When Vova was in Shenzhen, he rented a bike and spent most of the time
cycling around the city. Vova was approaching one of the city parks
when he noticed the park plan hanging opposite the central entrance. The
plan had several marble statues marked on it. One of such statues stood
right there, by the park entrance. Vova wanted to ride in the park on the
bike and take photos of all statues. The park territory has multiple
bidirectional cycling roads. Each cycling road starts and ends at a marble
statue and can be represented as a segment on the plane. If two cycling
roads share a common point, then Vova can turn on this point from one
road to the other. If the statue stands right on the road, it doesn't
interfere with the traffic in any way and can be photoed from the road.
Can Vova get to all statues in the park riding his bike along cycling
roads only?
Input
The first line contains integers n and m that are the number of statues and
cycling roads in the park (1 ≤ m < n ≤ 200). Then n lines
follow, each of them contains the coordinates of one statue on the park plan.
The coordinates are integers, their absolute values don't exceed
30 000. Any two statues have distinct coordinates. Each of the
following m lines contains two distinct integers from 1 to n that are the numbers of the statues that have a cycling road between them.
Output
Print “YES” if Vova can get from the park entrance to all the park
statues, moving along cycling roads only, and “NO” otherwise.
Samples
input  output 

4 2
0 0
1 0
1 1
0 1
1 3
4 2
 YES

4 3
0 0
1 0
1 1
0 1
1 2
2 1
3 4
 NO

3 2
0 0
1 0
1 1
1 3
3 2
 YES

Problem Source: Open Ural FU Personal Contest 2013