Running Rivalry

Alice and Bob have taken up running and are interested in tracking their progress by comparing their daily distances.

For a stretch of $NN$ days, Alice ran $A_{i}A\_i$ meters and Bob ran $B_{i}B\_i$ meters on day $ii$.

On any given day,

• Alice feels discontent if Bob's distance is more than double hers, and content otherwise.
• Bob feels discontent if Alice's distance is more than double his, and content otherwise.

For instance, on a specific day:

• Should Alice run $200200$ meters and Bob $500500$, Alice would be discontent while Bob would be content.
• Should Alice cover $500500$ meters and Bob $240240$, Alice would be content while Bob would be discontent.
• If Alice runs $300300$ meters and Bob $500500$, both would find contentment.

Determine the number of days where both Alice and Bob felt content.

Input Format

• The initial line of input presents a single integer $TT$, representing the count of test cases.
• Each test case is divided into three lines.
  • The opening line of a test case states a single integer $NN$ — the count of days.
  • The subsequent line lists $NN$ integers separated by spaces $A_1,A_2,\dots ,A_{N}A\_1,\; A\_2,\; \backslash ldots,\; A\_N$ — the distances Alice ran each day.
  • The last line also lists $NN$ integers separated by spaces $B_1,B_2,\dots ,B_{N}B\_1,\; B\_2,\; \backslash ldots,\; B\_N$ — the distances Bob ran each day.

Output Format

For every test case, report in a new line the tally of days when both Alice and Bob were content.

Constraints

• $1\le T\le 10001\; \backslash leq\; T\; \backslash leq\; 1000$
• $1\le N\le 1001\; \backslash leq\; N\; \backslash leq\; 100$
• $1\le A_i,B_i\le 10^{5}1\; \backslash leq\; A\_i,\; B\_i\; \backslash leq\; 10^5$

Sample Test Cases (with explanations)

Case #1:

Input:

4
3
100 200 300
300 200 100
4
1000 1000 1000 1000
400 500 600 1200
4
800 399 1400 532
2053 2300 3400 23
5
800 850 900 950 1000
600 800 1000 1200 1400

Output:

1
3
0
5

Explanation

Test case $11$: Alice is discontent on the first day, as her $100100$ meters is significantly less than Bob's $300300$; Bob's distance being over twice of Alice's.
On the contrary, Bob is discontent on the third day.
The second day sees both Alice and Bob content, leading to the answer being $11$.

Test case $22$: Day $11$ has Bob discontent but content on the remaining days, whereas Alice is content throughout, making them both content on three days — the second, third, and fourth days.

Test case $33$: Days $1,2,31,\; 2,\; 3$ see Alice discontent and day $44$ sees Bob discontent.

Test case $44$: Across all five days, both Alice and Bob are content.