Problem Statement

You are trying to implement collision detection in a 3D game.

In a 3-dimensional space, let C(a,b,c,d,e,f) denote the cuboid with a diagonal connecting (a,b,c) and (d,e,f), and with all faces parallel to the xy-plane, yz-plane, or zx-plane.
(This definition uniquely determines C(a,b,c,d,e,f).)
Given two cuboids C(a,b,c,d,e,f) and C(g,h,i,j,k,l), determine whether their intersection has a positive volume.

Input

The input is given from Standard Input in the following format:
a b c d e f
g h i j k l

Output

Print Yes if the intersection of the two cuboids has a positive volume, and No otherwise.

Constraints

• $0 \leq a < d \leq 1000$
• $0 \leq b < e \leq 1000$
• $0 \leq c < f \leq 1000$
• $0 \leq g < j \leq 1000$
• $0 \leq h < k \leq 1000$
• $0 \leq i < l \leq 1000$
• All input values are integers.

Sample Input 1

0 0 0 4 5 6
2 3 4 5 6 7

Sample Output 1

Yes

The positional relationship of the two cuboids is shown in the figure below, and their intersection has a volume of 8.

Sample Input 2

0 0 0 2 2 2
0 0 2 2 2 4

Sample Output 2

No

The two cuboids touch at a face, where the volume of the intersection is 0.

Sample Input 3

0 0 0 1000 1000 1000
10 10 10 100 100 100

Sample Output 3

Yes

见题面 Input 部分

见题面 Output 部分