Description

You are the leader of a school programming competition team in Chongqing for the CCPC. To enhance team bonding after the contest, you wish to organize a group dinner. However, since the budget was exhausted on hotpot before the competition, the cost of the meal must be split equally (that is, if $k$ people attend a meal with a total cost of $W$, each person pays $\frac{W}{k}$) among all participants.

There are $n$ classmates in the team. Each classmate who attends the dinner will order exactly one dish. The $i$-th classmate orders a dish costing $w_i$. Each classmate also has a budget constraint $r_i$: if the final shared cost of the meal exceeds $r_i$, the $i$-th classmate will stay at the hotel and order takeout instead.

As the leader, you want to maximize the number of classmates attending the dinner. Your goal is to select a subset of $m$ classmates such that if they each order their respective dishes, the shared cost (the sum of their $m$ dish prices divided by $m$) does not exceed the budget $r_i$ of any of the $m$ selected classmates. Find the maximum possible value of $m$.

If no such subset exists for $m \ge 1$, output $0$.

Input

There are multiple test cases in a single test file. The first line of the input contains a single integer $T$ ($1 \le T \le 10^5$), indicating the number of test cases.

For each test case:

• The first line of the input contains a single integer $n$ ($1 \le n \le 10^5$), representing the number of classmates.
• Next, input a line with $n$ integers, where the $i$-th integer $w_i$ ($1 \le w_i \le 10^9$) represents the price of the dish ordered by the $i$-th classmate.
• Then, input a line with $n$ integers, where the $i$-th integer $r_i$ ($1 \le r_i \le 10^9$) represents the maximum price the $i$-th classmate is willing to pay.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.

Output

For each test case, output a line with a single integer, representing the answer.

Example

Sample Input 1

2
5
1 2 3 4 5
5 4 3 2 1
10
3 1 4 1 5 9 2 6 5 3
5 8 9 7 9 3 2 3 8 4

Sample Output 1

3
7