Migrated from Lutece 56 The Most Wonderful Competition

All parts of this problem, including description, images, samples, data and checker, might be broken. If you find bugs in this problem, please contact the admins.

Description

Last week, School of Applied Mathematics held a competition of flying kite, contestants are divided into pairs, and one contestant competes with another in each pair. As we know, different way dividing pairs may bring different splendid level value, which appears as a real numbers. Now Miss Ye wants to know how to divide the competitor in order to attain maximum splendid level.

Input

The first line of the input contains one integer $T$, which indicate the number of test case.

For each test case, in the first line there is an integer $N$ ($N \leq 16$, $N$ is always an even number) indicating there are $N$ contestants taking part the competition.

In the next $N$ line, each line contains $N$ real numbers. The j-th number in the i-th line is the splendid level value when the i-th contestant and the j-th constant are made in one pair. You can assume the j-th number in the i-th line is equal to the i-th number in the j-th line.

Output

For each case, output the maximum total splendid level value accurate to two digits after the radix point.

Samples

1
2
0.0 1.0
1.0 0.0

1.00

Resources

电子科技大学第七届ACM程序设计大赛 初赛