Problem Statement

There are $2N$ people, numbered $1, 2, \dots, 2N$. Shirotsume is going to put a red or blue hat on each of them. $1$ person wears exactly $1$ hat, which is either red or blue.

Points are awarded according to the colors of the hats.

For each $i$ $(1 \leq i \leq 2N)$, putting a red hat on person $i$ gives $A_i$ points, and putting a blue hat on them gives $B_i$ points.

In addition, for each $i$ $(1 \leq i \leq N)$, a bonus of $X_i$ points is obtained if person $2i - 1$ and person $2i$ have hats of the same color, and a bonus of $Y_i$ points is obtained if their colors differ.

What is the maximum possible score when the hat colors for the $2N$ people are chosen appropriately?

Constraints

• All input values are integers
• $1 \leq N \leq 10^5$
• $1 \leq A_i \leq 10^9$ ($1 \leq i \leq 2N$)
• $1 \leq B_i \leq 10^9$ ($1 \leq i \leq 2N$)
• $1 \leq X_i \leq 10^9$ ($1 \leq i \leq N$)
• $1 \leq Y_i \leq 10^9$ ($1 \leq i \leq N$)

Input

$N$
$A_1$ $A_2$ $\dots$ $A_{2N}$
$B_1$ $B_2$ $\dots$ $B_{2N}$
$X_1$ $X_2$ $\dots$ $X_N$
$Y_1$ $Y_2$ $\dots$ $Y_N$

Output

Print the answer.

Sample

2
3 1 4 1
5 9 2 6
1 5
4 1

29

4
31415 92653 58979 32384 62643 38327 95028 84197
27182 81828 45904 52353 60287 47135 26624 97757
11111 33333 55555 77777
88888 66666 44444 22222

806700

5
132369990 154684955 399557792 6898866 892085082 475405438 178727727 496378193 391115300 392312020
929620757 339762612 478146585 237867511 112947139 932164889 474129303 798212953 843175854 899264953
148258026 932749041 478171985 880111286 733483895
647484075 34641657 473409219 391218034 474131840

10306590358