LIS2 - Another Longest Increasing Subsequence Problem

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Given a sequence of N pairs of integers, find the length of the longest increasing subsequence of it.

An increasing sequence A1..An is a sequence such that for every i < j, Ai < Aj.

A subsequence of a sequence is a sequence that appears in the same relative order, but not necessarily contiguous.

A pair of integers (x1, y1) is less than (x2, y2) iff x1 < x2 and y1 < y2.

Input

The first line of input contains an integer N (2 ≤ N ≤ 100000).

The following N lines consist of N pairs of integers (xi, yi) (-109xi, yi ≤ 109).

Output

The output contains an integer: the length of the longest increasing subsequence of the given sequence.

Example

Input:
8
1 3
3 2
1 1
4 5
6 3
9 9
8 7
7 6

Output:
3

Added by:Bin Jin
Date:2008-01-20
Time limit:0.345s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel Pentium G860 3GHz)
Languages:All except: C++ 4.9 SCM chicken

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Chandrakanth : 2015-06-12 11:08:45

Wrong answer test #1. Isn't the first test case the one given in the example itself?If it is then my program gives the correct output 3.

Last edit: 2015-06-12 11:10:17
anando_du: 2015-03-04 19:50:41

-_- are u kidding with me !!! wrong ans#1 ?

mkrjn99: 2014-12-03 15:08:52

Binary search continues to amaze me!

Sagar Shah: 2014-05-26 19:04:28

How to do this problem???
Can anybody please give a hint??

Ghost Of Perdition: 2014-01-27 12:55:15

N log^2 is getting TLE !!!

Ravi Kiran: 2014-01-02 10:27:09

My N * log^2 N implementation passed with 0.38s (in case you are skeptical about the time limit).

ROHIT RAWAT: 2013-10-28 07:14:13

Last edit: 2014-01-12 19:24:24
Ayush Nigam: 2013-08-29 17:03:26

my O(nlogn) is giving tle!!!

Mukit09: 2013-08-02 20:04:23

Running...(4)
Running...(9)
then wrong answer #1
What is this case ?? I've just used LIS in nlogn... Where am I doing wrong ???

Bharath Reddy: 2013-07-02 06:45:18

O(n^2) won't work..
You have to do it in O(nlogn)