Welcome to ZOJ
 Problem Sets Information Select Problem Runs Ranklist
ZOJ Problem Set - 3607
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?

#### Input

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.

#### Output

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

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

#### Sample Output

```4.000000 2.500000
1.000000 4.000000
```

Author: WU, Zejun
Contest: The 9th Zhejiang Provincial Collegiate Programming Contest
Submit    Status