RESTAURANTS

As the network manager of a restaurant chain, you must choose where to open stores along the new national road. ~N~ candidate positions have been preselected, and stores can be opened at any of these. For each candidate position ~1 \le i \le N~, the expected profit from opening a store there has been calculated based on whether stores will open at neighboring positions. If no store opens at positions ~i-1~ and ~i+1~, the expected profit from the store at position ~i~ is ~a_i~. If a store opens at one of positions ~i-1~ or ~i+1~, the expected profit is ~b_i~. If stores open at both positions ~i-1~ and ~i+1~, the expected profit is ~c_i~ (~c_1~ and ~c_N~ are not defined, and for each position ~i~, it holds that ~a_i \ge b_i \ge c_i \ge 0~).

Write a program that selects the positions where stores should be opened to maximize profit.

Input

The first line of input contains the number of candidate positions ~N~. The second line contains ~N~ numbers, the values of ~a_1~, ~...~, ~a_N~. The third line contains ~N~ numbers, the values of ~b_1~, ~...~, ~b_N~. Finally, the fourth line contains ~N - 2~ numbers, the values of ~c_2~, ~...~, ~c_{N-1}~.

Output

The output must consist of one line containing exactly one integer, the maximum profit that can be obtained

Constraints

~2 \le N \le 1.000.000~
~0 \le c_i \le b_i \le a_i \le 1.000~
Maximum Execution Time: 2 sec
Available Memory: 64 MB

Example of Input - Output

STDIN (restaurants.in)

8
10 9 15 8 18 12 6 8
6 5 8 7 16 10 5 7
3 6 6 12 9 4

STDOUT (restaurants.out)

61

Explanation of the Example

The optimal solution is to open restaurants at positions ~1~, ~3~, ~5~, ~6~, ~7~, and ~8~. Thus, the expected profit is ~61~ ~(10 + 0 + 15 + 0 + 16 + 9 + 4 + 7)~.