Problem J
Galaxy Quest

NASA recently confirmed the discovery of parallel universes (PUs) occupying alternate dimensions. These universes are quite different from our own universe, in the following ways:

• Each PU is a two-dimensional square that stretches ${10}^9$ light years from left to right and from top to bottom.

• Each PU has a galactic diameter of $d$ light years, where $d$ is an integer.

• Each star is exactly $x$ light years from its universe’s left edge and $y$ light years from its universe’s bottom edge, where $x$ and $y$ are non-negative integers.

• Stars are clustered into galaxies. Each galaxy consists of one or more stars. Each star is at most $d$ light years from every other star in its galaxy. Any two stars from different galaxies are more than $d$ light years apart.

  It is crucial to understand the implications of this. The locations of the stars determine the galaxies. The galaxy to which a star $s$ belongs consists of $s$ plus all other stars that are within $d$ light years of $s$. Suppose you draw a circle of diameter $d$ around all of the stars of a galaxy. Any star not belonging to the galaxy will be outside the circle and will be more than $d$ light years from every star in the galaxy.

For each PU, NASA has obtained all of its stellar coordinates and has measured its value of $d$.

Given the description of a PU, NASA would like to be able to determine whether that PU has a galaxy that contains more than half of the stars in the PU. NASA has turned to you.

Input

The input describes a single PU. All numbers in the input are integers.

The first line of the input contains the PU’s galactic diameter $d$ ($1\le d\le {10}^6$) and star count $k$ ($1\le k\le {10}^6$).

There are exactly $k$ more lines. Each line contains the $x$ ($0\le x\le {10}^9$) and $y$ ($0\le y\le {10}^9$) coordinates of a star in the PU. No two of these lines are identical, as a black hole would result!

The star positions and $d$ are guaranteed to obey the clustering constraint discussed above.

Output

If the PU described by the input has a galaxy containing more than half of the stars, display the number of stars in that galaxy. Otherwise, display NO.

10 4
45 46
90 47
45 54
90 43

NO

20 7
1 1
100 100
1 3
101 101
3 1
102 102
3 3

4