Alexa has two stacks of non-negative integers, stack $a[n]$ and stack $b[m]$ where index $0$ denotes the top of the stack. Alexa challenges Nick to play the following game:

In each move, Nick can remove one integer from the top of either stack $\class{ML__boldsymbol}{\boldsymbol{a}}$ or stack $\boldsymbol{b}$.
Nick keeps a running sum of the integers he removes from the two stacks.
Nick is disqualified from the game if, at any point, his running sum becomes greater than some integer $maxSum$ given at the beginning of the game.
Nick's final score is the total number of integers he has removed from the two stacks.

Given $\class{ML__boldsymbol}{\boldsymbol{a}}$, $\boldsymbol{b}$, and $maxSum$ for $\mathrm{~g~}$ games, find the maximum possible score Nick can achieve.

Example

$a=[1,2,3,4,5]$

$b=[6,7,8,9]$

The maximum number of values Nick can remove is $\begin{array}{c}4\end{array}$. There are two sets of choices with this result.

Remove $1,2,3,4$ from $\class{ML__boldsymbol}{\boldsymbol{a}}$ with a sum of $10$.
Remove $1,2,3$ from $\class{ML__boldsymbol}{\boldsymbol{a}}$ and $\boldsymbol{6}$ from $\boldsymbol{b}$ with a sum of $12$.

Function Description

Complete the twoStacks function in the editor below.

twoStacks has the following parameters:
- int maxSum: the maximum allowed sum

• int a[n]: the first stack

• int b[m]: the second stack

Returns

• int: the maximum number of selections Nick can make

Input Format

The first line contains an integer, $\mathrm{~g~}$ (the number of games). The $3\cdot g$ subsequent lines describe each game in the following format:

The first line contains three space-separated integers describing the respective values of $n$ (the number of integers in stack $\class{ML__boldsymbol}{\boldsymbol{a}}$), $m$ (the number of integers in stack $\boldsymbol{b}$), and $maxSum$ (the number that the sum of the integers removed from the two stacks cannot exceed).
The second line contains $n$ space-separated integers, the respective values of $a[i]$.
The third line contains $m$ space-separated integers, the respective values of $b[i]$.

Constraints

$1\leq g\leq50$
$1\leq n,m\leq10^5$
$0\leq a[i],b[i]\leq10^6$
$1\leq\textit{maxSum}\leq10^9$

Subtasks

$1\le n,m,\le100$ for $50\%$ of the maximum score.

Sample Input 0
1
5 4 10
4 2 4 6 1
2 1 8 5

Sample Output 0
4

Explanation 0

The two stacks initially look like this:

The image below depicts the integers Nick should choose to remove from the stacks. We print $\begin{array}{c}4\end{array}$ as our answer, because that is the maximum number of integers that can be removed from the two stacks without the sum exceeding $x=10$.

(There can be multiple ways to remove the integers from the stack, the image shows just one of them.)

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