Wish

문제

Each second Martynas catches a glimpse of the sky through his telescope expecting to see a falling star. Every time he sees a falling star he makes a wish upon it.

Martynas believes that the more falling stars he will see while making a wish, the higher the probability the wish will come true.

Calculate the largest possible number of stars Martynas can see during a glimpse through his telescope.

The sky can be modelled as an endless plane. Martynas can see an area limited by a circle with center $(0,0)(0,\; 0)$ and radius $RR$.

Before opening his telescope Martynas checked the star chart:

• There are $NN$ stars in the sky;
• During the first glimpse the coordinates of the $ii$’th star will be $a_{i}a\_i$, $b_{i}b\_i$;
• During the second glimpse (which will take place $11$ sec. after the first one) the $ii$’th star will be $c_{i}c\_i$, $d_{i}d\_i$;
• All the stars are moving at constant speed;
• The position of each star will change between the first and the second glimpse.

Martynas can keep looking at the stars forever.

입력

The first input line contains two numbers: the total amount of stars $NN$ and the radius of the circle $RR$.

Each of remaining $NN$ lines contains $44$ integers each: $a_{i}a\_i$, $b_{i}b\_i$, $c_{i}c\_i$, $d_{i}d\_i$ describing the position of $ii$’th star during the first and the second glimpse.

출력

The first and the only output line should contain one integer – largest possible number of stars visible through the telescope.

3 2
-5 0 -4 0
3 0 2 0
10 0 9 0

2

2 1
-3 -2 -1 -1
-2 2 -1 1

2

2 2
3 0 5 0
-2 1 2 1

0