Wish

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 $(0, 0)$ and radius $R$.

Before opening his telescope Martynas checked the star chart:

• There are $N$ stars in the sky;
• During the first glimpse the coordinates of the $i$’th star will be $a\_i$, $b\_i$;
• During the second glimpse (which will take place $1$ sec. after the first one) the $i$’th star will be $c\_i$, $d\_i$;
• 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.

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

Each of remaining $N$ lines contains $4$ integers each: $a\_i$, $b\_i$, $c\_i$, $d\_i$ describing the position of $i$’th star during the first and the second glimpse.

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

• $1 ≤ N ≤ 200\\,000$
• $1 ≤ R ≤ 100\\,000\\,000$
• $-100\\,000\\,000 ≤ a\_i , b\_i , c\_i , d\_i ≤ 100\\,000\\,000$ (a star will move, i.e.: $(a\_i , b\_i) \ne (c\_i , d\_i)$)