题目描述

:::align{center} :::

In the three dimensional Euclidean space $(X, Y, Z)$, the intersection of several half spaces and $\{X \le 0, Y \le 0, Z \le 0\}$ forms an area with positive volume.

Here each half space is represented as a linear inequation $AX + BY + CZ \le D$. Our problem is to find the largest available ball fully locating in the area.

输入格式

The input contains several test cases. The first line of input contains an integer $T (1 \le T \le 160)$ indicating the number of cases.

For each case, the first line contains an integer $N (1 \le N \le 100)$ indicating the number of half spaces. Each of the following lines describes a half space given by four integers $A,B,C$ and $D$ corresponding to the linear inequation $AX+BY +CZ \le D$,where $-100 \le A,B,C,D \le 100$. The summation of N in input is up to $6200$.

输出格式

For each test case, output a line. If the size of available balls is unrestricted, output “Infinity”. Else, output the largest radius of an available ball with the precision of $4$ digits after the decimal point.

5
3
1 0 0 1
0 1 0 1
0 0 1 1
1
1 1 1 1
2
-1 -1 -1 -2
1 2 3 7
2
1 0 0 1
0 0 1 1
1
1 -1 0 0

0.5000
0.2113
0.5901
0.5000
Infinity