Problem:
Area

For a given polygon g, computes the area of the polygon.

g is represented by a sequence of points p1, p2,..., pn where line segments connecting pi and pi+1 (1 ≤ i ≤ n-1) are sides of g. The line segment connecting pn and p1 is also a side of the polygon.

Note that the polygon is not necessarily convex.

Input

The input consists of coordinates of the points p1,..., pn in the following format:

n
x1 y1
x2 y2
:
xn yn

The first integer n is the number of points. The coordinate of a point pi is given by two integers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them.

Output

Print the area of the polygon in a line. The area should be printed with one digit to the right of the decimal point.

Constraints

3 ≤ n ≤ 100

-10000 ≤ xi, yi ≤ 10000

No point will occur more than once.

Two sides can intersect only at a common endpoint.

Sample Input 1

3
0 0
2 2
-1 1

Sample Output 1

2.0

Sample Input 2

4
0 0
1 1
1 2
0 2

Sample Output 2

1.5

Solution in C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            Point[] points = new Point[n];

            double sum = 0.0;
            for (int i = 0; i < n; i++)
            {
                string[] input = Console.ReadLine().Split(' ');
                double x = double.Parse(input[0]);
                double y = double.Parse(input[1]);
                points[i] = new Point(x, y);

                if (i != 0)
                {
                    sum += (points[i - 1] - points[0]).Cross(points[i] - points[0]);
                }
            }
            Console.WriteLine("{0:f1}", sum / 2);
        }
    }

    class Point : IComparable<Point>
    {
        static readonly double EPS = 1E-10;

        internal double x, y;

        public Point(double x, double y)
        {
            this.x = x;
            this.y = y;
        }

        public double Abs { get { return Math.Sqrt(Norm); } }
        public double Norm { get { return x * x + y * y; } }

        public double Dot(Point p) { return x * p.x + y * p.y; }
        public double Cross(Point p) { return x * p.y - y * p.x; }

        public static Point operator +(Point a, Point b) { return new Point(a.x + b.x, a.y + b.y); }
        public static Point operator -(Point a, Point b) { return new Point(a.x - b.x, a.y - b.y); }
        public static Point operator *(Point p, double d) { return new Point(p.x * d, p.y * d); }
        public static Point operator /(Point p, double d) { return new Point(p.x / d, p.y / d); }
        public static bool operator <(Point a, Point b) { return Math.Abs(a.x - b.x) > EPS ? a.x < b.x : a.y < b.y; }
        public static bool operator >(Point a, Point b) { return Math.Abs(a.x - b.x) > EPS ? a.x > b.x : a.y > b.y; }
        public static bool operator ==(Point a, Point b) { return Math.Abs(a.x - b.x) < EPS && Math.Abs(a.y - b.y) < EPS; }
        public static bool operator !=(Point a, Point b) { return Math.Abs(a.x - b.x) >= EPS || Math.Abs(a.y - b.y) >= EPS; }

        public int CompareTo(Point other)
        {
            return x != other.x ? (int)(x - other.x) : (int)(y - other.y);
        }

        public override bool Equals(object obj)
        {
            Point other = obj as Point;
            return Math.Abs(x - other.x) < EPS && Math.Abs(y - other.y) < EPS;
        }

        public override int GetHashCode()
        {
            return x.GetHashCode() ^ y.GetHashCode();
        }

        public override string ToString()
        {
            return string.Format("{0:f10} {1:f10}", x, y);
        }
    }

    class Segment
    {
        internal Point p1, p2;

        public Segment(Point p1, Point p2)
        {
            this.p1 = p1;
            this.p2 = p2;
        }
    }

    class Circle
    {
        internal Point p;
        internal double r;

        public Circle(Point p, double r)
        {
            this.p = p;
            this.r = r;
        }
    }
}