include <set>
#include <vector>
#include <map>
#include <algorithm>
#include <cmath>
#include <stack>

#define INF 0x3f3f3f3f
#define LINF 0x3f3f3f3f3f3f3f3f
#define ll long long
#define ull unsigned long long
#define uint unsigned int

using namespace std;
struct point {
	double x, y;
}p[60];
int n;
double dp[60][60];
double area(point a, point b, point c) {
	return abs((b.x - a.x)*(c.y - a.y) - (c.x - a.x)*(b.y - a.y)) / 2.0;
}
int judge(int a, int b, int c) {
	for (int i = 0; i < n; ++i) {
		if (i != a && i != b && i != c) {
			double tmp = area(p[a], p[b], p[i]) + area(p[a], p[i], p[c]) + area(p[i], p[b], p[c]);
			if (abs(tmp - area(p[a], p[b], p[c])) < 1e-6)
				return 0;
		}
	}
	return 1;
}
void solve() {
	double minv = INF;
	for (int l = 2; l < n; ++l)
		for (int i = 0; i < n; ++i) {
			int j = (i + l) % n;
			dp[i][j] = INF;
			for (int k = (i + 1) % n; k != j; k = (k + 1) % n) {
				if (judge(i, k, j)) {
					dp[i][j] = min(dp[i][j], max(max(dp[i][k], dp[k][j]), area(p[i], p[k], p[j])));
				}
			}
			if (l == n - 1)
				minv = min(minv, dp[i][j]);
		}
	printf("%.1lf\n", minv);
}
int main()
{
	int t;
	scanf("%d", &t);
	while (t--) {
		scanf("%d", &n);
		for (int i = 0; i < n; ++i)
			scanf("%lf%lf", &p[i].x, &p[i].y);
		solve();
	}
	return 0;
}