Description
Problem brought to you by NTHU Amusement Programming Club.
There is a TV show titled Easygoing Yuri, and Akarin is the protagonist in it. Over the years as more and more new characters appear, Akarin has less and less screen time. She is mortified when being told that she will have only 1 second of screen time in the new episode!
Akarin doesn’t want people to forget her, so she decides to appear in the second where she can be seen by as many as possible.
Fortunately, the audience of Easygoing Yuri is very predictable, so Akarin knows exactly the time any person starts and finishes watching. Formally, there are N people that watch Easygoing Yuri, with the i-th person watching from some integer second li until some other integer second ri, inclusively. If Akarin appears in time t with li ≤ t ≤ ri, she will be seen by the i-th person. For simplicity, she can only choose an integer-numbered second.
Can you help Akarin find out what is the maximum number of people getting to see her, if she chooses the second t optimally?
Input
There will be only one testcase in each input file.
The first line of any testcase contains a single integer N; hence comes N lines, the i-th of which contains two integers that are the li and ri whose meaning are as described in the problem statements.
1 <= N <= 2*105
0 <= li, ri <= 109 for i=1...N
Output
Output a single integer that is the maximum number of people that Akarin can get to see her.