**Problem**

*lykoo* is a chinese girl pursuing the bachelor's degree in economics in Holland. Recently she found a part time job of sending newspapers to keep balance. It's really a hard job. Because *lykoo* needs to get up 4 o'clock every morning, first goes to the post office nearby to fetch newspapers, then delivers them to 8 bookstores. When she finished the work, it's usually about 6 o'clock and she will go back home to continue her sweet dream.

On QQ, *wiltord* usually heard her complaint about that job. As the best friend of *lykoo*, *wiltord* wants to help her choose the shortest round path, so that she has more time to sleep.

**Input**

The first line of the input contains an integer T (T <= 1010) indicating the number of test cases. For each test case, ten pairs of integers will be given in a line; the first is the coordinate of *lykoo*'s house, the second is the post office, the rests are eight bookstores. You may assume there is a straight road between each pair of them. Coordinate will be in the range of [0, 1000].

**Output**

For each test case, print the minimum distance *lykoo* has to finish in a single line with precision of three decimal places.

**Sample Input**

1

0 0 1 0 2 0 3 0 4 0 4 1 3 1 2 1 1 1 0 1

**Sample Output**

10.000