Union of circles

Input

The first line contains the number of test cases $K$ ( $1 \leq K \leq 10$ 1 \leq K \leq 10).

The first line of each test case contains the number of circles $N$ ( $1 \leq N \leq 100$ 1 \leq N \leq 100). The following $N$ lines each contain the center's coordinates and the radius of a circle, as $x_{i}$ x_i $y_{i}$ y_i $r_{i}$ r_i. All coordinates are integers not exceeding $1000$ in absolute value. The radius is a positive integer no greater than $1000$ .

Output

For each test case, output the area of the union of the circles, with $6$ digits after the decimal point.

Examples

Example 1

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