# Tree Cuts

There are N trees arranged in a straight horizontal line numbered 1 to N from left to right. The distance between tree

_{i}and tree

_{i+1}is d

_{i}, and the height of tree

_{i}is h

_{i}.

To make them look beautiful, you try make the topmost points of all the trees collinear. You are allowed to cut the tress by any length (not necessarily an integer). Different tress can be cut by different lengths. What is the minimum number of trees you need to cut?

**Input**

First line contains the number of test cases.

Each test case has three lines, first line has single integer N. Second line has N-1 integers d

_{1}...d

_{N-1}, third line contains N integers h

_{1}...h

_{N}.

**Output**

Print one line per test case containing one integer representing the minimum number of trees you need to cut.

**Constraints**

Test cases < 300

1 <= N <= 50

1 <= d

_{i}<= 1000

1 <= h

_{i}<= 1000

**Sample Input**

```
```

5

3

2 2

1 3 10

3

3 3

3 1 3

3

1 3

4 4 4

3

4 2

9 8 5

3

2 2

2 1 2

**Sample Input**

```
```

1

2

0

1

1

**Explanation**

*Problem Setter : Shikhar Sharad*

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