# Poj Solution 1265

```http://poj.org/problem?id=1265

//* @author: ccQ.SuperSupper
import java.io.*;
import java.util.*;
class Point{
int x,y;
}
public class Main {

static final int N = 100+10;
static int n;
static Point Area[] = new Point[N];
static void start(){
for(int i=0;i< N;++i)
Area[i] = new Point();
}
public static void main(String []args) throws Exception{

int t,cs=1,i,x,y;

start();
t = Get_Num(cin);
while(t--!=0){
n = Get_Num(cin);
Area[0].x = Area[0].y = 0;
for(i=1;i<=n;++i){
Area[i].x = Get_Num(cin)+Area[i-1].x;
Area[i].y = Get_Num(cin)+Area[i-1].y;
}
solve(cs++);
}
}
static int Get_Num(StreamTokenizer cin) throws Exception{
cin.nextToken();
return (int) cin.nval;
}
static int GCD(int a,int b){
if(b==0) return a;
return GCD(b,a%b);
}
static int node_in_line(Point a,Point b){
int x,y;
x = abs(a.x-b.x);
y = abs(a.y-b.y);
return GCD(x,y);
}
static int abs(int a){
if(a>=0) return a;
return -a;
}
static int get_area(Point a,Point b,Point c){
return (c.x-a.x)*(b.y-a.y) - (b.x-a.x)*(c.y-a.y);
}
static void solve(int cs){
int I,E=0,area=0,i;
for(i=0;i< n;++i){
E+=node_in_line(Area[i],Area[(i+1)%n]);
}
for(i=2;i< n;++i){
area += get_area(Area[0],Area[i-1],Area[i]);
}
area = abs(area);
I = (area-E+2)/2;

System.out.print("Scenario #"+cs+":n"+I+" "+E+" ");
if(area%2==0) System.out.println(area/2+".0n");
else System.out.println(area/2+".5n");
}
}

```
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