Polygon Area

/problems/polygonarea/file/statement/en/img-0001.png
Sample test cases.

Compute the area of a simple polygon, and the direction (clockwise or counterclockwise) in which its vertices are given.

Input

Input contains up to $25$ test cases. Each test case begins with an integer $n$ ($3 \leq n \leq 1\, 000$). Then follow the $n$ vertices of a simple polygon, one per line, each of the form $x\ y$. The points may be given in either clockwise or counterclockwise order. Coordinates are integers with absolute value bounded by $10\, 000$. The input is terminated by a case beginning with $0$.

Output

For each test case, output a line $D\ A$, where $D$ is one of “CW” or “CCW”, indicating whether the polygon was given in clockwise or counterclockwise order, respectively. $A$ is the area of the polygon, given with exactly one digit after the decimal point.

Sample Input 1 Sample Output 1
3
0 0
10 0
0 10
5
41 -6
-24 -74
-51 -6
73 17
-30 -34
0
CCW 50.0
CW 3817.5