Problem Description

On a vast and boundless plain, there are $N$ magnet stones scattered around.

The properties of each magnet stone can be described by a 5-tuple $(x,y,m,p,r)$, where $x,y$ are its coordinates, $m$ is the mass of the stone, $p$ is the magnetic force, and $r$ is the attraction radius.

If the distance between magnet stone $A$ and magnet stone $B$ is no greater than the attraction radius of $A$, and the mass of $B$ is no greater than the magnetic force of $A$, then $A$ can attract $B$.

Xiaoqujiu brings his own magnet stone $L$ to the position $(x_0,y_0)$ on this plain, and we can treat the coordinates of magnet stone $L$ as $(x_0,y_0)$.

Xiaoqujiu holds magnet stone $L$ and stays at the same place. All magnet stones that can be attracted by $L$ will be pulled over.

At any moment, he may choose to switch to any magnet stone he has already obtained (which can also be the original magnet stone $L$) at $(x_0,y_0)$ to attract more magnet stones.

Xiaoqujiu wants to know: at most how many magnet stones can he obtain?

Input Format

The first line contains five integers $x_0,y_0,p_L,r_L,N$, representing Xiaoqujiu's position, the magnetic force and attraction radius of magnet stone $L$, and the number of scattered magnet stones on the plain.

The next $N$ lines each contain five integers $x,y,m,p,r$, describing the properties of one magnet stone.

Output Format

Output one integer, representing the maximum number of scattered magnet stones that can be obtained (not including the initially carried magnet stone $L$).

0 0 5 10 5
5 4 7 11 5
-7 1 4 7 8
0 2 13 5 6
2 -3 9 3 4
13 5 1 9 9

3

Hint

For $30\%$ of the testdata, $1 \le N \le 1000$.

For another $30\%$ of the testdata, $p=r$.

For $100\%$ of the testdata, $1 \le N \le 250000$, $-10^9 \le x,y \le 10^9$, $1 \le m,p,r \le 10^9$.

Translated by ChatGPT 5