# 原始题目

## Area

• Time Limit: 1000MS
• Memory Limit: 10000K
• Total Submissions: 21457
• Accepted: 5826

### Description

You are going to compute the area of a special kind of polygon. One vertex of the polygon is the origin of the orthogonal coordinate system. From this vertex, you may go step by step to the following vertexes of the polygon until back to the initial vertex. For each step you may go North, West, South or East with step length of 1 unit, or go Northwest, Northeast, Southwest or Southeast with step length of square root of 2.

For example, this is a legal polygon to be computed and its area is 2.5:

### Input

The first line of input is an integer t (1 ≤ t ≤ 20), the number of the test polygons. Each of the following lines contains a string composed of digits 1-9 describing how the polygon is formed by walking from the origin. Here 8, 2, 6 and 4 represent North, South, East and West, while 9, 7, 3 and 1 denote Northeast, Northwest, Southeast and Southwest respectively. Number 5 only appears at the end of the sequence indicating the stop of walking. You may assume that the input polygon is valid which means that the endpoint is always the start point and the sides of the polygon are not cross to each other.Each line may contain up to 1000000 digits.

### Output

For each polygon, print its area on a single line.

### Sample Input

4
5
825
6725
6244865

### Sample Output

0
0
0.5
2

### Source

POJ Monthly--2004.05.15 Liu Rujia@POJ

# 题目大意

• 在二维坐标系中点向8个方向移动，经过一系列移动后回到原点，并且边不相交（构成闭合的多边形），求其面积。

# 解题思路

• 由于坐标都是整数且很大，由于精度考虑，按照long long计算最后再除以2.

# 收获与反思

• 整数坐标注意开long long。
• 多边形有向面积模板题。