There is a white sheet of paper lying on a rectangle table. The sheet is a rectangle with its sides parallel to the sides of the table. If you will take a look from above and assume that the bottom left corner of the table has coordinates (0, 0), and coordinate axes are left and bottom sides of the table, then the bottom left corner of the white sheet has coordinates (x_1, y_1), and the top right — (x_2, y_2).

After that two black sheets of paper are placed on the table. Sides of both black sheets are also parallel to the sides of the table. Coordinates of the bottom left corner of the first black sheet are (x_3, y_3), and the top right — (x_4, y_4). Coordinates of the bottom left corner of the second black sheet are (x_5, y_5), and the top right — (x_6, y_6). 

<image> Example of three rectangles.

Determine if some part of the white sheet can be seen from the above after the two black sheets are placed. The part of the white sheet can be seen if there is at least one point lying not strictly inside the white sheet and strictly outside of both black sheets.

Input

The first line of the input contains four integers x_1, y_1, x_2, y_2 (0 ≤ x_1 < x_2 ≤ 10^{6}, 0 ≤ y_1 < y_2 ≤ 10^{6}) — coordinates of the bottom left and the top right corners of the white sheet.

The second line of the input contains four integers x_3, y_3, x_4, y_4 (0 ≤ x_3 < x_4 ≤ 10^{6}, 0 ≤ y_3 < y_4 ≤ 10^{6}) — coordinates of the bottom left and the top right corners of the first black sheet.

The third line of the input contains four integers x_5, y_5, x_6, y_6 (0 ≤ x_5 < x_6 ≤ 10^{6}, 0 ≤ y_5 < y_6 ≤ 10^{6}) — coordinates of the bottom left and the top right corners of the second black sheet.

The sides of each sheet of paper are parallel (perpendicular) to the coordinate axes.

Output

If some part of the white sheet can be seen from the above after the two black sheets are placed, print "YES" (without quotes). Otherwise print "NO".

Examples

Input


2 2 4 4
1 1 3 5
3 1 5 5


Output


NO


Input


3 3 7 5
0 0 4 6
0 0 7 4


Output


YES


Input


5 2 10 5
3 1 7 6
8 1 11 7


Output


YES


Input


0 0 1000000 1000000
0 0 499999 1000000
500000 0 1000000 1000000


Output


YES

Note

In the first example the white sheet is fully covered by black sheets.

In the second example the part of the white sheet can be seen after two black sheets are placed. For example, the point (6.5, 4.5) lies not strictly inside the white sheet and lies strictly outside of both black sheets.
import java.util.*;

public class WhiteSheet
{



    public static void main(String[] args)
    {
        Scanner sc = new Scanner(System.in);
        List<Rect> rects = new ArrayList<>();
        Rect white = Rect.read(sc);
        Rect black1 = Rect.read(sc);
        Rect black2= Rect.read(sc);

        // look at every cell. so we need the lower l and upper r coords
        // of every subcell
        Set<Integer> ys = new HashSet<>(List.of(black1.y1, black1.y2, black2.y1, black2.y2, white.y1, white.y2));
        Set<Integer> xs = new HashSet<>(List.of(black1.x1, black1.x2, black2.x1, black2.x2, white.x1, white.x2));
        List<Integer> ys_list = new ArrayList<>(ys);
        List<Integer> xs_list = new ArrayList<>(xs);
        ys_list.sort(Comparator.naturalOrder());
        xs_list.sort(Comparator.naturalOrder());

        for (int y = 0; y < ys_list.size() - 1; y++)
        {
            for (int x = 0; x < xs_list.size() - 1; x++)
            {
                double yPoint = ys_list.get(y) + 0.5;
                double xPoint = xs_list.get(x) + 0.5;

                // It's NOT in the black sheet AND it IS in the white sheet
                // It's less than the lower edge of black1 or more than the upper edge of black1 and 
                // It's less than the left edge of black1 or more than the right edge of black1
                if (!(black1.contains(xPoint, yPoint) || black2.contains(xPoint, yPoint)) && white.contains(xPoint, yPoint))
                {
                    System.out.println("YES");
                    return;
                }
            }
        }
        System.out.println("NO");
    }
}


class Rect
{

    public int x1;
    public int y1;
 
    public int x2;
    public int y2;

    public Rect(int x1, int y1, int x2, int y2)
    {
        this.x1 = x1;
        this.y1 = y1;

        this.x2 = x2;
        this.y2 = y2;
    }

    public boolean contains(double x, double y)
    {
        return x1 <= x && x <= x2 && y1 <= y && y <= y2;
    }

    public static Rect read(Scanner sc)
    {
        int x1, y1, x2, y2;
        x1 = sc.nextInt();
        y1 = sc.nextInt();
        x2 = sc.nextInt();
        y2 = sc.nextInt();
        return new Rect(x1, y1, x2, y2);
    }
}