Running Comparison CodeChef Solution

Problem

Alice and Bob recently got into running, and decided to compare how much they ran on different days.

They each ran for $N$ days — on the ��ℎith day, Alice ran ��Ai​ meters and Bob ran ��Bi​ meters.

On each day,

• Alice is unhappy if Bob ran strictly more than twice her distance, and happy otherwise.
• Similarly, Bob is unhappy if Alice ran strictly more than twice his distance, and happy otherwise.

For example, on a given day

• If Alice ran $200$ meters and Bob ran $500$, Alice would be unhappy but Bob would be happy.
• If Alice ran $500$ meters and Bob ran $240$, Alice would be happy and Bob would be unhappy.
• If Alice ran $300$ meters and Bob ran $500$, both Alice and Bob would be happy.

On how many of the $N$ days were both Alice and Bob happy?

Input Format

• The first line of input will contain a single integer $T$, denoting the number of test cases.
• Each test case consists of three lines of input.
  • The first line of each test case contains a single integer $N$ — the number of days.
  • The second line of each test case contains $N$ space-separated integers �1,�2,…,��A1​,A2​,…,AN​ — the distances run by Alice on the $N$ days.
  • The third line of each test case contains $N$ space-separated integers �1,�2,…,��B1​,B2​,…,BN​ — the distances run by Bob on the $N$ days.

Output Format

For each test case, output on a new line the number of days when both Alice and Bob were happy.

Constraints

Sample 1:

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

1
3
0
5

Explanation:

Test case $1$: Alice is unhappy on the first day, since she ran $100$ meters but Bob ran $300$; and $300$ is more than twice of $100$.
Similarly, Bob is unhappy on the third day.
Both Alice and Bob are happy on the second day, so the answer is $1$.

Test case $2$: Bob is unhappy on day $1$ and happy on every other day, while Alice is happy on every day. So, they’re both happy on three days — the second, third, and fourth.

Test case $3$: Alice is unhappy on days $1,2,3$ and Bob is unhappy on day $4$.

Test case $4$: Alice and Bob are both happy on all five days.