A9923. Sasha Circle

Berlanders like to eat cones after a hard day. Misha Square and Sasha Circle are local authorities of Berland. Each of them controls its points of cone trade. Misha has $n$ points, Sasha — $m$ . Since their subordinates constantly had conflicts with each other, they decided to build a fence in the form of a circle, so that the points of trade of one businessman are strictly inside a circle, and points of the other one are strictly outside. It doesn't matter which of the two gentlemen will have his trade points inside the circle.

Determine whether they can build a fence or not.

The first line contains two integers $n$ and $m$ $(1<=n,m<=10000)$ , numbers of Misha's and Sasha's trade points respectively.

The next $n$ lines contains pairs of space-separated integers $M_{x},M_{y}$ ( $-10^{4}<=M_{x},M_{y}<=10^{4}$ ), coordinates of Misha's trade points.

The next $m$ lines contains pairs of space-separated integers $S_{x},S_{y}$ ( $-10^{4}<=S_{x},S_{y}<=10^{4}$ ), coordinates of Sasha's trade points.

It is guaranteed that all $n+m$ points are distinct.

The only output line should contain either word "YES" without quotes in case it is possible to build a such fence or word "NO" in the other case.

In the first sample there is no possibility to separate points, because any circle that contains both points $(-1,0),(1,0)$ also contains at least one point from the set $(0,-1),(0,1)$ , and vice-versa: any circle that contains both points $(0,-1),(0,1)$ also contains at least one point from the set $(-1,0),(1,0)$

In the second sample one of the possible solution is shown below. Misha's points are marked with red colour and Sasha's are marked with blue.