Problem Statement

There are $N$ slices of bread, numbered $1,2,\dots,N$ in order. Each slice has a front side and a back side. The deliciousness of slice $i$ is $A_i$ when neither its front nor its back is toasted, $B_i$ when only one side is toasted, and $C_i$ when both sides are toasted.

You will now toast the bread, using the toaster at most $2$ times. When using the toaster, you specify integers $l, r$ satisfying $1 \le l \le r \le N$, and for each slice whose number is between $l$ and $r$, inclusive, you can specify one side, front or back, that has not been toasted yet and toast it. The side to toast can be chosen independently for each slice, but you cannot choose a side that has already been toasted, nor can you leave a slice without toasting either side.

Find the maximum achievable value of the sum of the deliciousness of the $N$ slices.

Input

$N$
$A_1$ $A_2$ $\dots$ $A_N$
$B_1$ $B_2$ $\dots$ $B_N$
$C_1$ $C_2$ $\dots$ $C_N$

Constraints

• $1 \le N \le 2 \times 10^5$
• $1 \le A_i, B_i, C_i \le 10^9 \quad (1 \le i \le N)$
• All input values are integers.

Output

Output the answer in $1$ line.

Sample

5
1 3 4 2 3
3 1 3 5 1
2 5 1 1 2

19

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

27

1
10
1
1

10