Photos

For his seventh birthday, little Bajtek got a camera from his parents. Ever since, he has loved taking a photo of every person he newly meets. Every photo he takes, he pins to the cork board in his room. A few months have passed since his birthday, and the board is already packed. Some photos are completely covered, others only partly, and the newest ones are fully visible.

Whenever Bajtek pins up new photos, he wonders how many of the previously displayed photos each new pin pierces. He is curious how many photos a single pin can pierce at most. Help Bajtek satisfy his curiosity.

Write a program that

• reads from standard input the description of the photos on Bajtek's cork board,
• determines the maximum number of photos that a pin stuck into the board can pierce,
• prints the result to standard output.

The first line contains a single integer $n$ ($1 \le n \le 100\,000$), the number of photos on the board. Each of the next $n$ lines contains four integers. Line $i+1$ holds $L_i$, $D_i$, $P_i$, $G_i$ ($-200\,000 \le L_i, D_i, P_i, G_i \le 200\,000$, with $L_i < P_i$ and $D_i < G_i$), separated by single spaces. These are the coordinates of a photo on the board seen as a Cartesian plane: $(L_i, D_i)$ is the lower-left corner and $(P_i, G_i)$ is the upper-right corner. A pin stuck at point $(x, y)$ pierces this photo if $L_i \le x \le P_i$ and $D_i \le y \le G_i$.

In the first and only line of output, print a single integer: the maximum number of photos that a pin stuck somewhere on the board can pierce.

The hatched area in the figure marks the part of the board where a pin should be stuck in order to pierce 3 photos. Note that two of the photos on the board (the first and the fourth) overlap exactly.