H. Shuffle for the Waffle
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
You are given two arrays $$$a$$$ and $$$w$$$, each of length $$$n$$$.

You may reorder the elements of $$$a$$$ arbitrarily. Let $$$b$$$ be the array obtained after reordering. The array $$$w$$$ is not reordered: $$$w_i$$$ always belongs to position $$$i$$$.

A position $$$i$$$ ($$$1 \le i \le n$$$) is called good if $$$b_i \le i$$$. The score of $$$b$$$ is the sum of weights of all good positions. In other words, for every good position $$$i$$$, add $$$w_i$$$ to the score.

Find the maximum possible score.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first line of a test case contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the length of the arrays.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$).

The third line contains $$$n$$$ integers $$$w_1, w_2, \ldots, w_n$$$ ($$$0 \le w_i \le 10^9$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, print one integer — the maximum possible score.

Example

Input
2
5
2 4 1 7 2
5 3 9 4 8
4
10 10 10 10
1 2 3 4
Output
26
0
Note

In the first sample, one optimal reordered array is $$$b=[1,7,2,2,4]$$$. Positions $$$1$$$, $$$3$$$, $$$4$$$, and $$$5$$$ are good, so the score is $$$5+9+4+8=26$$$. In the second sample, every element of $$$a$$$ is greater than every valid position index, so no position can be good and the answer is $$$0$$$.