In The Green Zone CodeChef Solution | CodeChef Problem Solution 2022

In The Green Zone CodeChef Solution | CodeChef Problem Solution 2022

There are N$N$ cans lying on the X-axis at points Xi$X_i$ (1≤i≤N)$(1\le i\le N)$. Each of the N cans is associated with two values Ai$A_i$ and Bi$B_i$. Also, the segment between the points L$L$ and R$R$ (L≤R)$(L\le R)$ is considered to be green zone including the points L$L$ and R$R$. There are two types of operations -

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

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

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

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Find the maximum possible net coins you can earn.

Input Format

• First line will contain T$T$, number of testcases. Then the testcases follow.
• Each of the testcases consists of four lines.
• First lines consists of three integers N$N$, L$L$ and R$R$.
• Next line consist of N$N$ space separated integers X1,X2,...,XN$X_1,X_2,...,X_N$.
• Next line consist of N$N$ space separated integers A1,A2,...,AN$A_1,A_2,...,A_N$.
• Next line consist of N$N$ space separated integers B1,B2,...,BN$B_1,B_2,...,B_N$.

Output Format

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

Constraints

• 1≤T≤1000$1\le T\le 1000$
• 1≤N≤3⋅105$1\le N\le 3\cdot {10}^5$
• 1≤Ai,Bi≤109$1\le A_i,B_i\le {10}^9$
• −109≤L≤R≤109$-{10}^9\le L\le R\le {10}^9$
• −109≤Xi≤109$-{10}^9\le X_i\le {10}^9$
• Sum of N$N$ over all test cases does not exceed 3⋅105$3\cdot {10}^5$

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$1$ : Lets choose the axis at X=5$X=5$ and Shift the green zone in the range [0,3]$[0,3]$, such that can lies in green zone. So, there is no need for operation of type 1$1$ and total number of coins earned is A1$A_1$, i.e. 6$6$.

Test case 2$2$ : Choose the axis at X=8$X=8$, so the new green zone lies in the region [6,9]$[6,9]$. Move the can 1$1$ to X=6$X=6$. Number of coins received is equal to A1+A2$A_1+A_2$ and number of coins spent is 4⋅B1$4\cdot B_1$. So, the net coins earned is 20+6−4=22$20+6-4=22$. This is also the maximum possible.

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