Forest for the Trees

문제

You are playing hide-and-go-seek in a forest with Belle.  The forest has one tree at each of the positive integer lattice points.  That is, there is a tree at every point $(x,y)(x,y)$ where $xx$ and $yy$ are both positive integers.  You may consider each tree as a point.  A logging company has cut down all of the trees in some axis-aligned rectangle, including those on the boundary of the rectangle.

You are standing at $(0,0)(0,0)$ and Belle is standing at $(x_b,y_b)(x\_b,y\_b)$. You can see Belle if and only if there is no tree blocking your line of sight to Belle. If there is a tree at $(x_b,y_b)(x\_b,y\_b)$, Belle will make it easier for you to find her by standing on the side of the tree facing your location.

For example, suppose that Belle is standing at $(2,6)(2,6)$.  If the trees in the rectangle with corners at $(1,1)(1,1)$ and $(5,4)(5,4)$ are cut down (blue rectangle in figure), then you can see Belle.  However, if the rectangle was at $(3,5)(3,5)$ and $(5,7)(5,7)$ (red rectangle in figure), then the tree at $(1,3)(1,3)$ would be in the way.

Given the rectangle and Belle's location, can you see her?

입력

The first line of input contains two integer $x_{b}x\_b$ and $y_{b}y\_b$ ($1\le x_b,y_b\le {10}^{12}1\; \backslash leq\; x\_b,y\_b\; \backslash leq\; 10^\{12\}$), which are the coordinates that Belle is standing on.

The second line of input contains four integers $x_{1}x\_1$, $y_{1}y\_1$, $x_{2}x\_2$ and $y_{2}y\_2$ ($1\le x_1\le x_2\le {10}^{12}1\; \backslash leq\; x\_1\; \backslash leq\; x\_2\; \backslash leq\; 10^\{12\}$ and $1\le y_1\le y_2\le {10}^{12}1\; \backslash leq\; y\_1\; \backslash leq\; y\_2\; \backslash leq\; 10^\{12\}$), which specify two opposite corners of the rectangle at $(x_1,y_1)(x\_1,\; y\_1)$ and $(x_2,y_2)(x\_2,\; y\_2)$.

출력

If you can see Belle, display Yes.

Otherwise, display No and the coordinates of the closest tree that is blocking your view.

2 6
1 1 5 4

Yes

2 6
3 5 5 7

No
1 3

830844890448 39710592053
821266 42860 402207107926 423171345006

No
402207964848 19223704203