Problem:
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A Point in a Triangle

There is a triangle formed by three points $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$ on a plain.

Write a program which prints "YES" if a point $P$ $(x_p, y_p)$ is in the triangle and "NO" if not.

Input

Input consists of several datasets. Each dataset consists of:

$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_p$ $y_p$

All the input are real numbers. Input ends with EOF. The number of datasets is less than or equal to 100.

Constraints

You can assume that:

$ -100 \leq x_1, y_1, x_2, y_2, x_3, y_3, x_p, y_p \leq 100$

1.0 $\leq$ Length of each side of a tringle

0.001 $\leq$ Distance between $P$ and each side of a triangle

Output

For each dataset, print "YES" or "NO" in a line.

Sample Input

0.0 0.0 2.0 0.0 2.0 2.0 1.5 0.5
0.0 0.0 1.0 4.0 5.0 3.0 -1.0 3.0

Output for the Sample Input

YES
NO

Solution in JAVA (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line = "";

		double x1, y1, x2, y2, x3, y3, xp, yp;
		StringTokenizer st;

		while ((line = br.readLine()) != null && !line.isEmpty()) {
			st = new StringTokenizer(line);
			x1 = Double.parseDouble(st.nextToken());
			y1 = Double.parseDouble(st.nextToken());
			x2 = Double.parseDouble(st.nextToken());
			y2 = Double.parseDouble(st.nextToken());
			x3 = Double.parseDouble(st.nextToken());
			y3 = Double.parseDouble(st.nextToken());
			xp = Double.parseDouble(st.nextToken());
			yp = Double.parseDouble(st.nextToken());

			// 点Pを原点に移動
			x1 -= xp;
			x2 -= xp;
			x3 -= xp;
			x1 -= xp;
			y2 -= yp;
			y3 -= yp;
			yp -= yp;
			xp = yp = 0;

			// ベクトルの内積
			if (x1 * x2 + y1 * y2 < 0 && x1 * x3 + y1 * y3 < 0) {
				System.out.println("YES");
			} else if (x2 * x1 + y2 * y1 < 0 && x2 * x3 + y2 * y3 < 0) {
				System.out.println("YES");
			} else if (x3 * x1 + y3 * y1 < 0 && x3 * x2 + y3 * y2 < 0) {
				System.out.println("YES");
			} else {
				System.out.println("NO");
			}
		}
	}
}