Problem Statement

Takahashi is on an xy-plane.
Initially, he is at point (s _ x,s _ y),
and he wants to reach point (t _ x,t _ y).
On the xy-plane is $a rectangle R\coloneqq\lbrace(x,y)\mid a-0.5\leq x\leq b+0.5,c-0.5\leq y\leq d+0.5\rbrace$.
Consider the following operation:

• Choose a lattice point (x,y) contained in the rectangle R. Takahashi teleports to the point symmetric to his current position with respect to point (x,y).

Determine if he can reach point (t _ x,t _ y) after repeating the operation above between 0 and 10^6 times, inclusive.
If it is possible, construct a sequence of operations that leads him to point (t _ x,t _ y).

Input

The input is given from Standard Input in the following format:
s _ x s _ y
t _ x t _ y
a b c d

Output

In the first line, print Yes if Takahashi can reach point (t _ x,t _ y) after repeating the operation between 0 and 10^6 times, inclusive, and No otherwise.
If and only if you print Yes in the first line, print d more lines, where d is the length of the sequence of operations you have constructed (d must satisfy $0\leq d\leq10^6)$.
The $(1+i)-th line (1\leq i\leq d)$ should contain the space-separated coordinates of the point $(x, y)\in$ R, in this order, that is chosen in the i-th operation.

Constraints

• $0\leq s _ x,s _ y,t _ x,t _ y\leq2\times10^5$
• $0\leq a\leq b\leq2\times10^5$
• $0\leq c\leq d\leq2\times10^5$
• All values in the input are integers.

Sample Input 1

1 2
7 8
7 9 0 3

Sample Output 1

Yes
7 0
9 3
7 1
8 1

For example, the following choices lead him from (1,2) to (7,8).

• Choose (7,0). Takahashi moves to (13,-2).
• Choose (9,3). Takahashi moves to (5,8).
• Choose (7,1). Takahashi moves to (9,-6).
• Choose (8,1). Takahashi moves to (7,8).

Any output that satisfies the conditions is accepted; for example, printing
Yes
7 3
9 0
7 2
9 1
8 1

is also accepted.

Sample Input 2

0 0
8 4
5 5 0 0

Sample Output 2

No

No sequence of operations leads him to point (8,4).

Sample Input 3

1 4
1 4
100 200 300 400

Sample Output 3

Yes

Takahashi may already be at the destination in the beginning.

Sample Input 4

22 2
16 7
14 30 11 14

Sample Output 4

No

见题面 Input 部分

见题面 Output 部分