## GUPTA MECHANICAL

IN THIS WEBSITE I CAN TELL ALL ABOUT TECH. TIPS AND TRICKS APP REVIEWS AND UNBOXINGS ALSO TECH. NEWS .............

## In The Green Zone CodeChef Solution | CodeChef Problem Solution 2022

There are $N$ cans lying on the X-axis at points ${X}_{i}$ $\left(1\le i\le N\right)$. Each of the N cans is associated with two values ${A}_{i}$ and ${B}_{i}$. Also, the segment between the points $L$ and $R$ $\left(L\le R\right)$ is considered to be green zone including the points $L$ and $R$. There are two types of operations -

$1.$ Select a can $i$ out of the $N$ cans and move it one unit in either direction along the axis, i.e. if before the operation can is at ${X}_{i}$ then after the operation, it moves to either ${X}_{i}+1$ or ${X}_{i}-1$. This costs ${B}_{i}$ coins and it can be performed any number of times for each of the cans.

$2.$ Choose any integer $k$ and shift the green zone to the segment between ${L}^{\prime }$ and ${R}^{\prime }$, where ${L}^{\prime }$ and ${R}^{\prime }$ are the mirror images of points $R$ and $L$ with respect to line $X=k$ respectively. This operation should be performed exactly once.

After all the operations, you get number of coins equal to sum of values of ${A}_{i}$ of the cans which lie in the final green zone. We define the net coins as:
$\mathtt{\text{Number of coins you get - Number of coins spent}}$

$\mathtt{\text{}}$

Find the maximum possible net coins you can earn.

### Input Format

• First line will contain $T$, number of testcases. Then the testcases follow.
• Each of the testcases consists of four lines.
• First lines consists of three integers $N$$L$ and $R$.
• Next line consist of $N$ space separated integers ${X}_{1},{X}_{2},...,{X}_{N}$.
• Next line consist of $N$ space separated integers ${A}_{1},{A}_{2},...,{A}_{N}$.
• Next line consist of $N$ space separated integers ${B}_{1},{B}_{2},...,{B}_{N}$.

### Output Format

For each testcase, output in a single integer, the maximum number of net coins you can earn.

### Constraints

• $1\le T\le 1000$
• $1\le N\le 3\cdot {10}^{5}$
• $1\le {A}_{i},{B}_{i}\le {10}^{9}$
• $-{10}^{9}\le L\le R\le {10}^{9}$
• $-{10}^{9}\le {X}_{i}\le {10}^{9}$
• Sum of $N$ over all test cases does not exceed $3\cdot {10}^{5}$

### Sample Input 1

2
1 7 10
2
6
1
3 7 10
2 8 1
6 20 1
1 3 2


### Sample Output 1

6
22


### Explanation

Test case $1$ : Lets choose the axis at $X=5$ and Shift the green zone in the range $\left[0,3\right]$, such that can lies in green zone. So, there is no need for operation of type $1$ and total number of coins earned is ${A}_{1}$, i.e. $6$.

Test case $2$ : Choose the axis at $X=8$, so the new green zone lies in the region $\left[6,9\right]$. Move the can $1$ to $X=6$. Number of coins received is equal to ${A}_{1}+{A}_{2}$ and number of coins spent is $4\cdot {B}_{1}$. So, the net coins earned is $20+6-4=22$. This is also the maximum possible.