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70 - ZOJ Monthly, September 2008 - 1003
BS Wrong Sample II

Time Limit: 10 Seconds      Memory Limit: 32768 KB      Special Judge

You may know, murphy have reduced Fan's RP. But he is still in angry and he want to beat Fan. Fan knows it , so he want to protect himself. It is known that murphy have N(<=50) weapons and Fan have M(<=50) shields. After hacking God's computer (You're familar with it, yes?), you know the probability that each weapons can attach each shield successfully. Since Fan's RP have been reduced, his IQ is also very low. Murphy never know Fan's strategy (You can never imagine a silly people's behavior) and Fan can't know Murphy's strategy neither (Because he is silly^_^). But Murphy is very clever, so he will choose his strategy carefully, to make his win probability maximum whatever Fan's choice is. And he want you to tell him the probability that he will win(Because he is busy prepering his weapons).

Input

The first line is number of cases(<=50). Each case start with N and M. N line follows, each contain M numbers, where the j-th integer represents the percent probability that Murphy will win if weapon i is used by Murphy and shield j is used by Fan.

Output

One line for each case, the probability.

Sample Input

1
2 2
50 80
60 30

Sample Output

55.000000

Hint

Murphy can use weapon 1 and 2 at the probability 50%.
If Fan use shield 1, Murphy have 50%*50+50%*60=55% to win.
If Fan use shield 2, Murphy have 50%*80+50%*30=55% to win.
So the answer is 55%.

Author: SHANG, Zechao


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