### 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 $R=\lbrace(x,y)\mid a-0.5\leq x\leq b+0.5,c-0.5\leq y\leq d+0.5\rbrace$. 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.

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.

No

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

Yes

Takahashi may already be at the destination in the beginning.