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

hide comments
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).

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)

Master Wad7a: 2013-04-05 15:10:13

@problem setter: can u please tell me whats wrong with my last submission?? ID:9044708. I tried a lot of test cases but couldn't find whats wrong.

Ninja coder: 2013-01-28 09:43:52

@Sparik: All test cases. I doubt even 1 will pass :P

(Tjandra Satria Gunawan)(曾毅昆): 2012-10-06 18:06:03

wrong answer #1 means that you're getting wrong for case no:1

Saptarshi Chatterjee: 2012-10-06 16:18:00

"wrong answer #1 " what does this #1 means ? eoor in first output set or only 1 error ?

alculquicondor: 2012-10-04 16:25:41

Solve NICEDAY first.

a: 2012-09-20 16:41:05

will n^2 work...or an nlogn solution needs to be thought of?


Added by:Bin Jin
Date:2008-01-20
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: CPP