Problem: Long time ago Alex created an interesting problem about parallelogram. The input data for this problem contained four integer points on the Cartesian plane, that defined the set of vertices of some non-degenerate (positive area) parallelogram. Points not necessary were given in the order of clockwise or counterclockwise traversal.

Alex had very nice test for this problem, but is somehow happened that the last line of the input was lost and now he has only three out of four points of the original parallelogram. He remembers that test was so good that he asks you to restore it given only these three points.

Input

The input consists of three lines, each containing a pair of integer coordinates xi and yi ( - 1000 ≤ xi, yi ≤ 1000). It's guaranteed that these three points do not lie on the same line and no two of them coincide.

Output

First print integer k — the number of ways to add one new integer point such that the obtained set defines some parallelogram of positive area. There is no requirement for the points to be arranged in any special order (like traversal), they just define the set of vertices.

Then print k lines, each containing a pair of integer — possible coordinates of the fourth point.

Example

Input

0 0
1 0
0 1


Output

3
1 -1
-1 1
1 1

Note

If you need clarification of what parallelogram is, please check Wikipedia page:

https://en.wikipedia.org/wiki/Parallelogram

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;

public class MainB {
    MyScanner sc    = new MyScanner();
    Scanner   sc2   = new Scanner(System.in);
    final int MOD   = 1000000007;
    int[]     dx    = { 1, 0, 0, -1 };
    int[]     dy    = { 0, 1, -1, 0 };

    void run() {
        int x1 = sc.nextInt();
        int y1 = sc.nextInt();
        int x2 = sc.nextInt();
        int y2 = sc.nextInt();
        int x3 = sc.nextInt();
        int y3 = sc.nextInt();

        Point o1 = new Point(x1, y1);
        Point o2 = new Point(x2, y2);
        Point o3 = new Point(x3, y3);

        int d1_2 = getDist(x1, y1, x2, y2);
        int d1_3 = getDist(x1, y1, x3, y3);
        int d2_3 = getDist(x2, y2, x3, y3);

        List<Integer> ax = new ArrayList<>();
        List<Integer> ay = new ArrayList<>();
        for (int x = -3000; x <= 3000; x++) {
            for (int y = -3000; y <= 3000; y++) {
                if (x == x1 && y == y1 || x == x2 && y == y2 || x == x3 && y == y3)
                    continue;

                Point p = new Point(x, y);

                int p1 = getDist(x, y, x1, y1);
                int p2 = getDist(x, y, x2, y2);
                int p3 = getDist(x, y, x3, y3);

                // 6patern
                if (p1 == d2_3 && p2 == d1_3 && !lineCross(p, o1, o2, o3) && !lineCross(p, o2, o1, o3)) {
                    ax.add(x);
                    ay.add(y);
                    continue;
                }
                if (p2 == d1_3 && p1 == d2_3 && !lineCross(p, o2, o1, o3) && !lineCross(p, o1, o2, o3)) {
                    ax.add(x);
                    ay.add(y);
                    continue;
                }
                if (p1 == d2_3 && p3 == d1_2 && !lineCross(p, o1, o2, o3) && !lineCross(p, o3, o1, o2)) {
                    ax.add(x);
                    ay.add(y);
                    continue;
                }
                if (p2 == d1_3 && p3 == d1_2 && !lineCross(p, o2, o1, o3) && !lineCross(p, o3, o1, o2)) {
                    ax.add(x);
                    ay.add(y);
                    continue;
                }
                if (p1 == d2_3 && p3 == d1_2 && !lineCross(p, o1, o2, o3) && !lineCross(p, o3, o1, o2)) {
                    ax.add(x);
                    ay.add(y);
                    continue;
                }
                if (p2 == d1_3 && p3 == d1_2 && !lineCross(p, o2, o1, o3) && !lineCross(p, o3, o1, o2)) {
                    ax.add(x);
                    ay.add(y);
                    continue;
                }
            }
        }
        System.out.println(ax.size());
        for (int i = 0; i < ax.size(); i++) {
            System.out.println(ax.get(i) + " " + ay.get(i));
        }
    }

    int getDist(int a, int b, int c, int d) {
        return (a - c) * (a - c) + (b - d) * (b - d);
    }

    boolean lineCross(Point p1, Point p2, Point p3, Point p4) {
        double a = (p1.x - p2.x) * (p3.y - p1.y) + (p1.y - p2.y) * (p1.x - p3.x);
        double b = (p1.x - p2.x) * (p4.y - p1.y) + (p1.y - p2.y) * (p1.x - p4.x);
        double c = (p3.x - p4.x) * (p1.y - p3.y) + (p3.y - p4.y) * (p3.x - p1.x);
        double d = (p3.x - p4.x) * (p2.y - p3.y) + (p3.y - p4.y) * (p3.x - p2.x);
        return a * b <= 0 && c * d <= 0;
    }

    class Point {
        double x;
        double y;

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

    public static void main(String[] args) {
        new MainB().run();
    }

    void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }

    void debug2(int[][] array) {
        for (int i = 0; i < array.length; i++) {
            for (int j = 0; j < array[i].length; j++) {
                System.out.print(array[i][j]);
            }
            System.out.println();
        }
    }

    boolean inner(int h, int w, int limH, int limW) {
        return 0 <= h && h < limH && 0 <= w && w < limW;
    }

    void swap(int[] x, int a, int b) {
        int tmp = x[a];
        x[a] = x[b];
        x[b] = tmp;
    }

    // find minimum i (k <= a[i])
    int lower_bound(int a[], int k) {
        int l = -1;
        int r = a.length;
        while (r - l > 1) {
            int mid = (l + r) / 2;
            if (k <= a[mid])
                r = mid;
            else
                l = mid;
        }
        // r = l + 1
        return r;
    }

    // find minimum i (k < a[i])
    int upper_bound(int a[], int k) {
        int l = -1;
        int r = a.length;
        while (r - l > 1) {
            int mid = (l + r) / 2;
            if (k < a[mid])
                r = mid;
            else
                l = mid;
        }
        // r = l + 1
        return r;
    }

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

    long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }

    boolean palindrome(String s) {
        for (int i = 0; i < s.length() / 2; i++) {
            if (s.charAt(i) != s.charAt(s.length() - 1 - i)) {
                return false;
            }
        }
        return true;
    }

    class MyScanner {
        int nextInt() {
            try {
                int c = System.in.read();
                while (c != '-' && (c < '0' || '9' < c))
                    c = System.in.read();
                if (c == '-')
                    return -nextInt();
                int res = 0;
                do {
                    res *= 10;
                    res += c - '0';
                    c = System.in.read();
                } while ('0' <= c && c <= '9');
                return res;
            } catch (Exception e) {
                return -1;
            }
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        String next() {
            try {
                StringBuilder res = new StringBuilder("");
                int c = System.in.read();
                while (Character.isWhitespace(c))
                    c = System.in.read();
                do {
                    res.append((char) c);
                } while (!Character.isWhitespace(c = System.in.read()));
                return res.toString();
            } catch (Exception e) {
                return null;
            }
        }

        int[] nextIntArray(int n) {
            int[] in = new int[n];
            for (int i = 0; i < n; i++) {
                in[i] = nextInt();
            }
            return in;
        }

        int[][] nextInt2dArray(int n, int m) {
            int[][] in = new int[n][m];
            for (int i = 0; i < n; i++) {
                in[i] = nextIntArray(m);
            }
            return in;
        }

        double[] nextDoubleArray(int n) {
            double[] in = new double[n];
            for (int i = 0; i < n; i++) {
                in[i] = nextDouble();
            }
            return in;
        }

        long[] nextLongArray(int n) {
            long[] in = new long[n];
            for (int i = 0; i < n; i++) {
                in[i] = nextLong();
            }
            return in;
        }

        char[][] nextCharField(int n, int m) {
            char[][] in = new char[n][m];
            for (int i = 0; i < n; i++) {
                String s = sc.next();
                for (int j = 0; j < m; j++) {
                    in[i][j] = s.charAt(j);
                }
            }
            return in;
        }
    }
}