B. Sour Strip Shapes
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Sage started getting bored of eating the same sour strips every day, so she decided to play a game with them. Using the sour strips, she plans to use the strips to draw the perimeters of two squares on the coordinate plane. Each side of these squares will be parallel to either the $$$x$$$ or $$$y$$$ axis. However, if the perimeters ever overlap, then she won't be able to lay the strips on top of each other to make the shapes! Even if the perimeters intersect at a vertex, it is impossible. Can you check her plan to confirm it is feasible?

Input

The first line contains three integers $$$x_1, y_1, s_1$$$ ($$$0 \leq |x_1|, |y_1| \leq 10^3, 1 \leq s_1 \leq 10^3$$$) — the coordinates of the lower-left corner of the first square and its side length, respectively.

The second line contains three integers $$$x_1, y_1, s_1$$$ ($$$0 \leq |x_2|, |y_2| \leq 10^3, 1 \leq s_2 \leq 10^3$$$) — the coordinates of the lower-left corner of the second square and its side length, respectively.

Output

Output "YES" (without the quotes) if the squares overlap, and print "NO" otherwise. You can output the answer in any case.

Examples
Input
1 1 2
2 2 2
Output
YES
Input
0 0 1
2 2 2
Output
NO
Input
0 0 4
1 1 2
Output
NO
Input
0 0 1
1 1 1
Output
YES