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116 - The 9th Zhejiang Provincial Collegiate Programming Contest - H
Lazier Salesgirl

Time Limit: 2 Seconds      Memory Limit: 65536 KB

Kochiya Sanae is a lazy girl who makes and sells bread. She is an expert at bread making and selling. She can sell the i-th customer a piece of bread for price pi. But she is so lazy that she will fall asleep if no customer comes to buy bread for more than w minutes. When she is sleeping, the customer coming to buy bread will leave immediately. It's known that she starts to sell bread now and the i-th customer come after ti minutes. What is the minimum possible value of w that maximizes the average value of the bread sold?


There are multiple test cases. The first line of input is an integer T ≈ 200 indicating the number of test cases.

The first line of each test case contains an integer 1 ≤ n ≤ 1000 indicating the number of customers. The second line contains n integers 1 ≤ pi ≤ 10000. The third line contains n integers 1 ≤ ti ≤ 100000. The customers are given in the non-decreasing order of ti.


For each test cases, output w and the corresponding average value of sold bread, with six decimal digits.

Sample Input

1 2 3 4
1 3 6 10
4 3 2 1
1 3 6 10

Sample Output

4.000000 2.500000
1.000000 4.000000

Author: WU, Zejun
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