Problem: Arpa is taking a geometry exam. Here is the last problem of the exam.

You are given three points a, b, c.

Find a point and an angle such that if we rotate the page around the point by the angle, the new position of a is the same as the old position of b, and the new position of b is the same as the old position of c.

Arpa is doubting if the problem has a solution or not (i.e. if there exists a point and an angle satisfying the condition). Help Arpa determine if the question has a solution or not.

Input

The only line contains six integers ax, ay, bx, by, cx, cy (|ax|, |ay|, |bx|, |by|, |cx|, |cy| ≤ 109). It's guaranteed that the points are distinct.

Output

Print "Yes" if the problem has a solution, "No" otherwise.

You can print each letter in any case (upper or lower).

Examples

Input

0 1 1 1 1 0


Output

Yes


Input

1 1 0 0 1000 1000


Output

No

Note

In the first sample test, rotate the page around (0.5, 0.5) by <image>.

In the second sample test, you can't find any solution.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {

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

        new Main().go();
    }

    PrintWriter out;
    Reader in;
    BufferedReader br;

    Main() throws IOException {

        try {

            //br = new BufferedReader( new FileReader("input.txt") );
            in = new Reader("input.txt");
            out = new PrintWriter( new BufferedWriter(new FileWriter("output.txt")) );
        }
        catch (Exception e) {

            //br = new BufferedReader( new InputStreamReader( System.in ) );
            in = new Reader();
            out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );
        }
    }

    void go() throws IOException {

        int t = 1;
        while (t > 0) {
            solve();
            //out.println();
            t--;
        }

        out.flush();
        out.close();
    }

    int inf = 2000000000;
    int mod = 1000000007;
    double eps = 0.000000001;

    int n;
    int m;

    //ArrayList<Integer>[] g = new ArrayList[200010];

    void solve() throws IOException {

        int x1 = in.nextInt();
        int y1 = in.nextInt();

        int x2 = in.nextInt();
        int y2 = in.nextInt();

        int x3 = in.nextInt();
        int y3 = in.nextInt();

        long a = dist(x1, y1, x2, y2);
        long b = dist(x2, y2, x3, y3);
        long c = dist(x1, y1, x3, y3);

       // System.err.println(Math.abs(Math.sqrt(a)));



        boolean onLine = (x2-x1)/gcd(x2 - x1, y2 - y1) == (x3-x1)/gcd(x3 - x1, y3 - y1) && (y2-y1)/gcd(x2 - x1, y2 - y1) == (y3-y1)/gcd(x3 - x1, y3 - y1);

        if (a == b && !onLine) {

            out.print("Yes");
            return;
        }

        out.println("No");
    }

    long dist(int x1, int y1, int x2, int y2) {
        return 1l*(x1-x2)*(x1-x2) + 1l*(y1-y2)*(y1-y2);
    }

    long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a%b);
    }

    class Pair implements Comparable<Pair>{

        int a;
        int b;

        Pair(int a, int b) {

            this.a = a;
            this.b = b;
        }

        public int compareTo(Pair p) {

            if (a > p.a) return 1;
            if (a < p.a) return -1;
            if (b > p.b) return 1;
            if (b < p.b) return -1;
            return 0;
        }
    }

    class Item {

        int a;
        int b;
        int c;

        Item(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

    }

    class Reader {

        BufferedReader  br;
        StringTokenizer tok;

        Reader(String file) throws IOException {
            br = new BufferedReader( new FileReader(file) );
        }

        Reader() throws IOException {
            br = new BufferedReader( new InputStreamReader(System.in) );
        }

        String next() throws IOException {

            while (tok == null || !tok.hasMoreElements())
                tok = new StringTokenizer(br.readLine());
            return tok.nextToken();
        }

        int nextInt() throws NumberFormatException, IOException {
            return Integer.valueOf(next());
        }

        long nextLong() throws NumberFormatException, IOException {
            return Long.valueOf(next());
        }

        double nextDouble() throws NumberFormatException, IOException {
            return Double.valueOf(next());
        }


        String nextLine() throws IOException {
            return br.readLine();
        }

    }

}