题目描述

Bocchi the Builder just finished constructing her latest project: a laneway consisting of two rows of white equilateral triangular tiles. However, at the last moment, disaster struck! She accidentally spilled black paint on some of the tiles. Now, some of the tiles are wet and the other tiles are dry. Bocchi must place warning tape around the perimeters of all wet areas. Can you help her determine how many metres of tape she needs?

The first triangular tile will point upwards. Each pair of adjacent tiles (that is, tiles that share a common side) will point in opposite directions. Each tile has a side length of $1$ metre.

输入格式

The first line of input will consist of one positive integer $C$, representing the number of columns.

The next two lines will each consist of $C$ integers separated by spaces. Each integer represents the colour of a tile along the laneway, with 1 indicating that the tile is black (wet) and 0 indicating that the tile is white (dry).

The following table shows how the available 15 marks are distributed:

输出格式

Output a single integer representing the length of tape Bocchi needs,in metres.

5
1 0 1 0 1
0 0 0 0 0

9

7
0 0 1 1 0 1 0
0 0 1 0 1 0 0

11

提示

本题采用捆绑测试。

• Subtask $1$（$3$ points）：$C \leq 2 \times 10^3$，黑色三角形不相邻，第二行全部为白色三角形。
• Subtask $2$（$3$ points）：$C \leq 2 \times 10^3$，黑色三角形可能相邻，第二行全部为白色三角形。
• Subtask $3$（$5$ points）：$C \leq 2 \times 10^3$，黑色三角形可能相邻，第二行可能有黑色三角形。
• Subtask $4$（$4$ points）：$C \leq 2 \times 10^5$，黑色三角形可能相邻，第二行可能有黑色三角形。

样例 $1$ 图解：

样例 $2$ 图解：